Radio frequency mixing modules for superconducting qubit room temperature control systems

Quantum computing has the potential to solve computational problems that are classically intractable in the post-Moore era.^1,2 The superconducting quantum bit (qubit) is one of the most promising candidates that have demonstrated the basic quantum computing functionality.^3,4

High resolution, low noise RF (radio frequency) signals, which are typically in the 4–8 GHz frequency range with several hundreds of MHz bandwidth, are used to control and measure superconducting qubits.^5–7 These signals can be generated and detected using the standard heterodyne technique, as shown in Fig. 1. The intermediate frequency (IF) signals are generated or digitized by way of a digital-to-analog converter (DAC) or an analog-to-digital converter (ADC), respectively. Employing a limited IF bandwidth allows the system to use lower frequency ADCs and DACs for better noise performance and lower cost. The IF signals are shifted up or down in frequency by the RF mixing module and the low noise local oscillator (LO).⁸ 

Alternatively, a direct digital synthesis module can synthesize microwave waveforms in the GHz regime, which can potentially simplify the system. However, the current direct RF synthesis devices are still limited by their signal resolution, frequency range, cost, and usability.⁹ 

In traditional experimental systems, connectorized RF components are widely used because they are easy to assemble and interchange.¹⁰ However, each connector is bulky and can be a potential failure point in the long run, especially in extant systems. Based on the topology of a connectorized component configuration, we developed a series of compact RF mixing modules to reduce both cost and size as well as improve system reliability. Such integration and optimization will help the room-temperature-based control system keep pace with advancements in quantum information processor complexity and scale.

In this work, we developed RF mixing modules¹¹ and tested them with the superconducting quantum processors operating in the Quantum Nanoelectronics Laboratory (QNL) at the University of California, Berkeley. We compared the output of standard qubit benchmarks executed using our next generation electronics with standard connectorized modules. The solution proposed here exhibits low-noise, high-reliability operation and is now becoming the laboratory standard for microwave frequency modulation/demodulation across many different experimental configurations.

Specifically, we developed three RF mixing modules: one down converter module (DOWN: DN) and two up converter modules (UP: UPH, UPL) with different output power levels. The UPH and UPL labels correspondingly indicate the up converter module with higher and lower output power. The UP variants differ by an additional amplifier in the RF channel to accommodate varying degrees of cryogenic attenuation associated with different RF cable lengths and materials. For design simplicity, we start with one board per qubit and then study the crosstalk between boards.

The RF mixing module size should be as small as possible to support an increasing number of qubits. As shown in Fig. 2, the actual RF mixing bare board (up converter or down converter) size is 40 × 80 mm². The total number of RF mixing module channels scales linearly with the number of qubits, as does the cost of boards. The RF mixing module should also be designed with value engineering.

Every room temperature component has thermal noise, and active components contribute additional flicker and other noise to the system. Undesired signals can also come from adjacent channel crosstalk or environmental electromagnetic interference (EMI) along the whole signal transmission line. The noise performance of the RF mixing module directly affects the qubit performance. Therefore, the module needs to be implemented with low noise components. Typically, the higher signal power level can improve the signal-to-noise ratio (SNR), albeit at the expense of nonlinear effects in amplifiers or mixers. Thus, the signal power level needs to be designed to reach an optimal compromise between the signal-to-noise ratio and linearity.

All three RF mixing modules are comprised of several interconnected submodules, as shown in Fig. 3. Each submodule was designed independently and can be repurposed as a modular component to implement the overall module functionalities as needed.

The IQ mixer is used to shift the qubit control/readout frequency from/to the IF, which can be easily handled by the ADC/DACs. The mixer selection needs to cover the required frequency range in the superconducting qubit setup. Most 5G communication transceivers available on the market cut off at ∼6 GHz and are not applicable for qubit control. The passive IQ mixer HMC8193 from Analog Devices covers the RF and LO range from 2.5 to 8.5 GHz and the IF range from DC to 4 GHz,¹² thus meeting our requirement for UP and DN modules.

The amplifiers and attenuators are designed to adjust the power level to meet the gate pulse requirements, adjust the signal-to-noise ratio at different locations, and also to provide attenuation to suppress mismatch signals bouncing between discontinuities.

The LO signal is distributed from the LO generation chassis and is fanned out to multiple UP/DN modules. It is convenient to have an independent LO amplifier together with an attenuator for each channel to provide the required power for the mixer while also increasing the isolation between channels. At 8 GHz, the Mini-Circuits CMA-83LN+ provides ∼20 dB gain in the band, while its noise figure is 1.8 dB and the P1dB is 16 dBm.¹³ The same amplifier is also used in the RF channel.

Qubit readout resonator signals are typically amplified in the dilution refrigerator by a cryogenic superconducting traveling wave parametric amplifier (TWPA)¹⁴ and/or high-electron-mobility transistor (HEMT) to increase SNR. After down conversion at room temperature, the IF signal level is too low for ADC to directly digitize with enough resolution. A low noise IF amplifier after the mixer is needed to boost the voltage while minimally degrading SNR. The Mini-Circuits LHA-13LN + amplifier is employed as it can provide ∼22 dB gain in band, with a low noise figure of 1.1 dB across the band.¹⁵ 

Susumu PAT0510S series attenuators are used in the RF mixing modules, as they have <1.3 VSWR (voltage standing wave ratio, good attenuation flatness across the band, and compact footprint and are of low cost.¹⁶ 

An undesirable signal in the up conversion is LO leakage through the mixer, which can degrade qubit performance. This deleterious signal can be suppressed by precisely adjusting the DC bias level on the mixer I (in-phase) and Q (quadrature) ports. To combine the DC bias and RF signal, we choose the Mini-Circuits TCBT-14R+ as a bias-tee, which provides an ultra-wide frequency range with excellent isolation performance over the band. We also added two potentiometers to the up converter to tune the bias and null the LO. Furthermore, each potentiometer can be replaced by a jumper to allow for the automatic control of DC biases to compensate for the drift in the nulling signal.

Each amplifier is powered by a separate low dropout regulator (LDO) to minimize the potential crosstalk through the power line. All the LDOs share the same off board switcher regulator. Switcher supplies provide high efficiency in converting voltages close to the required amplifier voltage. A LDO further regulates the bias to the final voltage and rejects any switching noise from the switcher. Texas Instruments LP38798 is used in the RF mixing module, providing ultra-low output noise at 5 μV (rms) from 10 Hz to 100 kHz and a high power supply rejection ratio.¹⁷ Both up and down converters operate on a 6.3 V supply, while the up converter also uses an additional ±1.8 V supply for LO nulling.

Electromagnetic interference reduces electronic signal integrity and can limit the overall system performance. EMI shielding is implemented on the RF mixing boards to protect the sensitive signal from disturbances in the external electromagnetic environment and also to prevent the signal from leaking out and interfering with surrounding electronics. On the RF mixing boards, EMI shielding clips and custom-shaped covers are located around the RF sections of the boards as well as the SMA connector.

The back side of the board is designed to be a flat ground plane with no components to help with EMI. This flat back design also provides a simple way to attach an external heat sink or heat mess to cool or stabilize the board temperature.

The impedance is nominally designed to be 50 Ω across the board. In practice, however, values are impacted by variations in the trace impedance, footprints of components, and the SMA connectors themselves. The trace impedance is determined by the PCB (printed circuit board) process and the materials from the PCB vendor. We evaluated several SMA connectors and their footprints on different materials with the impedance control service from the PCB vendor. The impedance of the RF mixing board was measured to be 47 Ω by time-domain reflectometry (TDR) after assembly with SMA connectors (Cinch Connectivity Solutions Johnson 142-0771-831). The insertion loss was measured by determining the S21 of a coupon board of a similar length in the <10 GHz frequency band. We also compared the performance of Rogers (4003C) and FR4 substrates with respect to insertion loss in the band and measured ∼2 dB power loss across the board at 10 GHz. Since we have enough output power, we decided to use FR4 to reduce cost.

Both the UP and DN modules are designed to be four-layer PCB boards: signal layer, ground layer, power layer, and ground layer from top to bottom. This stack-up design can effectively reduce electromagnetic emissions and crosstalk and improve the signal integrity to provide a low inductance power distribution network. Besides the two ground layers, the large pieces of copper on the top signal layer cover the area without components and traces, thereby also connecting to the ground plane. Ground planes on different layers are connected through vias, which help reduce ground loops and keep the length of return loops short in the system.

The RF mixing board specifications are summarized in Tables I and II. The board faithfully maintains the excellent performance from the monolithic microwave integrated circuit (MMIC) mixer HMC8193.

The RF, LO, and IF pins are AC-coupled and matched to be 50 Ω. For the current application, the low pass filter in the IF channel cuts off the IF range to 500 MHz. However, the mixer offers a wide IF range of DC to 4 GHz, so it is easy to expand the IF range by replacing the low pass filter. Since an internal amplifier is included in the LO path, only 0 dBm power is needed for the LO drive level of the UP/DN module. The RF mixing board offers 27 dBc image rejection and thereby eliminates the need for filtering unwanted sidebands. Amplifiers and attenuators are cascaded in the RF/LO/IF path to enhance the isolation (∼50 dB) and suppress crosstalk.

To measure the noise performance of the RF mixing UP/DN modules, we used a QubiC (Qubit Control) prototype chassis¹⁸ with a set of UP/DN converters to implement a loopback test, as shown in Fig. 4. The QubiC system is an FPGA (field-programmable gate array) based qubit control system, developed at the Lawrence Berkeley National Laboratory.¹⁹ A QubiC prototype chassis provides 8-channel 16-bit DACs and 8-channel 16-bit ADCs at 1 giga samples per second (GSPS).

The QubiC FPGA and DACs generate I and Q components at IF. The transmitted I/Q signals form a complex signal that contains the amplitude and phase information. The UP module converts the I/Q signals from IF to RF, which is directly transmitted to the RF port of the DN module. On the receiver side, it is a two-stage mixing process, which is an analog mixing followed by a digital mixing. The first mixing is that the DN module receives the RF signal and converts it back to I/Q signals at IF. The second mixing is that the ADC digitizes the IF signal and the FPGA further down converts it to the baseband by digital mixing with the digital local oscillator (DLO). The baseband I and Q values are integrated by the accumulator and stored in the accumulator buffer, which is a complex signal and can be readout later. We can easily extract the amplitude and phase from this receiver integrated complex signal. To evaluate the noise performance of the UP and DN modules, we can measure the amplitude and phase responses of the integrated complex signal, while scanning the phase of the transmitted I/Q signal over the 2π period. We chose three different drive frequencies (6.5635, 6.7035, and 6.8635 GHz) as the example for this test. As shown in Fig. 5(a), the IQ curve is close to a circle, which indicates good amplitude and phase balance.

To quantify the noise performance, we defined the peak-to-mean ratio (V_pp/V_mean) for the “amplitude” and the detrended phase for the “phase.” The receiver integrated complex signal has homogeneous amplitude and phase noise performance while scanning the whole phase cycle of the transmitted I/Q signal, as shown in Fig. 5(b). The linearity of the amplitude response and phase response is summarized in Table III. Compared to the widely used commercial Marki mixers,²⁰ the RF mixing module has better amplitude performance and comparable phase performance.

We tested a series of RF mixing modules for statistics, yielding a high pass rate on amplitude and phase linearity. As shown in Fig. 6, the short-term amplitude and phase linearity of the RF mixing modules are typically measured to be 5 ×10⁻⁴ (V_pp/V_mean) and 1 ×10⁻³ radian (pk–pk).

Randomized benchmarking (RB) is a widely used randomization method for benchmarking quantum gates, which is not sensitive to the state preparation and measurement errors.²¹ In order to validate the functionality of RF mixing modules on quantum hardware, we integrated them with the QubiC system to perform the RB measurement on an eight-qubit quantum processor²² residing in the dilution refrigerator at the Quantum Nanoelectronics Laboratory (QNL) in the University of California, Berkeley. Using our automatic single qubit characterization²³ and two-qubit gate optimization²⁴ protocols, we obtained single-qubit and two-qubit RB results. The process infidelity, which is the total probability that an error acts on the targeted systems during a random gate, can be extracted from the RB data.²⁵ The streamlined RB (SRB)²⁶ is one of the RB protocols widely adopted by the community to characterize the process infidelity. We implemented the SRB protocol by using the True-Q software²⁷ to generate the randomized circuits and fit the data. The qubit control and data acquisition were realized by the QubiC system together with the RF mixing modules under test. As shown in Fig. 7, the single-qubit process infidelity was measured to be 9.3(3) ×10⁻⁴, while the two-qubit process infidelity was measured to be 2.7(1) ×10⁻².

The RB results demonstrated that the RF mixing modules are capable of delivering high fidelity gates on the state of the art device. We believe that the RF mixing module is not the current limiting factor for higher fidelity. The RF mixing modules have been routinely employed in QNL and Advanced Quantum Testbed (AQT) experimental activities.

We developed a series of compact RF mixing modules for superconducting qubit room temperature control systems. This is a starting point to overcome challenges in extensibility arising from connectorized analog front-end components for superconducting quantum processor control. The RF mixing module is designed to operate in the 2.5–8.5 GHz RF and LO range and offers 27 dBc (typical) image rejection and ∼50 dB (typical) isolation between channels. The loopback test showed the RF mixing module reached 5× 10⁻⁴ (V_pp/V_mean) amplitude linearity and 1× 10⁻³ radian (pk–pk) phase linearity over the whole phase cycle. Using the QubiC system assembled with this RF mixing module, we tested the operation of a superconducting quantum processor in a dilution refrigerator and measured 9.3(3) × 10⁻⁴ (single-qubit) and 2.7(1) × 10⁻² (two-qubit) process infidelities from randomized benchmarking characterization. This confirmed that the functionality and performance of the RF mixing modules met the desired qubit control requirements.

This work was supported by the High Energy Physics QUANTISED program, the Advanced Scientific Computing Research Testbeds for Science program, and the Quantum Systems Accelerator under the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The authors would like to thank Ravi Naik, Jean-Loup Ville, Bradley Mitchell, Jie Luo, and Brian Marinelli from the University of California, Berkeley; Alexis Morvan, Jan Balewski, Wim Lavrijsen, and Kasra Nowrouzi from the Lawrence Berkeley National Laboratory; and Quantum Benchmark, Inc., for their support.

The data that support the findings of this study are available from the corresponding author upon reasonable request.