Silicon photonic quantum computing with spin qubits

The technology for processing and transporting information continues to evolve at an astounding rate. Light has naturally played a key role in the transportation of information for centuries, largely owing to the relative ease with which that information can be encoded and transmitted quickly over comparatively long distances without the need for regeneration. In the era of automated information processing and transportation, light temporarily took a back seat to electrical transmission and distribution until optical fibers and compact, high-efficiency, bright electromagnetic wave sources and detectors were developed, to the point where most high-speed communication over macroscopic distances is now based on propagating electromagnetic waves.

In contrast, electronic circuits still dominate the realm of automated information processing, despite the stalled status of their raw speed and miniaturization. Meanwhile, optical data transmission assemblies continue to shrink as their data transfer rates grow. High-speed optical buses now interconnect many electronic processing nodes in data farms; the distinction between data processing and data transmission becomes blurred within the confines of the farm.

Of course, the vast majority of commercial information processing equipment is currently based on and can be modeled using classical physics and information theory. Most lay people are, nonetheless, at least vaguely aware of the numerous high-profile, worldwide research and development activities aimed at revolutionizing and commercializing information processing and transportation technologies by basing their operating principles on the fundamental properties of quantum mechanics that distinguish it from classical physics. With the history of classical information technology and transportation in mind, it is interesting to ponder what might be the role of light in future quantum-based information technologies.

The majority of this Perspective describes one of many approaches being considered to build a truly universal quantum computer. In a landscape that includes architectures entirely based on the quantum properties of electronic (matter-based) components and others that are entirely based on the quantum properties of light, our approach proposes to process quantum information using single photon and single electron spins in equal parts.

The remainder of this section is intended to introduce the high-level concepts that underpin quantum computing: (Sec. I B) in general, (Sec. I C) in all-optical approaches, and (Sec. I D) in a hybrid approach that best takes advantage of the distinct qualities of matter-based and photonic quantum states. Section II provides a thorough description of the proposed scheme for measurement-based, fault-tolerant universal quantum computing based on photon-enabled, matter-based graph states.¹ After generically describing the scheme, along with its components and dependencies in Sec. II, we discuss the cavity quantum electrodynamic (c-QED) essentials relevant to form the dual-rail spin-photon interface in Sec. III. In Sec. IV, we assess optically addressable spins and material platform candidates that might be expected to provide the best host for its implementation. Based on that assessment, the remainder of this Perspective focuses on an integrated silicon photonic platform that assumes the availability of isotopically pure planar silicon-on-insulator (SOI) wafers (see Sec. V). The current state of the art of required components is reviewed as quantitatively as possible. This Perspective finishes the roadmap with a prioritized list of outstanding challenges (see Sec. VI) and a pathway for immediate and future work.

The concept of a quantum computer (QC) goes back to the early 1980s, when physicist Richard Feynman proposed it as a means to perform exact simulations of (quantum) physical problems.² Computing systems rely on the ability to store, manipulate, and read information. In classical digital computers, this information is encoded in discrete bits that take the logic value of either zero or one. In the quantum analog of classical digital computers, information is encoded in the quantum mechanical states of some physical entity, such as a single electron, an atom or ion, or a single-photon mode.³ Most commonly, two particular states of a given system that can be well-isolated from other internal states and the environment are chosen to encode the information in what is commonly referred to as a quantum bit or qubit.³ In classical digital computers, the actual processing involves retrieving bits stored in memory elements and using them as inputs to devices (logic gates) that translate the information contained in the combination of input bits and sends the logical output bits to a storage element. One method of quantum computing (the gate-based approach) operates in an analogous manner, where unitary quantum gates transform information encoded in a set of input qubits and the transformed state is stored until it undergoes further processing. In order for a quantum processor to solve classically unsolvable problems, it must take advantage of the mysterious entanglement and superposition properties that many-entity quantum mechanical states can (but do not necessarily) possess. It is well-established that a truly universal gate-based quantum computer can be designed from a toolbox containing many examples of a small number of well-defined unitary gates, at least one of which must be capable of creating entanglement. Another approach to universal quantum computing adopts a different strategy. The entire memory bank of qubits is first prepared in a particular entangled resource state, and then, the quantum algorithm is carried out by making a series of single-qubit measurements on select qubits, in a very specific order. The type of measurements and the order in which they are performed are dictated by the algorithm. This approach is referred to as measurement-based quantum computing or one-way quantum computing (the use of measurements renders this approach irreversible).

Currently, both gate-based and measurement-based quantum computing schemes are being pursued using a host of different physical systems to comprise the qubits. Prominent examples are QCs based on superconducting qubits,^4–7 ion traps,^8–11 electron spins in Si,^12–15 and linear optical networks that employ non-classical light.^16,17 Of these, several involve physically localized (stationary) qubits (ion or atom traps, discrete electrons in artificial quantum dots or localized to impurity sites in a host lattice, etc.), while the all-photonic approach encodes the qubits in propagating modes of the electromagnetic field. Due to their localized nature, stationary qubits are relatively easily accessed and can store quantum information for a certain duration referred to as their coherence time, which is limited by the coupling of the qubit to its environment.¹⁸ In comparison, qubits encoded in propagating photon modes, or flying qubits, only weakly interact with their environment and with each other, which makes them ideally suited for transporting quantum information across large distances while preserving the underlying quantum states.¹⁸ Notably, photonic qubits are typically not limited by their coherence time, but by photon loss. Most superconducting approaches incorporate stationary qubits within microwave photonic circuits wherein circuit quantum electrodynamics (circuit-QED) is used to take advantage of both storage and distant coupling properties in a hybrid stationary/flying platform.⁷ 

In two recent, groundbreaking experiments, quantum advantage—roughly interpreted as successfully running an algorithm using a quantum processor that would be practically impossible using classical computational approaches—has been demonstrated separately using superconducting circuits⁴ and using all-photonic interferometric circuits.¹⁷ Despite these recent breakthroughs, it is still far from clear which platform(s) will eventually succeed in delivering qubits of sufficient quality and quantity to enable truly universal quantum computing.

The quantum nature of light provides a rich resource that can be harnessed for application in quantum information science and related technologies. When quantized, the in-phase and quadrature components of the electromagnetic field amplitude associated with each classical mode of the vacuum behave as the position and momentum coordinates of a harmonic oscillator with the corresponding natural frequency. A general state of the field can be expanded over the discrete Fock (photon number) eigenstates of the field Hamiltonian or over the continuous spectrum of the in-phase or quadrature components of the field amplitudes. Most practical implementations of quantum optics are based on wavepacket states that can be constructed from either the discrete Fock basis or the continuous eigenbasis of the position and momentum coordinates associated with a given mode. Wavepacket states associated with different modal degrees of freedom (polarization, orbital angular momentum, direction of travel, temporal localization, etc.) can be used to define flying qubits. Qubit wavepackets formed from discrete Fock states can be entangled in two or more degrees of freedom in many different ways, using very simple, passive optical elements, such as beamsplitters and polarization controllers.^19,20 Entangling qubit wavepackets defined in the continuum basis is slightly more complicated, as it involves squeezed states.

The all-photonic quantum information processing strategies that does not rely on the quantum states of matter, but rather solely on the quantum properties of the electromagnetic field. While single-photon Fock states represent a discrete variable (DV) quantum generalization of classical bits used in digital information processing, squeezed states of the quantized field represent the quantum generalization of continuous variable (CV) analog computers. The experimental demonstration that quantum teleportation of continuous quantum variables was possible²¹ led to a proposal for creating a universal quantum computer over continuous variables [continuous variable quantum computing (CVQC)] at the turn of the last century.²² This scheme provides the basis for generating and manipulating entangled CVs using only beamsplitters, phase shifters, squeezers, and some nonlinear optical element, along with the ability to perform homodyne and heterodyne measurements of the field. Soon after, a scheme for realizing a universal quantum computer based on manipulating the entanglement of a collection of discrete single-photon Fock states using just beamsplitters, phase shifters, and high-quality single-photon detectors was put forth [linear optical quantum computing (LOQC)].¹⁶ 

In the intervening period, various proposals and architectures for photonic quantum computers, whether universal or designed for customized problems, have been put forth, with some demonstrated and others even commercialized.^17,23–27 Special-purpose quantum photonic processors that implement specific computational algorithms, such as (Gaussian) boson sampling [G(BS)],^17,28 variational quantum eigensovlers (VQEs),²⁹ quantum phase estimation (QPE),³⁰ and quantum analog simulations,³¹ may lead to near-term quantum-enhanced applications in quantum chemistry.^32,33

However, most known quantum algorithms that have widespread practical applications, for example, Shor’s algorithm,³⁴ will likely offer a powerful quantum advantage only when run on a universal quantum computer of significant scale (or logical qubit-count), far beyond what is available in the current, near-term intermediate scale quantum (NISQ) computing era.³ It is generally accepted that such computers will have to be not only universal but also compatible with quantum error correction (QEC) codes. Both LOQC and CVQC schemes are universal by construction,^16,35,36 and fault-tolerant quantum computing (FTQC) architectures have been developed for both approaches.^24–26,37 These fault-tolerant error correction codes typically rely on the creation of highly entangled multi-particle quantum states known as graph states.³⁸ Graph states on which QEC can be implemented have been demonstrated for LOQC and CVQC.^39,40

One shortcoming inherent to all-photonic QC approaches is the lack of an efficient quantum information storage capability. This may or may not present a fundamental obstacle; however, some level of efficient interfacing to a relatively long-lived quantum memory will almost certainly be required, even if only to act as an interface to a distributed quantum network.⁴¹ There is a large body of work focused on developing technologies required for a quantum internet to be realized.^41–43 Such a network would not only serve as the backbone of a quantum “internet of things,” but it would also facilitate distributed quantum computing among several practical-sized processing nodes. Clearly, the flying nature of photon states makes them uniquely suited to the long-distance transportation of quantum information. Shared entangled photon pairs can be used as the basis of a long-distance quantum communication channel or network if they can be entangled with long-lived quantum memories. The proof of concept for a long-distance quantum communication channel was demonstrated using a satellite link in 2017,⁴⁴ which is part of the trusted-classical-node network between Beijing and Shanghai.⁴⁵ Various techniques for non-locally storing and retrieving photonically encoded quantum information include low-loss passive delay lines,^46,47 atomic ensembles,^48–50 and active quantum repeaters.^51,52 A multinode quantum network based on remote solid-state qubits and capable of real-time communication and feed-forward gate operations has recently been demonstrated.⁴¹ 

It turns out that many of the concepts involved in designing a useful quantum network closely overlap with the theory of measurement-based, fault-tolerant quantum computation, which, as noted above, is naturally suited to a photonic implementation. One candidate for a quantum memory element that might be used in a quantum network node would be a long-lived solid-state spin. These observations suggest that another approach to designing a quantum computing processor node would be to shrink a quantum network down to the size of a chip.

The creation of graph states in the all-photonic LOQC platform uses beamsplitters and phase shifters to perform unitary transformations on encoded and ancilla (outside the computational basis) single-photon qubit states and then pairwise entangles them via projective measurements of single-photon detection events.⁶⁵ As will be described in detail in Sec. II, graph states can be created in an analogous manner, i.e., using projective single-photon measurements, in arrays of matter qubits encoded in atomic-scale electronic states that have coherence times on the order of seconds or longer. Many of the required optical components are the same as in the LOQC platform (single-photon sources, detectors, beamsplitters, etc.). In addition, this photon-enabled, matter qubit graph state architecture requires an effective spin-photon entanglement interface that is provided using c-QED techniques.⁵³ This hybrid DV photon-measurement-based approach to quantum computing, employing matter-based graph states, could potentially overcome the qubit coupling challenges faced by many all-matter-based approaches while also reducing the overhead associated with the intrinsically probablistic nature of LOQC gates. To date, there has comparatively been little work done to flesh out this approach.

This section briefly reviews the fundamental building blocks and the quantum procedures required for constructing our recently proposed QC architecture based on spin qubits in an integrated photonic circuit.¹ We then add to the discussion of how some of the building block hardware imperfections can contribute to the quantum error model.

It is known that cQED photon-spin interactions can be used to entangle distant spin qubits by projective measurements of single photon detection events.^53–55 The fundamental building block of a recently proposed fault-tolerant QC architecture based on these principles¹ consists of two spin qubits, each embedded within identical, high-quality factor (Q) optical microcavities with proximate microwave (MW) gates. The two cavity-bound qubits are evanescently coupled to a dual-rail optical waveguide bus that can selectively access and route two single-photon sources and four single-photon detectors via active switches, as illustrated in Fig. 1(b). The switches, sources, detectors, and MW gates are reconfigurable to measure, initialize, and finally entangle adjacent spin qubit states (the fundamental operations required by the proposed QC architecture). As explained in Sec. III, these operations are facilitated by the spin-state-controlled scattering properties of optical microcavities containing single defects wherein the two non-degenerate computational basis states are each dipole-coupled to higher energy defect states.

The spin state of individual spin qubits can be measured and initialized by configuring the active switches, as shown in Fig. 1(a). Light in the form of single photons at the bare microcavity resonant frequency sent from source 1 is scattered by the cavity containing one of the spin qubits. If the |0⟩ component of the spin qubit has a dipole allowed resonance that matches the bare cavity mode frequency, then a single-photon wavepacket (a photonic qubit) tuned to the same bare cavity resonance will pass by the cavity and be detected by using detector 1 (the cavity is hidden from that photon). If the spin qubit is in the other computational basis state, with a dipole transition that is not resonant with the bare cavity mode, the photon wavepacket will transit through the cavity and be registered by using detector 2. This effectively represents a projective Z-measurement of the spin qubit state by means of the single-shot photo-detection of the photonic qubit.^56–58 Depending on the measurement outcome, the spin qubit will be projected to either one of the two computational basis states. The microwave (MW) gate can then prepare the spin qubit into a desired initial state.

With the active switches configured to allow the incident photon from source 1 to scatter from both cavities, as in Fig. 1(b), a photon detection event at detector 4 (3) is only possible if the two spin qubits are in the same (different) computational basis states. This procedure therefore performs a non-local ZZ parity measurement of the two spin qubit states, which can be used to prepare the remote spin qubits in an entangled state.

The cQED interactions and their impact on the design of the cavities are discussed in Sec. III, following a summary of how this building block must be controlled and programmed to enable universal and fault-tolerant measurement-based quantum computation(s). For the remainder of this article, the term qubit will refer to the spin qubit.

The known speedup of quantum computation arises in the limit of large computations, where QEC codes⁵⁹ must be implemented to maintain the quantum coherence of the logical qubits. The use of 3D cluster states (the Raussendorf lattice) provides topological protection against quantum errors, such as Pauli errors, with a high fault-tolerant threshold.^60–62 In our case, the prime example of a Pauli error would be the measurement of a photon in the wrong output port. Measurement-based quantum computation on the 3D cluster states is particularly suitable for physical implementations involving photonics, for the following reasons:

• The check operator measurements of a 3D cluster state only involve local measurements of qubits, which can be easily implemented through fast and efficient photo-detection.

• The 3D cluster is amenable to distributed quantum computation as it does not need to sharply distinguish between local and non-local implementations. This makes it naturally integrable with quantum communication channels.

There have been several proposals to implement a 3D cluster state architecture using all-photonic LOQC^24,25 and CVQC²⁶ approaches, as well as the hybrid spin-photon c-QED approach with spin qubits in diamond.⁶³ To be scalable and to take advantage of advanced lithographic and nano-fabrication technologies, it has been recognized for some time that it makes sense to work with just two 2D physical layers of the 3D cluster state and use time as the effective third dimension.⁶² In this scheme, quantum information flows back and forth between the two layers of physical qubits over time, as illustrated in Fig. 2.

The proposed architecture for the spin-photon interface requires the following quantum primitives:

1. Single-qubit unitary gates for all qubits, achieved using microwave gates.

2. Single-qubit Pauli Z-measurements for all qubits, achieved by single-qubit parity measurements [as in Fig. 1(a)].

3. Measurements of correlated observable ZZ for all adjacent qubits, achieved by two-qubit parity measurements [as in Fig. 1(b)].

It has previously been shown that parity measurements can be used to create cluster states.⁶⁴ Based on the listed quantum primitives, we further define two procedures for the creation of cluster states: knitting and fusing.^{24,25,35,65,66} The knitting procedure allows for the creation of tree-like cluster states, as illustrated in Fig. 3(a), where qubit “b” can be “knitted” to qubit “a.” The fusing procedure, on the other hand, can “fuse” two tree-like cluster states to form “loop” structures, as shown in Fig. 3(b). In the second step of the fusing procedure, a Pauli X measurement can be applied to either qubit “a” or “b”; the measured qubit will then be removed from the logical space.

Using these two procedures, two layers of 2D cluster states (indicated as blue and red as in Fig. 2) are first constructed in parallel and then fused together to form a two-layer 3D cluster state. During one computational step, the logical “bottom” layer is measured, re-initialized, and knitted/fused into a 2D cluster state and further fused to the other layer as the logical “top” layer. As the step is repeated, computation can take place fault-tolerantly.

A physical implementation of this scheme based on the building block identified in Sec. II A involves a “unit computational cell,” as shown in Fig. 4.¹ Not shown in this Fig. 4 are the microwave gates required for single-qubit unitary operations.

The fault-tolerant photon-mediated spin qubit architecture envisioned in Ref. 1 is susceptible to a variety of physical errors. Different types of physical errors will, in general, translate to specific Pauli error types that are relevant for assessing their impact on the fault-tolerant threshold. Assuming that the long intrinsic dephasing time of the qubit basis states in bulk samples is preserved in fabricated devices, imperfect knitting or fusion procedures will be due to one of three physical processes: (i) imperfect transport of the single photon between the receipt of the trigger pulse and the subsequent photon detection event, (ii) imperfect outcomes (spin/photon–path correlations) when the photons interact with the cavities, and (iii) imperfect unitary operations carried out on single qubits using microwave pulses. As discussed at the end of this section, the latter are likely to be less of a concern than the former. Errors of type (i) can be treated as photon routing or photon loss errors that occur independent of the state of the qubit, while errors of type (ii) are related to cQED processes (photon-spin interactions). The distinction is useful because the way physical errors translate to Pauli errors is quite different in the two cases. Subsections II C 1--II C 3 describe processes related to type (i) and type (ii) physical errors and their relationship to the Pauli errors used in fault-tolerant threshold calculations. Note that the fidelity threshold to achieve fault-tolerant universal QC with the proposed architecture has yet to be identified and will be a subject of future studies.

Classically controlled photon routing errors and photon loss external to the cavities can be due to a variety of processes: imperfect biasing of active switches, imperfect triggering of the photon source, detector inefficiency, detector latching, en-route absorption events, and scattering out of the single-mode guided electromagnetic basis that defines the c-QED photonic Hilbert space. Due to the dual-rail nature of our building block, these errors can reveal themselves as invalid detection patterns of the projective single-qubit (Z) and two-qubit (ZZ) measurements; for example, if both detectors click or neither detector clicks. A false detection due to a combination of errors, such as photon loss and a dark count, can directly contribute to a Pauli error that needs to be factored into estimating the fault tolerance of the cluster state. When such errors do not coincide, the detectable failed measurements can be mitigated, and only the net probability of error after mitigation (which can, in principle, introduce other sources of error) needs to be factored into the Pauli error rate in the cluster state.

As an example, the effect of a failed Z-measurement due to photon loss in the dual-rail bus is either the identity or the desired spin projection depending on whether the photon is lost before or after interacting with the spin-containing cavity. Therefore, detectable failed Z-measurements can be resolved using a multi-shot repeat-until-successful method, where photons are subsequently sent until an expected photo-detection is registered. This procedure would preclude such photon loss events from contributing to the Pauli error rate in the cluster state so long as the qubit coherence time is much longer than the time required to register an expected photo-detection event.

However, although detectable failures in the ZZ-measurements used in the knitting/fusing procedures can also be treated with the same multi-shot repeat-until-successful strategy (without the re-initialization of the two qubits), there is an unavoidable residual Pauli error rate in the cluster state, which increases with the number of repeats necessary. The fault-tolerant threshold under this method has been estimated to have a lower bound of 1% photon loss per measurement, assuming an average number of repetitions for every two-qubit measurement.¹ The error threshold can be further increased if the classical information (for example, the actual number of repetitions for each ZZ-measurement) is used to gain insights into to the error location.⁶⁷ 

We note that there is also a different strategy⁶³ that can be applied in the case of detectable ZZ-measurement failures, which can also effectively preclude photon loss in the dual-rail bus from contributing to Pauli errors in the cluster state. Instead of merely continuously sending probing photons, one can repeat the entire re-initialization and knitting/fusion procedure on the involved qubits, assuming the coherence time of the existing cluster state permits. The failure rate, then, only dampens the cluster state growth without introducing errors in the created cluster state. This type of error mitigation can be compared to the case of the LOQC probabilistic entangling gate that has been shown to have a photon loss tolerance of up to 50%.^66,68

There needs to be a well-defined spin-state-dependent scattering of photons from the qubit-containing cavity to avoid photon-spin correlation errors. Ideally, the scattering amplitudes into channel 1 (through port) and channel 2 (drop port) for both spin states should have perfect contrast, i.e., for the schematic in Fig. 5, the photon has a near-unity scattering amplitude into channel 1 (2) when the qubit is in the $Q 1$ (⁠$Q 2$⁠) state. In practice, the actual scattering amplitudes can deviate from the ideal values even if the scattering amplitude spectra are close to unity over some spectral range when the quantum emitter and cavity are in perfect resonance. This can occur if the three relevant frequencies (the cavity resonance, dipole transition, and the probing single photon) are not tuned in resonance or if the bandwidth of the single-photon wavepacket exceeds the range over which the scattering amplitudes approach unity. Of course, the scattering amplitudes can never reach unity because of the following reasons: (i) in a planar waveguide geometry, the quality factor of the bare cavity resonance will have some contribution from scattering into radiation modes outside the photonic Hilbert space of the circuit; (ii) even if the excited state of the resonant dipole transition had ideal cyclicity properties (no probability that radiative or non-radiative decay prevents it from returning to the resonant ground state),^69,70 there will always be some possibility of losing the photon via spontaneous emission into radiation modes; and (iii) even in the case of a strong spin-photon coupling with near-unity scattering (high cooperativity value, C; see Sec. III), the scattering probabilities always only approach the ideal values of unity and zero.

Factors that contribute to detuning and the loss of cavity-bound photons from the circuit are discussed in Sec. IV, and their mitigation will present significant engineering challenges. In the limit where these imperfections lead to peak scattering amplitudes not too far from unity, the contributions of imperfect state-dependent scattering to Pauli errors linearly scale in the scattering amplitude deviations.¹ We note that a more detailed treatment of spin-photon interface errors would also have to take into account non-ideal cyclicity wherein a decay of the emitter’s excited state may result in a spin-flip error.^69,71

Imperfect microwave pulses used for direct, unitary qubit manipulations, such as the Hadamard gate, can lead to spin rotation errors. For the proposed architecture, only single-qubit MW gates are required, which are typically “easier” than multi-qubit gates. A more likely source of error associated with microwave unitary manipulation will be crosstalk between adjacent qubits, which, of course, will strongly depend on the detailed circuit layout.

Photonic nanostructures, such as photonic crystal (PhC) waveguides and cavities, can be used to tailor the interaction between light and matter in the quantum limit of single photons and individual optical emitters, such as quantum dots or color centers.⁷² Elegant demonstrations of how a single atom can have a measurable effect on the transmission properties of ultra-compact, yet macroscopic high-Q Fabry Perot cavities represent a hallmark of early work on strong-atom-cavity coupling physics.⁷³ Much of the well-known theoretical analysis of this system⁷⁴ directly carries over to the analysis of integrated photonic circuit implementations. In integrated planar photonic circuits, single transverse modes of waveguides replace focused Gaussian excitation modes, and the multilayer dielectric mirrors that define the Fabry–Perot cavity mode shape and quality factor are replaced by distributed, two-dimensional diffractive arrays of holes etched through sub-wavelength-thick slab waveguides. This photonic bandgap cladding completely surrounds (in 2D) a 3D confined optical mode typically with effective mode volumes on the order of a qubic wavelength.⁷⁵ The coupling of the continuum waveguide modes to the 3D localized cavity modes is thus evanescent in nature (in the plane of the slab).

To describe in detail the interactions within our proposed Z-measurement photonic circuit (Fig. 1), we revisit the system in the context of a four-port photonic crystal cavity evanescently coupled to two parallel waveguides, as schematically illustrated in Fig. 5(a).

We assume that the defect center’s electronic structure has a Λ configuration, as illustrated in Fig. 5(a), and that it is located near the principal antinode of the cavity mode. The solution of the scattering probability from the input waveguide mode to either of the output channels is facilitated using a Jaynes–Cummings input/output formalism.⁵³  Table I summarizes the phenomenological parameters that influence the spectrum of this scattering probability using this formalism. If the cavity resonance is tuned to the optical transition between $Q 1$ and $X$⁠, then hν_C = hν₁, leaving the $Q 2 ⇔ X$ transition detuned from the cavity mode (hν_C = hν₂ + ΔE_qb).

Figures 5(b) and 5(c) show the state-controlled probabilities of the incident photon scattering into the through (⁠$P 1 | Q 1 〉 , P 1 | Q 2 〉$⁠) and drop (⁠$P 2 | Q 1 〉 , P 2 | Q 2 〉$⁠) ports, calculated as a function of incident photon detuning from the cavity resonance frequency using the Jaynes–Cummings model with a set of parameters chosen to illustrate a near-ideal regime of operation. Note that with these assumed parameters, if the incident photon detuning is zero, the quantum state of the qubit acts essentially as the control knob on a routing switch. If the qubit is in the state that has a dipole transition resonant with the bare cavity mode, an incident photon resonant with the cavity emerges in the through port (channel 1). If the qubit is in the state with a dipole transition off-resonance with the cavity mode, the incident photon tunnels through the cavity and emerges from the drop port (channel 2).

Detection of a single photon in either of the output ports projects the embedded qubit into a particular state. One would like to use this projective measurement to initialize the qubit into one or another of its basis states, |Q1⟩ or |Q2⟩, independent of what state it was in before interacting with the impinging photon. Assuming that the |Q1⟩ state dipole transition and the incident photon frequencies are in perfect resonance with the cavity mode, with the |Q2⟩ state fully detuned, a single-photon detection event in channel 1(2) would project the qubit into the |Q1⟩(|Q2⟩) state with perfect fidelity if $P 1 | Q 1 〉 = P 2 | Q 2 〉 =1$ and $P 2 | Q 1 〉 = P 1 | Q 2 〉 =0$⁠. (This would represent a perfect Z-measurement in the qubit basis.)

Any displacement of the emitter with respect to the cavity field maximum will reduce g and, hence, C.

Figure 6 shows a plot of $P 1 | Q 1 〉$ and $P 2 | Q 1 〉$⁠, along with the channel fidelities, as a function of C (recall this assumes that the off-resonant state is far-detuned from the cavity resonance, that the cavity is symmetrically coupled to the two waveguide buses, and that the cavity is overcoupled to the waveguide buses). Clearly, one needs to aim for a C value greater than 10 to achieve high single-shot fidelity, but note that the losses associated with spontaneous decay to radiation modes remain high even for C values of up to ∼40. These unavoidable losses (present even if the intrinsic cavity quality factor was infinite) motivate working at the largest possible C values when one considers other potential sources of error, such as imperfect cyclicity of the $Q 1 ⇔ X$ resonance.^69,78 The loss is associated with on-resonance excitation of the excited state that persists long enough to spontaneously decay without exciting the cavity mode. If that spontaneous decay is to radiation modes that leave the emitter in the resonant |Q₁⟩ state, no additional error channels would be introduced. However, if the emitter excited state can spontaneously decay into the |Q₂⟩ state, the associated spin-flip error would have to be taken into account when evaluating the fidelity of the state initialization.

Other practical considerations also motivate operation at high values of C. Of particular concern is the need to consider the finite bandwidth of the single-photon spectral intensity function. The preceding analysis implicitly assumed that the full spectral intensity would experience the same scattering probability when encountering the cavity. The wider the spectral intensity distribution around the resonant frequency, the faster the cluster state can be formed. It is therefore desirable to establish the widest possible spectral range over which the scattering probabilities are close to unity. Figure 7 shows three examples of $P 1 | Q 1 〉$ and $P 2 | Q 1 〉$ plotted as a function of the incident photon detuning for C values ranging from 10 to 200. The available bandwidth over which near-ideal scattering amplitudes are achieved clearly increases with C. At low C values, this bandwidth approaches the intrinsic, bulk dephasing linewidth of the resonant dipole transition, typically small, even for defects with large dipole transition moments and/or non-radiative decay rates. The bandwidth increases with increasing C as coupling to the cavity mode provides a Purcell enhancement of the resonant radiative transition rate. This can also reduce spin-flip errors due to imperfect cyclicity so long as the detuned state is far off-resonance. As g increases for a fixed γ, the strong-coupling regime is eventually reached where C ≫ 1, g > κ, g > γ, and 4g > (κ + γ). In this limit, the emitter transition cycles faster with the cavity mode than either the excited state or the cavity mode decays into radiation modes: the atom-cavity system’s elementary excitations become two polariton modes that are each detuned from the bare cavity resonance by an energy ±ℏg. On-resonance photons that encounter the cavity can only weakly excite these detuned polariton modes, minimizing loss and maximizing the bandwidth over which near-unity scattering probabilities can be realized.

To this point, the proposed architecture could, in principle, be implemented in any planar photonic circuit platform capable of hosting high-quality spin qubits. To inform a comparison of different platform options, we first discuss the demands that the proposed architecture and c-QED physics impose on the spin-qubit’s optical properties and the corresponding implications for the photonic circuitry.

Table II provides a list of candidate spin qubits that have been studied in a variety of host materials, along with relevant spin and c-QED-related optical properties. While the III–V based artificial quantum dots offer by far the best c-QED-related optical properties (high radiative efficiency and large dipole transition moments), their spin relaxation rates (owing to a dense nuclear spin bath) exclude them from serious consideration for the proposed architecture.

The much-studied NV center in diamond offers a good combination of long spin coherence times and relatively attractive c-QED-related optical properties.⁷⁹ It is not surprising that the design for a related c-QED architecture for a fault-tolerant QC was based on NV centers.⁶³ However, the cluster state in that scheme consists of qubits encoded in the ¹⁵N nuclear spin degree of freedom.⁶³ This might be necessary in the NV system because the dephasing rate of the electron qubits that become entangled through their interaction with the photons might be too fast to serve as the cluster state qubits, as they do in our scheme. To protect against this, the protocol in Ref. 63 only uses the electron qubits as a temporary quantum memory, before a combination of microwave and radio frequency pulses transfers the entanglement to the nuclear qubits that have very long dephasing times. The photon-measurement-based protocol for building the NV nuclear cluster state is therefore more complicated than that proposed in the current architecture, where it is assumed that the electron qubits have very long dephasing times. What is not shown in Table II is the sensitivity of the NV center’s transition frequency to electric fields. This manifests itself in significant inhomogeneous broadening when the NV centers are located near interfaces.^80–82 Recent work has focused on exploring alternative defects in diamond that may suffer less from this effect. Group IV defects, including silicon, germanium, and lead, have garnered attention,^79,83 but the Si-vacancy defect has been studied most extensively so far.⁸⁴ Note that the good spin and optical properties of the SiV-center in diamond can only be accessed at mK temperatures.^85–87 

A variety of rare earth ions in different host materials have also received considerable attention in the context of spin-photon interactions. Perhaps the most studied is erbium (Er³⁺), which has a well-known optical transition in the telecommunication band near 1.55 μm associated with a ground state spin manifold with reasonably long spin relaxation times at very low (sub-1 K) temperatures in Y₂SiO₅.⁷⁰ These near infrared transitions can have extremely small dipole transition moments, and in some cases, their linewidths are close to radiatively limited. Near radiatively limited linewidths would mean that the cooperativity C of a cavity coupled to the ion is independent of the dipole transition moment,⁸⁸ but, nevertheless, the ratio of $Q/ V$ needed to reach the strong-coupling regime is large and likely difficult to achieve. In addition, dependent on the exact emitter–host combination, rare earth ions can suffer from strong inhomogeneous broadening and related spectral diffusion compared to their homogeneous linewidth.^69,89,90 It is expected that the broadening can be further reduced in isotopically purified samples.⁹¹ 

The aptitude of the different emitters to be integrated within distributed and blind quantum computing networks^41,109–111 will be mainly affected by their ZPL transition wavelengths. Emitters that have a ZPL transition located within one of the telecommunication O, C, or E bands offer the advantage of seamless integration into existing telecommunication infrastructure, whereas emitters in the visible or mid-infrared spectrum would require the use of specialized optical fibers, such as ZBLAN-fibers (for mid-infrared interfacing), or efficient wavelength conversion.¹¹² 

The silicon lattice is host to a plethora of luminescent centers in the near- and mid-infrared.¹¹³ Many are associated with localized defects formed by bombarding silicon with energetic ions and/or electrons, followed by annealing. Single-photon emission from a silicon defect known as the G-center has recently been observed.^114–116 Most of the damage centers do not have a native spin, but the T-center is an exception. It has a dipole allowed transition from a set of viable qubit basis states to a higher lying defect state at an energy of 935 meV, well within the transparency band of silicon. The spin coherence times are over T₂ ≈ 2 ms at or below 4 K.⁹³ Their radiative efficiency is currently unknown, and their estimated dipole transition moment is based on a measured population lifetime, assuming unity radiative efficiency.⁹³ 

When the chalcogenides of group-VI, such as S, Se, and Te, substitute for a silicon atom, they act as deep double donors that have relatively well-understood electronic states. When singly ionized, the remaining electron exhibits a hydrogen-like orbital structure with large binding energies of 614, 594, and 411 meV, respectively.¹¹⁷ The energy diagram of ⁷⁷Se⁺ in Si is shown in Fig. 8. The ⁷⁷Se⁺ isotope has a non-zero nuclear spin 1/2, which leads to a zero-field hyperfine splitting of the electron ground state into the singlet $S$ and triplet $T$⁠, with transition energy ΔE_GS = 6.87 μeV. The excited state $Γ 7$ can be optically accessed and is located 427 meV above the ground state(s), which corresponds to a zero-photon line (ZPL) at 2.9 μm. The relevant Λ-system is then defined as follows: $S ⇔ T$ forms the qubit transition $Q 1 ⇔ Q 2$ with the transition energy ΔE_qb = ΔE_GS = 6.87 μeV and $S ⇔ Γ 7$ is the optical transition that would be used for cavity coupling, $Q 1 ⇔ X$⁠, at an energy E_ph = 427 meV.^77,92,118 Compared to the T-center, these ground states have enhanced spin coherence times on the order of ∼2 s at or below 4 K. Other Se isotopes have similar spin relaxation rates, coherence times, and optical properties, but there is no zero-field splitting.^118,119 This may not pose a fundamental obstacle, as the qubit basis state separation could be set by Zeeman splitting by a uniform magnetic field.

This survey of quantum emitter candidates is far from exhaustive, and some of the characteristics listed in Table II may be limited by the current state of the art in materials synthesis and/or nanofabrication. Indeed, efforts to better control the surface of diamond have succeeded in dramatically improving the spectral diffusion and inhomogeneous broadening of NV center emission.¹²⁰ Rare earth ions might be more viable than this summary suggests, and further experimental studies of, e.g., Er³⁺ in isotopically pure host materials are encouraged. With these caveats, we now turn our attention to consider the photonic circuit platform options, informed by this survey.

An ideal material platform for implementing the architecture presented in Sec. II would support the scalable fabrication of sophisticated, integrated photonic circuitry, and it would be host to high-quality, optically accessible spin qubits. If the ideal qubit could only be hosted in one material, and the ideal photonic circuit platform in another, then so long as the optical transition fell within the transparency window of the circuit platform material, another option could be to evanescently couple the emitters to the photonic cavities.^69,70,112

While efforts at developing scalable photonic circuit capabilities in diamond or SiC are ongoing,^{102,121–123} current capabilities in this regard are in their infancy. This contrasts with silicon photonics technology that is now proven capable of integrating a large number of classical optical functions on a chip using highly evolved CMOS fabrication infrastructure.^124,125 Because optical quantum computing technologies will require millions of uniformly high-quality components,^24,126,127 there is a strong effort directed at establishing a large-scale integrated quantum photonics technology platform,^112,128,129 with much of that based on silicon.^24,130 Many of the all-photonic (LOQC, CVQC) systems mentioned previously have exploited various material sub-platforms of silicon photonics, such as silica-on-silicon (SOS), silicon nitride (SiN), silicon-on-insulator (SOI), etc. Strategies for integrating diamond-based defect spin qubits with these platforms are being pursued.¹³¹ Recent hybrid advances with rare earth ions coupled to Si photonic nanocavities have been reported.^69,71,132 The silicon platform not only offers the potential for high-volume, large-scale production at low cost¹³³ but also already boasts foundry-specific process design kits (PDKs) and complementary high-resolution electron beam lithography PDK support for rapid-prototyping.¹³⁴ 

Given these current realities, we believe that the integrated photonic circuit platform should be based on silicon photonics. This all but rules out the use of well-studied diamond-hosted defect qubits with transitions above the bandgap of silicon, although they could possibly be evanescently coupled to an oxide- or nitride-on-silicon photonic circuit platform. This would just add to the already significant technological challenges. Er³⁺ or other rare earth ions hosted in some glass would not be similarly ruled out, as they have near-infrared transitions compatible with evanescent coupling to silicon-based cavities. However, even if one used Purcell enhancement to broaden the spectral window over which near-unity cavity routing fidelities could be expected, it seems unlikely that these centers would support the photon wavepacket bandwidths required to form the cluster state fast enough to beat decoherence (the single-photon pulse duration required to match the spectral linewidth exceeds the spin coherence time). The typically large inhomogeneous broadening characteristics of rare earth ions of over several GHz are also a concern but could be used to single-out individual emitters.^69,70

Considering the above factors, together with the fact that isotopically pure silicon itself is host to quantum emitters with very good to outstanding spin coherence times up to 4 K, with dipole transitions that exhibit no inhomogeneous broadening and homogeneous linewidths compatible with high-speed ZZ parity measurements, we consider Se⁺ and the T-center as the leading qubit candidates. S⁺ and Te⁺ are likely also viable, but the Se⁺ impurity has been more extensively characterized.

The T-center transition would force operation at a wavelength 200 nm shorter than the standard telecommunication operating wavelengths of SOI circuits, 1.55 μm, whereas the Se⁺ transition would force operation at almost double this standard wavelength. Scaling down by 200 nm would mean a critical feature size reduction by ≈30%. This might not seem significant but could critically impact device performance and reproducibility, in particular for sub-wavelength structures on the order of 100 nm, as can be found, e.g., in PhC cavities. In comparison, the lithography tolerances would be relaxed by scaling up all dimensions by a factor of 2. On the other hand, much effort will be required to realize high-quality, low dark count single-photon detectors at 2.9 μm, whereas existing integrated superconducting single-photon detectors would work well for the T-center. Figure 9 shows a mode profile comparison of SOI single-mode strip waveguides for the three different operational wavelengths: (a) T-center zero-phonon line (ZPL) at λ = 1.33 μm, (b) telecommunication C band at λ = 1.55 μm, and (c) Se⁺ ZPL at λ = 2.90 μm, including a cross-sectional scanning electron microscope (SEM) image demonstrating highly anisotropic etching with low surface roughness. Another consideration has to do with the nature of the defects. Se is a substitutional donor with an isotropic dipole transition moment and relatively simple and well-understood electronic properties. The T-center, by comparison, is a complicated defect that is believed to involve two carbon atoms and a hydrogen atom.¹³⁵ It can take on 11 distinct orientations within the Si lattice (stochastically), each with an anisotropic dipole transition moment. While the transmission dipole moments and dephasing parameters differ somewhat between the T-center and Se⁺, their net impact from a c-QED perspective is negligible, as the ratios $Q / V ̄ C = 1$ and $Q / V ̄ S C$ are similar for the two.

Due to the trade-offs involved, it is not currently obvious which center is the most promising. The T-center operates within the advantageous telecommunication O-band, potentially with a higher QE, yet as a radiation damage center, it suffers from probabilistic creation with 11 orientational subsets within the Si host lattice.⁹³ Its significantly shorter spin coherence time, similar to the NV center in diamond, may require a much more complicated nuclear cluster state formation procedure.^{63  77}Se⁺ offers long spin coherence times directly compatible with our architecture, zero-field ground state splitting, and the promise of scalability due to its atomic nature. It suffers from an optical transition in the challenging mid-IR spectral region and a relatively low radiative quantum efficiency (QE). An ideal defect spin candidate in Si has yet to be found.

In this section, we itemize the principal elements that the foregoing analysis suggests are crucial in order to realize the proposed architecture using silicon photonic circuitry. Where possible, target specifications are summarized, alternate approaches are identified, and the state of the art is reviewed.

In order to realize a large spin coherence time, it is important to eliminate the magnetic noise from neighboring crystal lattice defects as much as possible. It is therefore fortunate that silicon can be grown with a high degree of isotopic purity. Natural silicon is comprised of three stable isotopes: ²⁸Si, ²⁹Si, and ³⁰Si with natural isotopic abundances of 92.22%, 4.69%, and 3.09%, respectively.¹³⁶ Besides their different masses, these three isotopes also differ in their nuclear spin: ²⁸Si and ³⁰Si are spin-free, while ²⁹Si has a nuclear spin of $1 2$⁠.¹³⁷ As a result, the physical properties of a Si crystal can differ greatly depending on its isotopic composition. Enriched ²⁸Si has a thermal conductivity up to ten times higher than natural Si.¹³⁶ With regard to spin-photon interfaces, isotopically pure ²⁸Si offers two major advantages over natural silicon.

First, inhomogeneous broadening of optical transitions is essentially eliminated due to the absence of local variations in the bandgap and binding energy.^93,138–140 High-resolution photoluminescence excitation spectra of T-center ensembles in a ²⁸Si host imply a residual inhomogeneous broadening of <0.14 μeV (<33 MHz).⁹³ For single emitters, this can lead to optical linewidths limited only by their excited state lifetime. Hyperfine-resolved optical transitions can be observed—a feature that had been once reserved for isolated atoms and ions in vacuum.^118,141 It should be noted that in nanophotonic devices, fabrication-induced strain, surface charges, or co-doping for charge carrier compensation are likely to increase the inhomogeneity, at least at the prototype stage. The extent to which emitters in Si will be subject to these additional broadening mechanisms will need to be determined in future studies. In this context, it should be noted that the inhomogeneity and spectral diffusion of NV centers in micrometer-thin etched diamond membranes has gradually been improved to values <0.41 μeV (<100 MHz),¹²⁰ which suggests that for optimized fabrication of ²⁸Si structures, even less inhomogeneous broadening might be expected.

Second, due to the absence of nuclear spins in ²⁸Si, a main source of spin decoherence is no longer present.¹⁴¹ Isolated in such a semiconductor vacuum, some spin qubits have demonstrated coherence times exceeding several hours.^141,142 Note that these experiments were conducted on the nuclear spin of the singly ionized P, which is not optically addressable.

Most of the ²⁸Si studied for fundamental academic or metrologic purposes originates from the International Avogadro Project.^143,144 These bulk crystals are of no use for integrated photonics; however, there has been significant recent progress in growing the isotopically pure ²⁸Si thin films required to implement integrated photonic components. UHV-compatible direct beam Penning ion sources^145,146 have been used to create films with isotopic purity beyond 99.9998% ²⁸Si,¹⁴⁷ and mono-crystalline isotopically purified epilayers have been grown by chemical vapor deposition (CVD) on 300 mm substrates in the state-of-the-art industrial CMOS foundries using isotopically enriched silane (²⁸SiH₄).^148,149

To ensure optimal spin-photon coupling and scalable fabrication of Si quantum photonic integrated circuits, emitter placement must be achieved with high spatial precision and number control. Imperfect spatial coupling of the spin center with the photonic mode will result in an increased error rate related to the spin-photon interface (see Sec. II C) due to a reduced cooperativity. Both criteria (to ensure that the emitter is placed at the primary antinode of the cavity mode and that there is exactly one emitter present) are equally important. Depending on the complexity of the defect center composition, the method and yield can drastically differ.

Deterministic implantation of single individual atoms and ions has been demonstrated with sufficient precision (tens of nm),¹⁵⁰ but this has yet to be demonstrated for most relevant quantum emitters. More refined placement methods with atomic precision may be applicable if they can be tailored to the target impurity. For example, the scanning tunneling microscopy (STM) hydrogen lithography technique has been used to embed single P atoms into a Si substrate.^151–153 Precise charge control of the implanted atoms is crucial. A way to ensure the presence of Se⁺ in its singly ionized state is by engineering the background doping, which has commonly been achieved using B as an acceptor.^92,119 A higher level of control might be realized by B co-implantation. For multi-atom radiation damage centers, such as the T-center, localized electron beam irradiation and annealing may limit the yield of precisely placed, single centers.¹⁵⁴ 

Although scalability may become an issue, an alternative to site-selective defect placement is to use deterministic post-fabrication of the nanophotonic structures around proven-high-quality, stochastically placed centers.^112,155 Various works have proven the viability of this approach, both at the single-device level and in large-scale circuits, using pick-and-place technologies,^122,156 in situ (electron beam) lithography,^157–159 or high-resolution (hyperspectral) imaging.^160,161

The cavity design requirements on Q and V are determined by the optical and spin properties of the emitter, as summarized in Eqs. (5), (7), and (8) from Sec. IV A. The cavity linewidth and mode volume should be chosen to operate at large cooperativities, ideally in the strong-coupling limit, to minimize deleterious effects of optical cyclicity and the finite bandwidth of the single-photon wavepackets. Figure 10(a) shows relevant cavity design restrictions in Q–V space, assuming the qubit to be the ⁷⁷Se⁺ impurity in Si. The lines would not be substantially different for the T-center as can be appreciated from the near identical requirements (see Table II). The strong-coupling criterion is indicated by the black solid line. The minimum Q factor required to achieve C > 1 is shown as the red line. The vertical line toward the right-hand side denotes the fact that the absolute largest value of $V ̄$ for which strong coupling could theoretically be achieved is 124 [Eq. (8)]. Various geometries of high Q, low V PhC microcavities have been shown compatible with the green-shaded region above the strong-coupling limit, below the maximum Q limit, and above the minimum V limit. Most of these demonstrations were at wavelengths of λ ≈ 1.55 μm. Cavity types labeled “L3,” “H0,” “nanobeam,” etc. have been extensively studied.^162–167 For reference, two points on the graph in Fig. 10(a) are inserted in the green-shaded region corresponding to “L3” and “H0” cavities reported in the literature. Both of these cavity types are based on hexagonal 2D photonic crystal cladding regions, differing only in the symmetry of the central defect region where 3 or 0 etched holes have been removed, respectively, and the adjacent holes are modified in some fashion (shift of location and the change of hole radius). It is important to note that in order to avoid unwanted scattering into the third output channel of our dual-rail-coupled cavity architecture, more sophisticated mode engineering is required.⁷⁶ 

We have fabricated prototypes of the two-qubit coupled cavity building block associated with the ZZ parity measurement scheme, as shown in Fig. 13(a), designed to operate near 1.55 μm. These incorporate two nominally identical H0-type cavities and do not include any intervening active switches. The room-temperature transmission spectra shown in Fig. 13(c) illustrate a number of critical issues. First, the Q and V values [indicated as diamonds in Fig. 10(a)] are encouraging, as is their trend with the waveguide coupling strength, as illustrated in Fig. 10(b). The fact that the two resonances are separated by more than the bare cavity linewidths, when they were designed to be nominally identical, reflects the realities of current electron beam lithography based process variability. Further process development should help in this regard, but it will be necessary to incorporate a cryogenic cavity resonant frequency tuning mechanism, something that we address below.

All these cavity results near 1.55 μm are based on SOI with device layer thicknesses in the 200–220 nm range. We have also fabricated a series of waveguide-coupled PhC cavities designed for a resonance wavelength of λ = 2.90 μm, using 500 nm thick device layers. An SEM image of a waveguide-coupled PhC cavity designed for a resonance at λ = 2.90 μm is shown in Fig. 10(b), and two crosses in Fig. 10(a) correspond to two types of these mid-IR cavities. The Q factors of Q_H0 ≈ 8.0 × 10³ and Q_L3 ≈ 2.6 × 10⁴ compare well with the state-of-the-art mid-IR PhC cavities and MRRs with typical Q ≈ 10⁴. While both mid-IR cavities satisfy the C > 1 conditions, higher Q factors are needed to achieve strong coupling of a Se⁺ donor. A recent demonstration of SOI MRRs at λ ≈ 3.7 μm with Q = 10⁶ implies that mid-IR resonators can be expected to have similar quality factors as their telecommunication C-band counter parts.¹⁶⁸ 

Implied in Fig. 10(a), and all of the discussion to this point, is the assumption that the as-fabricated cavities exhibit model Jayne–Cummings response characteristics. There are various possible fabrication-related sources of deviation from this ideal behavior (insertion loss at the interface of ridge and PhC waveguides, asymmetries in the waveguide coupling, etc.) that we are in the process of characterizing. There are more fundamental deviations from ideal Jaynes–Cummings response due to the fact that the off-resonant transition from the $Q 2$ state cannot always be assumed to be decoupled from the cavity mode (for small mode volumes). This is illustrated by revisiting the fidelity of the Z-measurement circuit, relaxing the assumption that the $Q 2$ state is fully decoupled.

More realistic Z-measurement fidelities F_D1 (orange line) and F_D1 (blue line) were calculated, as shown in Fig. 11, as a function of detuning and assuming a ⁷⁷Se⁺ emitter and $V ̄ =1$⁠. Close inspection shows that near-unity fidelity can still be achieved with these system parameters, but it would be necessary to operate at small positive detuning of the incident photon from the bare cavity resonance. The blue-shift of the F_D2 peak is a direct result of non-negligible cavity coupling of the detuned qubit state $Q 2$⁠. The amount of the blue-shift scales with the cavity mode volume by $∝1/ V$⁠. This has practical implications for our QC building block design and sets a lower bound for V as unity fidelity for channels 1 and 2 will not be reached simultaneously for a smaller mode volume characteristic of the H0 cavity.

The resulting fidelities F_D1 and F_D2 are shown in Fig. 12 for κ_nc = 0.01, 0.05, 0.1, 0.2, and 0.5κ, as black and red lines, respectively.

The crucial ZZ parity measurements require that each qubit has the same dipole resonance transition frequency, at least to within the range over which the cavity transmission maintains high fidelity, as discussed in Sec. III. Although there is no evidence of inhomogeneous broadening of the T or Se⁺ transitions in bulk isotopically pure silicon, it remains to be seen to what extent their incorporation in the nanofabricated photonic cavities might introduce inhomogeneous broadening and/or spectral diffusion. If either are encountered, it might be possible to refine the materials processing and preparation procedures to overcome the problem, as was the case with NV centers in diamond. If spectral diffusion beyond the homogeneous linewidth persists, then another quantum emitter would have to be sought. If some level of (static) inhomogeneous broadening persists, a qubit-selective dipole transition tuning mechanism would have to be developed.

Assuming that the qubit transitions are identical, there remains the problem that the as-fabricated cavity mode resonant frequencies will not all precisely coincide, given even optimistic projections of progress in nanofabrication tolerances. As evident from Fig. 13, in order to carry out the crucial ZZ parity measurement, it will be necessary to tune each cavity’s resonant frequency at least on the order of a few nm, at cryogenic temperatures, ideally without seriously impacting the cavity Q factor.

Tuning mechanisms can be either static (permanent) or dynamic. Static tuning mechanisms include precise post-fabrication steps that induce a shift of the cavity resonance by introducing a permanent change in the local dielectric environment. This can be achieved, for example, by laser-assisted local oxidation¹⁶⁹ or atomic layer deposition.¹⁷⁰ Notably, the Q factor can be maintained across large tuning ranges.^169,170 In contrast, dynamic tuning relies on some real-time electronic control mechanism. Fortunately, this tuning does not have to be done at high rates. The plasma dispersion method, widely used in silicon modulators,¹⁷¹ introduces large optical absorption that can compromise the cavity Q and lead to errors due to photon loss. Thermo-optic tuning of λ_C is also a widely used tuning mechanism at room temperature, however the thermo-optic coefficient of silicon at cryogenic temperatures is negligible.¹⁷² The deposition of a gas such as xenon onto a cold microcavity has successfully been used to tune λ_C in cryogenic conditions without drastically reducing Q.¹⁷³ However, this method by itself is not scalable as every cavity requires an individual amount of tuning, but gas condensation happens on a global scale. Individual tuning could be achieved in a subsequent step via local sublimation of the condensed gas (e.g., using a laser).

Figure 14 shows a PhC cavity design with nanoelectromechanical (NEMS) enabled resonance tuning.¹⁷⁴ The device consists of a fractured free-standing H0 cavity, as shown in Fig. 14(a), with its left and right segments attached to in-plane NEMS actuators (not shown). Tuning is achieved through controlling the gap width between the fixed and moving segments via mechanical movement (illustrated by the white arrows). Proof-of-principle measurements for resonance tuning and the cavity-Q preservation are shown in Figs. 14(b) and 14(c). These data were obtained from a series of “static” fractured cavities centered around 1.55 μm with different trench widths. The results indicate an opto-mechanical strength g_om of $g o m = 0.16 ± 0.02$ meV/nm, which corresponds to −0.32 nm of resonance tuning per 1 nm of mechanical actuation. Increasing the trench width is accompanied by an order of magnitude drop in Q, which decreases from Q = 2.24× 10⁴ at 20 nm trench width and approaches a value of $Q= 1.5 ± 0.5 ×1 0 3$ in the large trench limit. Future work along this path will be focusing on maintaining a higher Q throughout the dynamic tuning.

Each operation cycle of our protocol starts with the creation of a single photon that will subsequently be used to perform spin-initialization, probe, or entanglement operations. High-performance, easy-to-integrate on-demand single-photon sources (SPSs) matching the cavity resonance frequency (associated with the T or ⁷⁷Se⁺ qubits) are a key component of our spin-photonic QC technology. Notably, our cQED-based projective parity strategy does not put a high demand on the spectral purity or distinguishability of the single-photon wavepackets, in contrast to most all-photonic approaches. Linear, all-optical quantum processing of photons typically relies in some way on Hong–Ou–Mandel (HOM) interference, which is very sensitive to the state’s spectral amplitude. In contrast, the projective parity scheme is primarily sensitive to the spectral intensity of the photon wavepacket.

The generation of light in silicon is challenging due to its indirect bandgap. To date, there are mainly two approaches that can provide indistinguishable single photons in integrated silicon photonics, namely, heralded sources based on the χ³ nonlinearity of silicon^175,176 and hybrid integration of deterministic sources based on solid-state quantum emitters.^112,177

SPS based on single quantum emitters can, in principle, be of higher efficiency and quality, and they can operate on-demand, avoiding the need for heralding. The best performing solid-state SPSs are based on self-assembled III–V QDs. Engineering of their photonic environment allows for the operation of semiconductor quantum dots as near optimal sources of coherent single photons and photons pairs with simultaneously high efficiency and indistinguishability.^178–180 To avoid the fabrication challenges of hybrid integration, it would be desirable to realize deterministic on-demand SPS in silicon. Very recently, single-photon emission from the silicon-native G-center defect (at wavelength 1.28 μm)^114,115 and waveguide coupling of the silicon-native W center defect (at wavelength 1.22 μm)¹⁸¹ have been demonstrated. These results offer hope that silicon-based SPS might be realizable in silicon. The T-centers and Se⁺ centers are obviously themselves quantum emitters and would be the natural choice as they are perfectly matched to their spin-photon interface counterpart. The strategies employed in Refs. 181 and 182 may facilitate the development of on-demand single-photon sources at the required wavelengths. However, the relatively low radiative efficiency of the transitions of Se⁺ (QE of 0.8% and ZPL fraction of 16%)⁷⁷ will make for challenging cavity engineering.

The χ³ nonlinearity of silicon associated with spontaneous four-wave mixing (SFWM) has successfully been exploited for photon pair generation.¹⁸³ These photon pairs can be used to generate heralded single photons over a wide range of wavelengths by carefully engineering phase matching or mode spacing conditions. Several SFWM SPSs based on long waveguides, micro-ring resonators, and coupled PhC micro-cavities have been reported in the 1.550 μm wavelength range.^184,185 A mid-IR SFWM source has also recently been reported.¹⁸⁶ While the probabilistic nature of the SFWM process requires heralding and multi-pair generation limits the pair generation rate from individual devices, multiplexers have been developed to boost the rate at which heralded single photons can be accessed.^187,188 SFWM sources would likely have to be implemented as a geometrically separate “photon farm” and routed to the primary processing portion of the chip.

One challenge with SFWM sources is the need to filter the residual pump photons from the forwarded signal and idler photons. We have recently proposed and demonstrated grating-assisted contra-directional couplers (CDCs) as high extinction ratio pump rejection filters for on-chip photon-pair sources in silicon.¹⁸⁹ Recycling of the reflected pump power can be employed to pump multiple photon-pair sources.¹⁸⁹  Figure 15(a) shows the photonic circuit diagram of a micro-ring resonator SFWM on-chip single-photon source with a three-stage grating-assisted CDC. The CDC is designed for maximum reflection around the pump wavelength of λ_P = 1558.51 nm. From the transmission spectrum [see Fig. 15(b)], an extinction ratio of ER ≳ 60 dB can be extracted. The experimental CDC transmission loss for signal and idler photon of this device has been determined to be 1 dB for the single-stage CDC and 4.5 dB for the triple-stage device. Figure 15(c) shows an SEM image of a single CDC stage. The normalized signal-idler inter-beam coincidence spectrum is shown in Fig. 15(d) as a red line for an in-waveguide pump power of P = 0.31 mW. The coincidence spectrum in the dark is shown as a black line. The inset shows a pronounced coincidence peak at t = 9.1 ns. From the raw data, a coherence time of τ_coh = 0.33 ns and a dark count limited coincidence-to-accidental ratio of CAR = 10 (limited by the high dark count rate of the avalanche single-photon detectors used for the coincidence measurement) are extracted. Scaling these micro-ring resonator/CDC sources to match the T-center would face the general scaling problem of reduced critical dimensions and increased two-photon absorption that competes with the nonlinear SFWM process. Scaling to 2.9 μm would not only ease the critical dimension requirement, it would also effectively do away with the parasitic two-photon absorption.

Pump-induced heating is another predominant challenge of parametric sources, as they require pump powers in the order of μW–mW.^183,185 Fortunately, the pump power does not necessarily need to be dissipated on-chip, as the CDC drop port can be used to remove access pump light from the chip. Two-photon absorption as a remaining heating mechanism is mostly absent at 2.9 μm. In case pump-induced heating cannot be reduced sufficiently, it will most likely dictate that such sources would have to be located on a separate, thermally decoupled “photon farm.” In contrast, pump-induced heating of deterministic, emitter-based single-photon sources can be considered negligible. Resonant optical pumping schemes^190,191 enable π-pulse excitation with sub-100 pW average excitation power at a 83 MHz pulse repetition rate.¹⁹² To put these excitation powers into perspective, a cooling power of 1 mW would suffice to operate ≈10⁶ deterministic SPS at a GHz repetition rate.

The ability to detect single quanta of light is an essential prerequisite for optical quantum information technologies, which set extreme demands on detector performance. Out of all competing single-photon detector technologies,^193,194 superconducting nanowire single-photon detectors (SNSPDs) seem to be the natural choice for photonic quantum information processing.¹⁹⁵ SNSPDs exploit the phenomenon in which incident photons can cause a local breakdown of superconductivity by creating a hot spot.¹⁹⁶ The transition from a superconducting to conventionally conductive state can then be measured by the state-of-the-art high-speed electronics. Besides offering excellent detection efficiencies, low dark count rates, and high-speed timing resolution,^197,198 they can readily be applied to integrated quantum photonic circuits.^199,200 The integration of SNSPDs with nanophotonic waveguides can be considered a logical step toward enabling a broad range of classical and quantum technologies on a chip-scale platform.²⁰¹ The superior performance of SNSPDs compared to alternative detectors, such as avalanche photodiodes (APDs), justifies the requirement for cryogenic systems, a requirement that aligns with the cryogenic environment needed for the operation of optically addressable electron spin-centers in Si at T < 2 K.

The absolute performance metrics of SNSPDs can be engineered by a variety of intrinsic and extrinsic parameters, such as the choice of superconducting material and device geometry. For example, the cut-off wavelength of an SNSPD is limited by the superconducting energy-gap and the nanowire width. This insinuates that a minimum photon energy is required to create a hot spot. Since the hot spot size decreases with decreasing photon energy, the nanowire needs to be sufficiently narrow for a complete breakdown of the superconductivity. In NbTiN, mid-IR single-photon detection has been demonstrated for wavelengths of up to 5 μm, and experimental data suggest that detection of single photons at a target wavelength of 2.9 μm can be achieved for nanowire widths below 50 nm.²⁰² While waveguide-integrated SNSPDs for the mid-IR spectral region still need to be demonstrated, conventional mid-IR SNSPDs based on 60 nm wide NbTiN have recently been demonstrated for photon-counting LIDAR and quantum interference applications at wavelengths of 2.3 and 2.1 μm, respectively.^203,204 Novel superconducting materials, such as amorphous tungsten silicide (a-WSi), with improved structural homogeneity and a smaller superconducting gap with a single-photon detection of up to 10 μm pose an alternative to ultra-narrow nanowires.^205–208 

To ensure high detection efficiencies, waveguide-integrated SNSPDs require long coupling lengths (typically ≫100 μm), which strongly limits the detector performance. Dark count rate, dead time, and timing jitter all increase with increasing nanowire length. More importantly, it is rather challenging to guarantee the required uniformity and quality of sufficiently narrow nanowires (w ≪ 50 nm) over larger distances due to an increased probability of imperfections. In 2015, our group demonstrated a cavity-enhanced scheme to overcome the trade-off between detection efficiency at the expense of conversion efficiency, noise, speed, and timing jitter (see Fig. 16).²⁰⁹ The cavity was designed for a resonance at the telecommunication wavelength of 1.55 μm and enabled near-unity on-chip detection efficiency for a NbTiN nanowire that was only 8 μm long and 35 nm wide, thus meeting the size requirements for mid-IR detection at 2.9 μm wavelength.²⁰² 

To realize scalable, integrated single-photon detection at 2.9 μm with near-unity detection efficiency, we propose to adapt the cavity-enhanced (coherent perfect absorber, CPA) scheme by changing its geometrical parameters and introducing new designs and functionalities, such as a cross-wire geometry: by placing the nanowire perpendicular to the waveguide, its length can be further reduced to <1 μm.^210,211

Different detector performance parameters impact the proposed QC architecture performance. Latching, efficiency, and bandwidth can be mapped onto the error consideration in Sec. II C as photon loss events, whereas afterpulsing might cause dark counts. Fortunately, afterpulsing is typically not present in SNSPDs,¹⁹³ and if it occurs, it is mostly due to backreflections of the electronic circuitry.²⁰¹ If the afterpulsing event happens within the same clock-cycle as the original photo-detection, it can be disregarded. For latching to be of relevance, the detector would need to be operated near its maximum count rate, which is determined by the detector recovery time.²⁰¹ In integrated SNSPDs, the dead time is typically in the order of a few ns, but values as low as sub-500 ps have been reported for integrated SNSPDs,²¹¹ implying up to GHz count rates. The expected clock-cycle rates are far below the GHz range, which should eliminate the issue of latching.

SOI waveguides with propagation loss ranging from 0.6 to 5.3 dB/cm across the MIR range have been demonstrated.²¹² In the telecomm bands, the state-of-the-art 300 mm deep-UV immersion lithography processes offer waveguide propagation losses of <1 dB/cm in strip or rib waveguides²¹³ and <1 dB/cm in photonic crystal waveguides.²¹⁴ Propagation losses can be further reduced by using wide multi-mode waveguides for long-distance on-chip routing, where losses down to 0.026 dB/cm at 1.55 μm have been demonstrated; however, such waveguides can only be used for long straight sections and require tapers down to single-mode waveguides to incorporate bends.⁴⁶ 

Near-IR SOI waveguide crossings with ultra-low insertion loss as low as 0.007 dB have been demonstrated,^215,216 which provides a guideline for the optimization of mid-IR crossings. The spatial freedom provided by photonic wire bonds (PWBs; see Sec. V D 5) could be exploited as a means to simplify the circuit topology or bridging distant parts of the chip at the cost of an increased insertion loss of 0.7 dB for on-chip interconnects.²¹⁷ 

Active switching and phase modulation are crucial for the dynamic reconfiguration of the Z- and ZZ-measurements performed using the unit cell circuit [Fig. 1(b)], as required by the cluster formation protocol. The ideal active switch has negligible insertion loss, a high extinction ratio, and sub-ns switching speeds.²¹⁸ As discussed in the context of cryogenic cavity tuning (see Sec. V C), the requirements of scalability, low loss, and cryogenic compatibility rule out many options, leaving NEMS-based active components as one of the few promising candidates for this purpose. There have been proposals for low-loss NEMS-based modulators.^219,220 Reconfigurable on-chip single-photon routing at cryogenic temperature by NEMS switches has recently been demonstrated with insertion losses of 0.67 dB, extinction ratios of up to 28 dB, and sub-µs switching speeds.^221–223 These parameters suggest that current active switches need to be considered as a limiting element in determining the net photon loss of the unit cell, its switching speed, and its footprint. Of these, the insertion loss is the most crucial parameter for future optimization efforts.

Figure 17 shows an example of a switch with a potentially small footprint, in which NEMS structures are to be attached to the ring resonator. Photon routing is achieved by mechanically modifying the relative distance between the ring and the crossing.

A possible alternative to NEMS for implementing active switches would be provided by a material that is nearly lossless yet can have its index of refraction electrically tuned. Polymers have already been shown to function at cryogenic temperatures, and high-speed modulators have been demonstrated.²²⁴ This type of material could be explored in the search for a high-speed, low-loss cryogenic optical switch compatible with silicon photonic circuitry.

Similar to microelectronics, where electrical wire bonding has solved the obstacle of packaging and interfacing different functional chip elements, there is an increasing demand for its optical analog.²²⁵ This is especially true for our photonic approach to quantum computing with optically interfaced single spin centers. The requirement to operate on the single-photon level demands the lowest possible loss for all components.

Photonic wire bonding (PWB)²²⁶ is an optical packaging solution that solves the same challenges as electrical wire bonding in microelectronics for optical signal transmission both on- and off-chip.²²⁵ Instead of metallic wires, PWBs are 3D freeform polymer waveguides written by direct laser writing, utilizing two-photon polymerization. PWBs remove the prerequisite of high-precision active alignment and allow for arbitrary mode field connections, high interconnect densities, and scalable automated fabrication. Automated PWB mass production with an insertion loss of 0.7 dB (i.e., coupling efficiency >90%) has recently been demonstrated.²¹⁷ Photonic wire bonding can be utilized for both on- and off-chip interconnects. To date, chip to fiber array,²¹⁷ laser,^227,228 semiconductor optical amplifier connections,²²⁹ and re-configurable nanophotonic circuitry have been demonstrated.²³⁰ 

Figure 18 shows different configurations of photonic wire bonds 3D-printed with a Vanguard SONATA1000 system. Figure 18(a) shows a SEM image of a parallel array of on-chip interconnects. Evanescent coupling into the tapered PWB [see Fig. 18(b)] ensures low insertion loss and high coupling efficiency. Figure 18(c) shows an optical microscope image of a single-mode optical fiber array photonically wire bonded to an on-chip edge coupler array.

The optical parameters of the employed polymers are well-understood for room temperature and up to a spectral range of λ ≦ 2 μm.²³¹ Remaining challenges are mid-IR and cryogenic compatibility. Despite thermal shrinkage of the polymer, 3D-printed micro-optics have been proven to perform excellent in cryogenic environments as typically required by hybrid integrated quantum photonic circuits.¹¹² Recent examples include broadband low-loss fiber-to-chip couplers²³² and fiber-coupled semiconductor QD single-photon sources.^233,234

The normalized transmission and absorption spectra of the cured PWB and cladding polymer are shown in Fig. 19 as black and red lines, respectively. The blue shaded region highlights the direct spectral environment of the optical transition at 2.9 μm. Absorption is almost negligible for λ < 2.8 μm, which is why PWBs may be well suited for shorter wavelength quantum photonics (particularly in the industry standard O and C bands), such as for different spin centers (e.g., T-center), LOQC and CVQC. Both polymers display strong absorption lines at λ ≈ 2.9 μm, which can most likely be attributed to the C–H stretching vibrations. Detailed studies of the absolute optical properties covering the mid-IR spectral region are required to assess PWB compatibility with the Se⁺ spin-photon interface. Knowing these parameters would also be fruitful for other optical technologies in the mid-infrared, such as molecule and gas sensing.^235–237 While identifying an alternative polymer without strong absorption bands at λ ≈ 2.9 μm seems unlikely given the omnipresence of C–H bonds in organic materials, research is progressing in identifying alternate materials that can take advantage of two-photon polymerization. Recently, a fused silica nanocomposite resin has been used that can be structured and converted to transparent fused silica glass via thermal debinding and sintering.²³⁸ 

Apart from the single-photon parity measurements, local unitaries achieved by single-qubit spin rotation are required for the generation of qubit cluster states. For the ⁷⁷Se⁺ system, MW pulses matching the $S ⇔ T$ transition at a frequency of f = 1.66 GHz can be used to implement single-qubit gates. The coherent spin MW control technique has extensively been developed.^239–242 Here, we discuss the possibilities of adopting the existing techniques for our protocol. One main challenge of addressing individual spins is the trade-off between the spatial compactness limited by the long MW wavelength and the spin rotation errors due to crosstalk.

One way to avoid crosstalk is to introduce MW transition detuning between qubits such that the MW pulse designated for a specific qubit will not affect others, even if the MW pulse itself is broadcast across the entire qubit array. For example, a static magnetic gradient field can cause position-dependent Zeeman splitting.²⁴³ Field-insensitive “clock” transitions (as the ⁷⁷Se$+ S 0 ⇔ T 0$⁠) are robust against this technique.

Emitter-specific detuning could also be realized by a local electrostatic “A-gate” as described in Kane’s proposal.¹² A global AC magnetic field is applied, and individual qubits are tuned into and out of resonance a local Stark shift.²⁴⁴ One challenge of adopting the A-gate for our protocol is that the electrodes need to be placed far enough from the qubit to avoid optical absorption. As the A-gate will only be applied after single-photon Z- and ZZ-measurements, there is no interference with the optical transition. Detailed studies on the hyperfine Stark shift for deep donors in silicon are required for further evaluating this approach.²⁴⁵ 

Instead of global broadcasting, near-field MW pulses induced by local electrodes²⁴⁰ can be used to apply single-qubit gates. In this approach, the crosstalk can be minimized by carefully engineering the spatial MW extent for each qubit. It has been shown that local electrodes can be used to generate canceling fields to null the crosstalk, and the qubit spacing can be limited to less than 1/10 of the MW wavelength while maintaining low crosstalk.²⁴⁶ 

The cryogenic cooling requirements are far less demanding than for other QC schemes, such as superconducting qubits.⁴ For both T-center and Se⁺, an operational temperature of T < 2 K is required to guarantee long spin coherence time and a low emitter dephasing rate.^77,92,93,118 Standard commercially available closed cycle cryogenic systems suffice to provide a T < 2 K environment. Incorporating an additional cooling stage based on continuous adiabatic demagnetization refrigeration (cADR) or He absorption fridges allows for stable operation at T < 1 K, which also turns out to be the ideal operational temperature for integrated SNSPDs based on Nb(Ti)N or a-WSi. Considering the overall heat load of a full scale QC unit, the required cooling power will still pose a significant challenge. It is therefore of paramount importance to minimize the heat dissipated by active on-chip components and the heat introduced from classical control/readout lines connected to higher temperature stages. Custom cryogenic MW CMOS control units have been developed to address the heat load bottleneck,^241,242 but far more progress will be required. It should be noted that most if not all cryogenic approaches to fault-tolerant scale QC will face similar challenges. Even “all-photonic” approaches typically require cryogenically cooled detectors in large numbers.

In order to reach the goal of a fault-tolerant quantum computer, there are numerous tasks and challenges to complete and overcome. A roadmap outlining the immediate tasks that have been discussed and how they are connected is given in Fig. 20. Many of these tasks can be pursued in parallel and can be divided into three main groups: hardware and components, scalability and testing, and theory/error modeling and control.

Immediate physical hardware tasks include demonstrations of Purcell enhancement of emission and strong cavity coupling of defect centers in Si nanocavities. While preliminary studies can be performed with an ensemble of emitters, control over single individual emitters is required to observe on-demand single-photon emission, to characterize deterministic emitter placement, including charge-state control, and to study the influence of proximate (etched) surfaces of nanophotonic structures on the optical properties of the qubits.

Tuning and stabilizing the cavities to match the ZPL transition are essential to enable the Z and ZZ projective measurements. Perhaps there is a method by which each cavity could be individually and permanently tuned, obviating the need for an active tuning mechanism. If not, then something along the lines of the NEMS device discussed above (see Sec. V C) needs to be developed along with a control system to keep it locked. Alternatively, an electro-optic polymer may be appropriate for cavity tuning purposes, although the requirement to maintain high cavity Q values will likely be challenging. For any of these approaches, the possibility of introducing undesired strain on the spin qubit has to be considered. In short, much more work is required to develop a practical and scalable solution to the cryogenic cavity tuning problem.

Of equal importance is an integrated source of single photons tailored to the optical transition of the spin center of choice. These would ideally be on-demand, but multiplexed heralded sources may turn out to be more practical. All-photonic approaches to QC have similar requirements.

Integrated SPDs in the near-IR are close to having the required performance, but integrating them at the required scale will require significant progress in reducing the thermal load of the associated electronics. More effort is required at the materials and nanofabrication process levels to achieve the required performance in the mid-IR spectral region.

More work has to be done in regard to scalably controlling a dense array of spin qubits without incurring significant crosstalk and without compromising the quality factor of the optical microcavities.

Scaling up this system will require building a process development kit for mid-IR photonic components consisting of both passive and active devices that are tailored for the emitter’s dipole transitions. An automated testing apparatus¹²⁵ capable of characterizing the system in a cryogenic environment will also be required for efficient testing and iterations of designs. Individual components can be optimized by leveraging readily available rapid-prototyping at 1.55 μm on conventional 220 nm SOI¹³⁴ and subsequently be transferred to the target wavelength. It should be noted, that for quantum optical experiments including spin-dependent measurements, conventional SOI material will not suffice. Isotopically pure material is required (see Sec. V A). The largest obstacle for rapid development work at mid-IR wavelengths is the lack of readily available and easy-to-use equipment. For example, there is no commercially available single-frequency laser source at 2.9 μm with fast and wide-range scanning capability, which is why we custom-built our own system based on difference-frequency generation.²⁴⁷ 

For large photonic integrated circuit systems, device yield will be a concern. Although the proposed architecture fortunately only requires controllable pair-wise qubit interactions, it will be challenging to build systems with the thousands or millions of functioning physical qubits required for error correction. In the short term, and as a means of prototyping small systems (tens of qubits), it may be possible to first find working spin-cavity devices and use PWBs to connect multiple known-good qubits. In the long term, we envisage on-chip optical networks using low-loss multimode waveguide routing and built-in self-testing where the network can identify and select working qubits.

Finally, theoretical and modeling efforts must focus on developing a c-QED model for the building block operations that includes realistic (classically modeled and benchmarked against experiments) physical imperfections, such as frequency detuning, MW errors, photon loss, and detector dark counts. This model can then be used as the front end for quantum information simulators that will propagate these physical errors through the cluster building protocol to help pinpoint critical components that contribute most to the overall circuit error rates relevant to achieving the fault-tolerant threshold. This, in turn, can help prioritize individual component optimization efforts.

We have provided a roadmap to silicon photonic quantum computing with spin qubits that emerged from a critical analysis of the steps required to practically implement the recent proposals for optically addressable donor spin qubits in silicon⁹² and measurement-based QC using photons for entanglement and readout operations.^1,248 Encouraged by promising advances in isotopic engineering, it is now feasible to place a single luminescent spin center in a ²⁸Si semiconductor vacuum, which provides a long-lived quantum memory exceeding seconds that can be photonically interfaced.¹⁴¹ With sufficiently high-quality photonic and spin qubit performance, the proposed implementation fulfills DiVincenzo’s criteria for the physical implementation of a quantum computer,²⁴⁹ and the mature silicon photonic platform reduces the challenges of achieving high scalability. In addition, the photonically interfaced spins are naturally suited for integration with distributed and blind quantum computing networks.^{41,109–111,250} A concrete architecture and building block proposal was provided, and a prioritized list of numerous outstanding challenges was offered.

The authors acknowledge financial support from the Natural Sciences and Engineering Research Council, Canada, the Canadian Foundation for Innovation, the Stewart Blusson Quantum Matter Institute, the ReMAP Network, the SiEPICfab consortium members, and the British Columbia Knowledge Development Fund. The authors are thankful for fruitful scientific discussions with Robert Raussendorf from the University of British Columbia and Adam DeAbreu from Simon Fraser University.