With its rich dynamics, the quantum harmonic oscillator is an innate platform for understanding real-world quantum systems and could even excel as the heart of a quantum computer. A particularly promising and rapidly advancing platform that harnesses quantum harmonic oscillators for information processing is the bosonic circuit quantum electrodynamics (cQED) system. In this article, we provide perspectives on the progress, challenges, and future directions in building a bosonic cQED quantum computer. We describe the main hardware building blocks and how they facilitate quantum error correction, metrology, and simulation. We conclude with our views of the key challenges that lie on the horizon, as well as scientific and cultural strategies for overcoming them and building a practical quantum computer with bosonic cQED hardware.
REFERENCES
1.
P. W.
Shor
, “
Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
,” SIAM J. Comput.
26
, 1484
(1997
).2.
Y.
Cao
,
J.
Romero
, and
A.
Aspuru-Guzik
, “
Potential of quantum computing for drug discovery
,” IBM J. Res. Dev.
62
, 6
(2018
).3.
A.
Ajagekar
and
F.
You
, “
Quantum computing and quantum artificial intelligence for renewable and sustainable energy: A emerging prospect towards climate neutrality
,” Renewable Sustainable Energy Rev.
165
, 112493
(2022
).4.
A.
Giani
and
Z.
Eldredge
, “
Quantum computing opportunities in renewable energy
,” SN Comput. Sci.
2
, 393
(2021
).5.
R.
Orús
,
S.
Mugel
, and
E.
Lizaso
, “
Quantum computing for finance: Overview and prospects
,” Rev. Phys.
4
, 100028
(2019
).6.
S.
Lloyd
and
S. L.
Braunstein
, “
Quantum computation over continuous variables
,” Phys. Rev. Lett.
82
, 1784
(1999
).7.
S. L.
Braunstein
and
H. J.
Kimble
, “
Teleportation of continuous quantum variables
,” Phys. Rev. Lett.
80
, 869
(1998
).8.
T. C.
Ralph
and
P. K.
Lam
, “
Teleportation with bright squeezed light
,” Phys. Rev. Lett.
81
, 5668
(1998
).9.
L.
Vaidman
, “
Teleportation of quantum states
,” Phys. Rev. A
49
, 1473
(1994
).10.
W. P.
Bowen
,
N.
Treps
,
B. C.
Buchler
,
R.
Schnabel
,
T. C.
Ralph
,
H.-A.
Bachor
,
T.
Symul
, and
P. K.
Lam
, “
Experimental investigation of continuous-variable quantum teleportation
,” Phys. Rev. A
67
, 032302
(2003
).11.
A.
Furusawa
,
J. L.
Sørensen
,
S. L.
Braunstein
,
C. A.
Fuchs
,
H. J.
Kimble
, and
E. S.
Polzik
, “
Unconditional quantum teleportation
,” Science
282
, 706
(1998
).12.
T. C.
Zhang
,
K. W.
Goh
,
C. W.
Chou
,
P.
Lodahl
, and
H. J.
Kimble
, “
Quantum teleportation of light beams
,” Phys. Rev. A
67
, 033802
(2003
).13.
N. J.
Cerf
,
A.
Ipe
, and
X.
Rottenberg
, “
Cloning of continuous quantum variables
,” Phys. Rev. Lett.
85
, 1754
(2000
).14.
G.
Lindblad
, “
Cloning the quantum oscillator
,” J. Phys. A
33
, 5059
(2000
).15.
M.
Ban
, “
Quantum dense coding via a two-mode squeezed-vacuum state
,” J. Opt. B
1
, L9
(1999
).16.
S. L.
Braunstein
and
H. J.
Kimble
, “
Dense coding for continuous variables
,” Phys. Rev. A
61
, 042302
(2000
).17.
T. C.
Ralph
and
E. H.
Huntington
, “
Unconditional continuous-variable dense coding
,” Phys. Rev. A
66
, 042321
(2002
).18.
J.
Mizuno
,
K.
Wakui
,
A.
Furusawa
, and
M.
Sasaki
, “
Experimental demonstration of entanglement-assisted coding using a two-mode squeezed vacuum state
,” Phys. Rev. A
71
, 012304
(2005
).19.
S. F.
Pereira
,
Z. Y.
Ou
, and
H. J.
Kimble
, “
Quantum communication with correlated nonclassical states
,” Phys. Rev. A
62
, 042311
(2000
).20.
M.
Hillery
, “
Quantum cryptography with squeezed states
,” Phys. Rev. A
61
, 022309
(2000
).21.
T. C.
Ralph
, “
Continuous variable quantum cryptography
,” Phys. Rev. A
61
, 010303(R)
(1999
).22.
M. D.
Reid
, “
Quantum cryptography with a predetermined key, using continuous-variable Einstein-Podolsky-Rosen correlations
,” Phys. Rev. A
62
, 062308
(2000
).23.
N. J.
Cerf
,
M.
Lévy
, and
G. V.
Assche
, “
Quantum distribution of Gaussian keys using squeezed states
,” Phys. Rev. A
63
, 052311
(2001
).24.
F.
Grosshans
and
P.
Grangier
, “
Continuous variable quantum cryptography using coherent states
,” Phys. Rev. Lett.
88
, 057902
(2002
).25.
F.
Grosshans
,
G.
Van Assche
,
J.
Wenger
,
R.
Brouri
,
N. J.
Cerf
, and
P.
Grangier
, “
Quantum key distribution using gaussian-modulated coherent states
,” Nature
421
, 238
(2003
).26.
S. D.
Bartlett
,
B. C.
Sanders
,
S. L.
Braunstein
, and
K.
Nemoto
, “
Efficient classical simulation of continuous variable quantum information processes
,” Phys. Rev. Lett.
88
, 097904
(2002
).27.
J.
Niset
,
J.
Fiurášek
, and
N. J.
Cerf
, “
No-go theorem for Gaussian quantum error correction
,” Phys. Rev. Lett.
102
, 120501
(2009
).28.
J.
Eisert
,
S.
Scheel
, and
M. B.
Plenio
, “
Distilling Gaussian states with Gaussian operations is impossible
,” Phys. Rev. Lett.
89
, 137903
(2002
).29.
J. S.
Bell
and
A.
Aspect
, “
EPR correlations and EPW distributions
,” in Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy
, 2nd ed. (
Cambridge University Press
,
Cambridge
, 2004
), pp. 196
–200
.30.
C. D.
Bruzewicz
,
J.
Chiaverini
,
R.
McConnell
, and
J. M.
Sage
, “
Trapped-ion quantum computing: Progress and challenges
,” Appl. Phys. Rev.
6
, 021314
(2019
).31.
S.
Deléglise
,
I.
Dotsenko
,
C.
Sayrin
,
J.
Bernu
,
M.
Brune
,
J.-M.
Raimond
, and
S.
Haroche
, “
Reconstruction of non-classical cavity field states with snapshots of their decoherence
,” Nature
455
, 510
(2008
).32.
B.
Hacker
,
S.
Welte
,
S.
Daiss
,
A.
Shaukat
,
S.
Ritter
,
L.
Li
, and
G.
Rempe
, “
Deterministic creation of entangled atom–light Schrödinger-cat states
,” Nat. Photonics
13
, 110
(2019
).33.
S.
Ebadi
,
T. T.
Wang
,
H.
Levine
,
A.
Keesling
,
G.
Semeghini
,
A.
Omran
,
D.
Bluvstein
,
R.
Samajdar
,
H.
Pichler
,
W. W.
Ho
,
S.
Choi
,
S.
Sachdev
,
M.
Greiner
,
V.
Vuletić
, and
M. D.
Lukin
, “
Quantum phases of matter on a 256-atom programmable quantum simulator
,” Nature
595
, 227
(2021
).34.
A.
Ourjoumtsev
,
R.
Tualle-Brouri
,
J.
Laurat
, and
P.
Grangier
, “
Generating optical Schrödinger kittens for quantum information processing
,” Science
312
, 83
(2006
).35.
S.
Kotler
,
G. A.
Peterson
,
E.
Shojaee
,
F.
Lecocq
,
K.
Cicak
,
A.
Kwiatkowski
,
S.
Geller
,
S.
Glancy
,
E.
Knill
,
R. W.
Simmonds
,
J.
Aumentado
, and
J. D.
Teufel
, “
Direct observation of deterministic macroscopic entanglement
,” Science
372
, 622
(2021
).36.
Y.
Chu
and
S.
Gröblacher
, “
A perspective on hybrid quantum opto- and electromechanical systems
,” Appl. Phys. Lett.
117
, 150503
(2020
).37.
Q.
Hou
,
W.
Yang
,
C.
Chen
, and
Z.
Yin
, “
Generation of macroscopic Schrödinger cat state in diamond mechanical resonator
,” Sci. Rep.
6
, 37542
(2016
).38.
C.
Bulutay
, “
Cat-state generation and stabilization for a nuclear spin through electric quadrupole interaction
,” Phys. Rev. A
96
, 012312
(2017
).39.
G.
Calusine
,
A.
Melville
,
W.
Woods
,
R.
Das
,
C.
Stull
,
V.
Bolkhovsky
,
D.
Braje
,
D.
Hover
,
D. K.
Kim
,
X.
Miloshi
,
D.
Rosenberg
,
A.
Sevi
,
J. L.
Yoder
,
E.
Dauler
, and
W. D.
Oliver
, “
Analysis and mitigation of interface losses in trenched superconducting coplanar waveguide resonators
,” Appl. Phys. Lett.
112
, 062601
(2018
).40.
A.
Megrant
,
C.
Neill
,
R.
Barends
,
B.
Chiaro
,
Y.
Chen
,
L.
Feigl
,
J.
Kelly
,
E.
Lucero
,
M.
Mariantoni
,
P. J. J.
O'Malley
,
D.
Sank
,
A.
Vainsencher
,
J.
Wenner
,
T. C.
White
,
Y.
Yin
,
J.
Zhao
,
C. J.
Palmstrøm
,
J. M.
Martinis
, and
A. N.
Cleland
, “
Planar superconducting resonators with internal quality factors above one million
,” Appl. Phys. Lett.
100
, 113510
(2012
).41.
M.
Reagor
,
H.
Paik
,
G.
Catelani
,
L.
Sun
,
C.
Axline
,
E.
Holland
,
I. M.
Pop
,
N. A.
Masluk
,
T.
Brecht
,
L.
Frunzio
,
M. H.
Devoret
,
L.
Glazman
, and
R. J.
Schoelkopf
, “
Reaching 10 ms single photon lifetimes for superconducting aluminum cavities
,” Appl. Phys. Lett.
102
, 192604
(2013
).42.
B.
Aune
,
R.
Bandelmann
,
D.
Bloess
,
B.
Bonin
,
A.
Bosotti
,
M.
Champion
,
C.
Crawford
,
G.
Deppe
,
B.
Dwersteg
,
D. A.
Edwards
,
H. T.
Edwards
,
M.
Ferrario
,
M.
Fouaidy
,
P.-D.
Gall
,
A.
Gamp
,
A.
Gössel
,
J.
Graber
,
D.
Hubert
,
M.
Hüning
,
M.
Juillard
,
T.
Junquera
,
H.
Kaiser
,
G.
Kreps
,
M.
Kuchnir
,
R.
Lange
,
M.
Leenen
,
M.
Liepe
,
L.
Lilje
,
A.
Matheisen
,
W.-D.
Möller
,
A.
Mosnier
,
H.
Padamsee
,
C.
Pagani
,
M.
Pekeler
,
H.-B.
Peters
,
O.
Peters
,
D.
Proch
,
K.
Rehlich
,
D.
Reschke
,
H.
Safa
,
T.
Schilcher
,
P.
Schmüser
,
J.
Sekutowicz
,
S.
Simrock
,
W.
Singer
,
M.
Tigner
,
D.
Trines
,
K.
Twarowski
,
G.
Weichert
,
J.
Weisend
,
J.
Wojtkiewicz
,
S.
Wolff
, and
K.
Zapfe
, “
Superconducting TESLA cavities
,” Phys. Rev. Spec. Top. Accel. Beams
3
, 092001
(2000
).43.
M.
Reagor
,
W.
Pfaff
,
C.
Axline
,
R. W.
Heeres
,
N.
Ofek
,
K.
Sliwa
,
E.
Holland
,
C.
Wang
,
J.
Blumoff
,
K.
Chou
,
M. J.
Hatridge
,
L.
Frunzio
,
M. H.
Devoret
,
L.
Jiang
, and
R. J.
Schoelkopf
, “
Quantum memory with millisecond coherence in circuit QED
,” Phys. Rev. B
94
, 014506
(2016
).44.
C.
Axline
,
M.
Reagor
,
R.
Heeres
,
P.
Reinhold
,
C.
Wang
,
K.
Shain
,
W.
Pfaff
,
Y.
Chu
,
L.
Frunzio
, and
R. J.
Schoelkopf
, “
An architecture for integrating planar and 3D cQED devices
,” Appl. Phys. Lett.
109
, 042601
(2016
).45.
P.
Reinhold
,
S.
Rosenblum
,
W.-L.
Ma
,
L.
Frunzio
,
L.
Jiang
, and
R. J.
Schoelkopf
, “
Error-corrected gates on an encoded qubit
,” Nat. Phys.
16
, 822
(2020
).46.
M.
Kudra
,
J.
Biznárová
,
A.
Fadavi Roudsari
,
J. J.
Burnett
,
D.
Niepce
,
S.
Gasparinetti
,
B.
Wickman
, and
P.
Delsing
, “
High quality three-dimensional aluminum microwave cavities
,” Appl. Phys. Lett.
117
, 070601
(2020
).47.
O.
Milul
,
B.
Guttel
,
U.
Goldblatt
,
S.
Hazanov
,
L. M.
Joshi
,
D.
Chausovsky
,
N.
Kahn
,
E.
Çiftyürek
,
F.
Lafont
, and
S.
Rosenblum
, “
Superconducting cavity qubit with tens of milliseconds single-photon coherence time
,” PRX Quantum
4
, 030336
(2023
).48.
T.
Brecht
,
W.
Pfaff
,
C.
Wang
,
Y.
Chu
,
L.
Frunzio
,
M. H.
Devoret
, and
R. J.
Schoelkopf
, “
Multilayer microwave integrated quantum circuits for scalable quantum computing
,” npj Quantum Inf.
2
(1
), 16002
(2016
).49.
T.
Brecht
,
Y.
Chu
,
C.
Axline
,
W.
Pfaff
,
J. Z.
Blumoff
,
K.
Chou
,
L.
Krayzman
,
L.
Frunzio
, and
R. J.
Schoelkopf
, “
Micromachined integrated quantum circuit containing a superconducting qubit
,” Phys. Rev. Appl.
7
, 044018
(2017
).50.
S.
Chakram
,
A. E.
Oriani
,
R. K.
Naik
,
A. V.
Dixit
,
K.
He
,
A.
Agrawal
,
H.
Kwon
, and
D. I.
Schuster
, “
Seamless high-Q microwave cavities for multimode circuit quantum electrodynamics
,” Phys. Rev. Lett.
127
, 107701
(2021
).51.
A.
Koottandavida
,
I.
Tsioutsios
,
A.
Kargioti
,
C. R.
Smith
,
V. R.
Joshi
,
W.
Dai
,
J. D.
Teoh
,
J. C.
Curtis
,
L.
Frunzio
,
R. J.
Schoelkopf
et al, “
Erasure detection of a dual-rail qubit encoded in a double-post superconducting cavity
,” (2023
).52.
T.
Brecht
,
M.
Reagor
,
Y.
Chu
,
W.
Pfaff
,
C.
Wang
,
L.
Frunzio
,
M. H.
Devoret
, and
R. J.
Schoelkopf
, “
Demonstration of superconducting micromachined cavities
,” Appl. Phys. Lett.
107
, 192603
(2015
).53.
P.
Heidler
,
C. M. F.
Schneider
,
K.
Kustura
,
C.
Gonzalez-Ballestero
,
O.
Romero-Isart
, and
G.
Kirchmair
, “
Non-Markovian effects of two-level systems in a niobium coaxial resonator with a single-photon lifetime of 10 milliseconds
,” Phys. Rev. Appl.
16
, 034024
(2021
).54.
S.
Ganjam
,
Y.
Wang
,
Y.
Lu
,
A.
Banerjee
,
C. U.
Lei
,
L.
Krayzman
,
K.
Kisslinger
,
C.
Zhou
,
R.
Li
,
Y.
Jia
,
M.
Liu
,
L.
Frunzio
, and
R. J.
Schoelkopf
, “
Surpassing millisecond coherence times in on-chip superconducting quantum memories by optimizing materials, processes, and circuit design
,” (2023
).55.
K. D.
Crowley
,
R. A.
McLellan
,
A.
Dutta
,
N.
Shumiya
,
A. P.
Place
,
X. H.
Le
,
Y.
Gang
,
T.
Madhavan
,
M. P.
Bland
,
R.
Chang
et al, “
Disentangling losses in tantalum superconducting circuits
,” Phys. Rev. X
13
, 041005
(2023
).56.
C. U.
Lei
,
S.
Ganjam
,
L.
Krayzman
,
A.
Banerjee
,
K.
Kisslinger
,
S.
Hwang
,
L.
Frunzio
, and
R. J.
Schoelkopf
, “
Characterization of microwave loss using multimode superconducting resonators
,” Phys. Rev. Appl.
20
, 024045
(2023
).57.
M.
Hofheinz
,
H.
Wang
,
M.
Ansmann
,
R. C.
Bialczak
,
E.
Lucero
,
M.
Neeley
,
A. D.
O'Connell
,
D.
Sank
,
J.
Wenner
,
J. M.
Martinis
, and
A. N.
Cleland
, “
Synthesizing arbitrary quantum states in a superconducting resonator
,” Nature
459
, 546
(2009
).58.
P. J.
Leek
,
M.
Baur
,
J. M.
Fink
,
R.
Bianchetti
,
L.
Steffen
,
S.
Filipp
, and
A.
Wallraff
, “
Cavity quantum electrodynamics with separate photon storage and qubit readout modes
,” Phys. Rev. Lett.
104
, 100504
(2010
).59.
M. R.
Vissers
,
J.
Gao
,
D. S.
Wisbey
,
D. A.
Hite
,
C. C.
Tsuei
,
A. D.
Corcoles
,
M.
Steffen
, and
D. P.
Pappas
, “
Low loss superconducting titanium nitride coplanar waveguide resonators
,” Appl. Phys. Lett.
97
, 232509
(2010
).60.
R.
Barends
,
N.
Vercruyssen
,
A.
Endo
,
P. J.
de Visser
,
T.
Zijlstra
,
T. M.
Klapwijk
,
P.
Diener
,
S. J. C.
Yates
, and
J. J. A.
Baselmans
, “
Minimal resonator loss for circuit quantum electrodynamics
,” Appl. Phys. Lett.
97
, 023508
(2010
).61.
L.
Shi
,
T.
Guo
,
R.
Su
,
T.
Chi
,
Y.
Sheng
,
J.
Jiang
,
C.
Cao
,
J.
Wu
,
X.
Tu
,
G.
Sun
,
J.
Chen
, and
P.
Wu
, “
Tantalum microwave resonators with ultra-high intrinsic quality factors
,” Appl. Phys. Lett.
121
, 242601
(2022
).62.
Y.
Ma
,
Y.
Xu
,
X.
Mu
,
W.
Cai
,
L.
Hu
,
W.
Wang
,
X.
Pan
,
H.
Wang
,
Y. P.
Song
,
C.-L.
Zou
, and
L.
Sun
, “
Error-transparent operations on a logical qubit protected by quantum error correction
,” Nat. Phys.
16
, 827
(2020
).63.
D.
Zoepfl
,
P. R.
Muppalla
,
C. M. F.
Schneider
,
S.
Kasemann
,
S.
Partel
, and
G.
Kirchmair
, “
Characterization of low loss microstrip resonators as a building block for circuit QED in a 3D waveguide
,” AIP Adv.
7
, 085118
(2017
).64.
C. U.
Lei
,
L.
Krayzman
,
S.
Ganjam
,
L.
Frunzio
, and
R. J.
Schoelkopf
, “
High coherence superconducting microwave cavities with indium bump bonding
,” Appl. Phys. Lett.
116
, 154002
(2020
).65.
J.
Koch
,
T. M.
Yu
,
J.
Gambetta
,
A. A.
Houck
,
D. I.
Schuster
,
J.
Majer
,
A.
Blais
,
M. H.
Devoret
,
S. M.
Girvin
, and
R. J.
Schoelkopf
, “
Charge-insensitive qubit design derived from the Cooper pair box
,” Phys. Rev. A
76
, 042319
(2007
).66.
S.
Krinner
,
N.
Lacroix
,
A.
Remm
,
A.
Di Paolo
,
E.
Genois
,
C.
Leroux
,
C.
Hellings
,
S.
Lazar
,
F.
Swiadek
,
J.
Herrmann
,
G. J.
Norris
,
C. K.
Andersen
,
M.
Müller
,
A.
Blais
,
C.
Eichler
, and
A.
Wallraff
, “
Realizing repeated quantum error correction in a distance-three surface code
,” Nature
605
, 669
(2022
).67.
F.
Arute
,
K.
Arya
,
R.
Babbush
,
D.
Bacon
,
J. C.
Bardin
,
R.
Barends
,
R.
Biswas
,
S.
Boixo
,
F. G. S. L.
Brandao
,
D. A.
Buell
,
B.
Burkett
,
Y.
Chen
,
Z.
Chen
,
B.
Chiaro
,
R.
Collins
,
W.
Courtney
,
A.
Dunsworth
,
E.
Farhi
,
B.
Foxen
,
A.
Fowler
,
C.
Gidney
,
M.
Giustina
,
R.
Graff
,
K.
Guerin
,
S.
Habegger
,
M. P.
Harrigan
,
M. J.
Hartmann
,
A.
Ho
,
M.
Hoffmann
,
T.
Huang
,
T. S.
Humble
,
S. V.
Isakov
,
E.
Jeffrey
,
Z.
Jiang
,
D.
Kafri
,
K.
Kechedzhi
,
J.
Kelly
,
P. V.
Klimov
,
S.
Knysh
,
A.
Korotkov
,
F.
Kostritsa
,
D.
Landhuis
,
M.
Lindmark
,
E.
Lucero
,
D.
Lyakh
,
S.
Mandrà
,
J. R.
McClean
,
M.
McEwen
,
A.
Megrant
,
X.
Mi
,
K.
Michielsen
,
M.
Mohseni
,
J.
Mutus
,
O.
Naaman
,
M.
Neeley
,
C.
Neill
,
M. Y.
Niu
,
E.
Ostby
,
A.
Petukhov
,
J. C.
Platt
,
C.
Quintana
,
E. G.
Rieffel
,
P.
Roushan
,
N. C.
Rubin
,
D.
Sank
,
K. J.
Satzinger
,
V.
Smelyanskiy
,
K. J.
Sung
,
M. D.
Trevithick
,
A.
Vainsencher
,
B.
Villalonga
,
T.
White
,
Z. J.
Yao
,
P.
Yeh
,
A.
Zalcman
,
H.
Neven
, and
J. M.
Martinis
, “
Quantum supremacy using a programmable superconducting processor
,” Nature
574
, 505
(2019
).68.
Y.
Kim
,
A.
Eddins
,
S.
Anand
,
K. X.
Wei
,
E.
van den Berg
,
S.
Rosenblatt
,
H.
Nayfeh
,
Y.
Wu
,
M.
Zaletel
,
K.
Temme
, and
A.
Kandala
, “
Evidence for the utility of quantum computing before fault tolerance
,” Nature
618
, 500
(2023
).69.
L. G.
Lutterbach
and
L.
Davidovich
, “
Method for direct measurement of the Wigner function in cavity QED and ion traps
,” Phys. Rev. Lett.
78
, 2547
(1997
).70.
D. I.
Schuster
,
A. A.
Houck
,
J. A.
Schreier
,
A.
Wallraff
,
J. M.
Gambetta
,
A.
Blais
,
L.
Frunzio
,
J.
Majer
,
B.
Johnson
,
M. H.
Devoret
,
S. M.
Girvin
, and
R. J.
Schoelkopf
, “
Resolving photon number states in a superconducting circuit
,” Nature
445
, 515
(2007
).71.
S.
Ghosh
,
A.
Opala
,
M.
Matuszewski
,
T.
Paterek
, and
T. C. H.
Liew
, “
Quantum reservoir processing
,” npj Quantum Inf.
5
(1
), 35
(2019
).72.
H.-Y.
Huang
,
R.
Kueng
, and
J.
Preskill
, “
Predicting many properties of a quantum system from very few measurements
,” Nat. Phys.
16
, 1050
(2020
).73.
S.
Krastanov
,
V. V.
Albert
,
C.
Shen
,
C.-L.
Zou
,
R. W.
Heeres
,
B.
Vlastakis
,
R. J.
Schoelkopf
, and
L.
Jiang
, “
Universal control of an oscillator with dispersive coupling to a qubit
,” Phys. Rev. A
92
, 040303(R)
(2015
).74.
A.
Eickbusch
,
V.
Sivak
,
A. Z.
Ding
,
S. S.
Elder
,
S. R.
Jha
,
J.
Venkatraman
,
B.
Royer
,
S. M.
Girvin
,
R. J.
Schoelkopf
, and
M. H.
Devoret
, “
Fast universal control of an oscillator with weak dispersive coupling to a qubit
,” Nat. Phys.
18
, 1464
(2022
).75.
R. W.
Heeres
,
P.
Reinhold
,
N.
Ofek
,
L.
Frunzio
,
L.
Jiang
,
M. H.
Devoret
, and
R. J.
Schoelkopf
, “
Implementing a universal gate set on a logical qubit encoded in an oscillator
,” Nat. Commun.
8
, 94
(2017
).76.
Y.
Zhang
,
B. J.
Lester
,
Y. Y.
Gao
,
L.
Jiang
,
R. J.
Schoelkopf
, and
S. M.
Girvin
, “
Engineering bilinear mode coupling in circuit QED: Theory and experiment
,” Phys. Rev. A
99
, 012314
(2019
).77.
Z.
Leghtas
,
S.
Touzard
,
I. M.
Pop
,
A.
Kou
,
B.
Vlastakis
,
A.
Petrenko
,
K. M.
Sliwa
,
A.
Narla
,
S.
Shankar
,
M. J.
Hatridge
,
M.
Reagor
,
L.
Frunzio
,
R. J.
Schoelkopf
,
M.
Mirrahimi
, and
M. H.
Devoret
, “
Confining the state of light to a quantum manifold by engineered two-photon loss
,” Science
347
, 853
(2015
).78.
L.
Bretheau
,
P.
Campagne-Ibarcq
,
E.
Flurin
,
F.
Mallet
, and
B.
Huard
, “
Quantum dynamics of an electromagnetic mode that cannot contain N photons
,” Science
348
, 776
(2015
).79.
Y. Y.
Gao
,
B. J.
Lester
,
Y.
Zhang
,
C.
Wang
,
S.
Rosenblum
,
L.
Frunzio
,
L.
Jiang
,
S. M.
Girvin
, and
R. J.
Schoelkopf
, “
Programmable interference between two microwave quantum memories
,” Phys. Rev. X
8
, 021073
(2018
).80.
C.
Wang
,
C.
Axline
,
Y. Y.
Gao
,
T.
Brecht
,
Y.
Chu
,
L.
Frunzio
,
M. H.
Devoret
, and
R. J.
Schoelkopf
, “
Surface participation and dielectric loss in superconducting qubits
,” Appl. Phys. Lett.
107
, 162601
(2015
).81.
X. Y.
Jin
,
A.
Kamal
,
A. P.
Sears
,
T.
Gudmundsen
,
D.
Hover
,
J.
Miloshi
,
R.
Slattery
,
F.
Yan
,
J.
Yoder
,
T. P.
Orlando
,
S.
Gustavsson
, and
W. D.
Oliver
, “
Thermal and residual excited-state population in a 3D transmon qubit
,” Phys. Rev. Lett.
114
, 240501
(2015
).82.
M.
Spiecker
,
P.
Paluch
,
N.
Gosling
,
N.
Drucker
,
S.
Matityahu
,
D.
Gusenkova
,
S.
Günzler
,
D.
Rieger
,
I.
Takmakov
,
F.
Valenti
,
P.
Winkel
,
R.
Gebauer
,
O.
Sander
,
G.
Catelani
,
A.
Shnirman
,
A. V.
Ustinov
,
W.
Wernsdorfer
,
Y.
Cohen
, and
I. M.
Pop
, “
Two-level system hyperpolarization using a quantum Szilard engine
,” Nat. Phys.
19
, 1320
(2023
).83.
D.
Willsch
,
D.
Rieger
,
P.
Winkel
,
M.
Willsch
,
C.
Dickel
,
J.
Krause
,
Y.
Ando
,
R.
Lescanne
,
Z.
Leghtas
,
N. T.
Bronn
,
P.
Deb
,
O.
Lanes
,
Z. K.
Minev
,
B.
Dennig
,
S.
Geisert
,
S.
Günzler
,
S.
Ihssen
,
P.
Paluch
,
T.
Reisinger
,
R.
Hanna
,
J. H.
Bae
,
P.
Schüffelgen
,
D.
Grützmacher
,
L.
Buimaga-Iarinca
,
C.
Morari
,
W.
Wernsdorfer
,
D. P.
DiVincenzo
,
K.
Michielsen
,
G.
Catelani
, and
I. M.
Pop
, “
Observation of Josephson harmonics in tunnel junctions
,” (2023
).84.
X.
Pan
,
J.
Schwinger
,
N.-N.
Huang
,
P.
Song
,
W.
Chua
,
F.
Hanamura
,
A.
Joshi
,
F.
Valadares
,
R.
Filip
, and
Y. Y.
Gao
, “
Protecting the quantum interference of cat states by phase-space compression
,” Phys. Rev. X
13
, 021004
(2023
).85.
V. V.
Sivak
,
A.
Eickbusch
,
B.
Royer
,
S.
Singh
,
I.
Tsioutsios
,
S.
Ganjam
,
A.
Miano
,
B. L.
Brock
,
A. Z.
Ding
,
L.
Frunzio
,
S. M.
Girvin
,
R. J.
Schoelkopf
, and
M. H.
Devoret
, “
Real-time quantum error correction beyond break-even
,” Nature
616
, 50
(2023
).86.
N. E.
Frattini
,
U.
Vool
,
S.
Shankar
,
A.
Narla
,
K. M.
Sliwa
, and
M. H.
Devoret
, “
3-wave mixing Josephson dipole element
,” Appl. Phys. Lett.
110
, 222603
(2017
).87.
T.
Hillmann
,
F.
Quijandría
,
G.
Johansson
,
A.
Ferraro
,
S.
Gasparinetti
, and
G.
Ferrini
, “
Universal gate set for continuous-variable quantum computation with microwave circuits
,” Phys. Rev. Lett.
125
, 160501
(2020
).88.
B. J.
Chapman
,
S. J.
de Graaf
,
S. H.
Xue
,
Y.
Zhang
,
J.
Teoh
,
J. C.
Curtis
,
T.
Tsunoda
,
A.
Eickbusch
,
A. P.
Read
,
A.
Koottandavida
,
S. O.
Mundhada
,
L.
Frunzio
,
M.
Devoret
,
S.
Girvin
, and
R.
Schoelkopf
, “
High-on-off-ratio beam-splitter interaction for gates on bosonically encoded qubits
,” PRX Quantum
4
, 020355
(2023
).89.
A.
Gyenis
,
A.
Di Paolo
,
J.
Koch
,
A.
Blais
,
A. A.
Houck
, and
D. I.
Schuster
, “
Moving beyond the transmon: Noise-protected superconducting quantum circuits
,” PRX Quantum
2
, 030101
(2021
).90.
S. E.
Rasmussen
,
K. S.
Christensen
,
S. P.
Pedersen
,
L. B.
Kristensen
,
T.
Baekkegaard
,
N. J. X.
Loft
, and
N. T.
Zinner
, “
Superconducting circuit companion—An introduction with worked examples
,” PRX Quantum
2
, 040204
(2021
).91.
F.
Valadares
,
N.-N.
Huang
,
K.
Chu
,
A.
Dorogov
,
W.
Chua
,
K.
Lingda
,
P.
Song
, and
Y. Y.
Gao
, “
On-demand transposition across light-matter interaction regimes in bosonic CQED
,” (2023
).92.
O.
Gargiulo
,
S.
Oleschko
,
J.
Prat-Camps
,
M.
Zanner
, and
G.
Kirchmair
, “
Fast flux control of 3D transmon qubits using a magnetic hose
,” Appl. Phys. Lett.
118
, 012601
(2021
).93.
Y.
Lu
,
A.
Maiti
,
J. W. O.
Garmon
,
S.
Ganjam
,
Y.
Zhang
,
J.
Claes
,
L.
Frunzio
,
S. M.
Girvin
, and
R. J.
Schoelkopf
, “
High-fidelity parametric beamsplitting with a parity-protected converter
,” Nat. Commun.
14
, 5767
(2023
).94.
P.
Groszkowski
and
J.
Koch
, “
Scqubits: A Python package for superconducting qubits
,” Quantum
5
, 583
(2021
).95.
A.
Miano
,
V. R.
Joshi
,
G.
Liu
,
W.
Dai
,
P. D.
Parakh
,
L.
Frunzio
, and
M. H.
Devoret
, “
Hamiltonian extrema of an arbitrary flux-biased Josephson circuit
,” PRX Quantum
4
, 030324
(2023
).96.
D.
Gottesman
,
A.
Kitaev
, and
J.
Preskill
, “
Encoding a qubit in an oscillator
,” Phys. Rev. A
64
, 012310
(2001
).97.
P.
Campagne-Ibarcq
,
A.
Eickbusch
,
S.
Touzard
,
E.
Zalys-Geller
,
N. E.
Frattini
,
V. V.
Sivak
,
P.
Reinhold
,
S.
Puri
,
S.
Shankar
,
R. J.
Schoelkopf
,
L.
Frunzio
,
M.
Mirrahimi
, and
M. H.
Devoret
, “
Quantum error correction of a qubit encoded in grid states of an oscillator
,” Nature
584
, 368
(2020
).98.
M. H.
Michael
,
M.
Silveri
,
R. T.
Brierley
,
V. V.
Albert
,
J.
Salmilehto
,
L.
Jiang
, and
S. M.
Girvin
, “
New class of quantum error-correcting codes for a bosonic mode
,” Phys. Rev. X
6
, 031006
(2016
).99.
L.
Hu
,
Y.
Ma
,
W.
Cai
,
X.
Mu
,
Y.
Xu
,
W.
Wang
,
Y.
Wu
,
H.
Wang
,
Y. P.
Song
,
C.-L.
Zou
,
S. M.
Girvin
,
L.-M.
Duan
, and
L.
Sun
, “
Quantum error correction and universal gate set operation on a binomial bosonic logical qubit
,” Nat. Phys.
15
, 503
(2019
).100.
Z.
Leghtas
,
G.
Kirchmair
,
B.
Vlastakis
,
R. J.
Schoelkopf
,
M. H.
Devoret
, and
M.
Mirrahimi
, “
Hardware-efficient autonomous quantum memory protection
,” Phys. Rev. Lett.
111
, 120501
(2013
).101.
N.
Ofek
,
A.
Petrenko
,
R.
Heeres
,
P.
Reinhold
,
Z.
Leghtas
,
B.
Vlastakis
,
Y.
Liu
,
L.
Frunzio
,
S. M.
Girvin
,
L.
Jiang
,
M.
Mirrahimi
,
M. H.
Devoret
, and
R. J.
Schoelkopf
, “
Extending the lifetime of a quantum bit with error correction in superconducting circuits
,” Nature
536
, 441
(2016
).102.
J. M.
Gertler
,
B.
Baker
,
J.
Li
,
S.
Shirol
,
J.
Koch
, and
C.
Wang
, “
Protecting a bosonic qubit with autonomous quantum error correction
,” Nature
590
, 243
(2021
).103.
Z.
Ni
,
S.
Li
,
X.
Deng
,
Y.
Cai
,
L.
Zhang
,
W.
Wang
,
Z.-B.
Yang
,
H.
Yu
,
F.
Yan
,
S.
Liu
,
C.-L.
Zou
,
L.
Sun
,
S.-B.
Zheng
,
Y.
Xu
, and
D.
Yu
, “
Beating the break-even point with a discrete-variable-encoded logical qubit
,” Nature
616
, 56
(2023
).104.
S.
Puri
,
L.
St-Jean
,
J. A.
Gross
,
A.
Grimm
,
N. E.
Frattini
,
P. S.
Iyer
,
A.
Krishna
,
S.
Touzard
,
L.
Jiang
,
A.
Blais
,
S. T.
Flammia
, and
S. M.
Girvin
, “
Bias-preserving gates with stabilized cat qubits
,” Sci. Adv.
6
, eaay5901
(2020
).105.
A.
Grimm
,
N. E.
Frattini
,
S.
Puri
,
S. O.
Mundhada
,
S.
Touzard
,
M.
Mirrahimi
,
S. M.
Girvin
,
S.
Shankar
, and
M. H.
Devoret
, “
Stabilization and operation of a Kerr-cat qubit
,” Nature
584
, 205
(2020
).106.
R.
Lescanne
,
M.
Villiers
,
T.
Peronnin
,
A.
Sarlette
,
M.
Delbecq
,
B.
Huard
,
T.
Kontos
,
M.
Mirrahimi
, and
Z.
Leghtas
, “
Exponential suppression of bit-flips in a qubit encoded in an oscillator
,” Nat. Phys.
16
, 509
(2020
).107.
C.
Berdou
,
A.
Murani
,
U.
Réglade
,
W.
Smith
,
M.
Villiers
,
J.
Palomo
,
M.
Rosticher
,
A.
Denis
,
P.
Morfin
,
M.
Delbecq
,
T.
Kontos
,
N.
Pankratova
,
F.
Rautschke
,
T.
Peronnin
,
L.-A.
Sellem
,
P.
Rouchon
,
A.
Sarlette
,
M.
Mirrahimi
,
P.
Campagne-Ibarcq
,
S.
Jezouin
,
R.
Lescanne
, and
Z.
Leghtas
, “
One hundred second bit-flip time in a two-photon dissipative oscillator
,” PRX Quantum
4
, 020350
(2023
).108.
A. Yu.
Kitaev
, “
Fault-tolerant quantum computation by anyons
,” Ann. Phys.
303
, 2
(2003
).109.
C.
Chamberland
,
K.
Noh
,
P.
Arrangoiz-Arriola
,
E. T.
Campbell
,
C. T.
Hann
,
J.
Iverson
,
H.
Putterman
,
T. C.
Bohdanowicz
,
S. T.
Flammia
,
A.
Keller
,
G.
Refael
,
J.
Preskill
,
L.
Jiang
,
A. H.
Safavi-Naeini
,
O.
Painter
, and
F. G. L.
Brandão
, “
Building a fault-tolerant quantum computer using concatenated cat codes
,” PRX Quantum
3
, 010329
(2022
).110.
F.-M. L.
Régent
,
C.
Berdou
,
Z.
Leghtas
,
J.
Guillaud
, and
M.
Mirrahimi
, “
High-performance repetition cat code using fast noisy operation
,” Quantum
7
, 1198
(2023
).111.
K. S.
Chou
,
T.
Shemma
,
H.
McCarrick
,
T.-C.
Chien
,
J. D.
Teoh
,
P.
Winkel
,
A.
Anderson
,
J.
Chen
,
J.
Curtis
,
S. J.
de Graaf
,
J. W. O.
Garmon
,
B.
Gudlewski
,
W. D.
Kalfus
,
T.
Keen
,
N.
Khedkar
,
C. U.
Lei
,
G.
Liu
,
P.
Lu
,
Y.
Lu
,
A.
Maiti
,
L.
Mastalli-Kelly
,
N.
Mehta
,
S. O.
Mundhada
,
A.
Narla
,
T.
Noh
,
T.
Tsunoda
,
S. H.
Xue
,
J. O.
Yuan
,
L.
Frunzio
,
J.
Aumentado
,
S.
Puri
,
S. M.
Girvin
,
J.
Moseley
, and
R. J.
Schoelkopf
, “
Demonstrating a superconducting dual-rail cavity qubit with erasure-detected logical measurements
,” arXiv:org/abs/2307.03169v3 (2023
).112.
J. D.
Teoh
,
P.
Winkel
,
H. K.
Babla
,
B. J.
Chapman
,
J.
Claes
,
S. J.
de Graaf
,
J. W. O.
Garmon
,
W. D.
Kalfus
,
Y.
Lu
,
A.
Maiti
,
K.
Sahay
,
N.
Thakur
,
T.
Tsunoda
,
S. H.
Xue
,
L.
Frunzio
,
S. M.
Girvin
,
S.
Puri
, and
R. J.
Schoelkopf
, “
Dual-rail encoding with superconducting cavities
,” Proc. Natl. Acad. Sci. U. S. A.
120
, e2221736120
(2023
).113.
J. M.
Gertler
,
S.
van Geldern
,
S.
Shirol
,
L.
Jiang
, and
C.
Wang
, “
Experimental realization and characterization of stabilized pair-coherent states
,” PRX Quantum
4
, 020319
(2023
).114.
J.
Sahota
and
N.
Quesada
, “
Quantum correlations in optical metrology: Heisenberg-limited phase estimation without mode entanglement
,” Phys. Rev. A
91
, 013808
(2015
).115.
J.
Abadie
,
B. P.
Abbott
,
R.
Abbott
,
T. D.
Abbott
,
M.
Abernathy
,
C.
Adams
,
R.
Adhikari
,
C.
Affeldt
,
B.
Allen
,
G. S.
Allen
,
E.
Amador Ceron
,
D.
Amariutei
,
R. S.
Amin
,
S. B.
Anderson
,
W. G.
Anderson
,
K.
Arai
,
M. A.
Arain
,
M. C.
Araya
,
S. M.
Aston
,
D.
Atkinson
,
P.
Aufmuth
,
C.
Aulbert
,
B. E.
Aylott
,
S.
Babak
,
P.
Baker
,
S.
Ballmer
,
D.
Barker
,
B.
Barr
,
P.
Barriga
,
L.
Barsotti
,
M. A.
Barton
,
I.
Bartos
,
R.
Bassiri
,
M.
Bastarrika
,
J.
Batch
,
J.
Bauchrowitz
,
B.
Behnke
,
A. S.
Bell
,
I.
Belopolski
,
M.
Benacquista
,
J. M.
Berliner
,
A.
Bertolini
,
J.
Betzwieser
,
N.
Beveridge
,
P. T.
Beyersdorf
,
I. A.
Bilenko
,
G.
Billingsley
,
J.
Birch
,
R.
Biswas
,
E.
Black
,
J. K.
Blackburn
,
L.
Blackburn
,
D.
Blair
,
B.
Bland
,
O.
Bock
,
T. P.
Bodiya
,
C.
Bogan
,
R.
Bondarescu
,
R.
Bork
,
M.
Born
,
S.
Bose
,
P. R.
Brady
,
V. B.
Braginsky
,
J. E.
Brau
,
J.
Breyer
,
D. O.
Bridges
,
M.
Brinkmann
,
M.
Britzger
,
A. F.
Brooks
,
D. A.
Brown
,
A.
Brummitt
,
A.
Buonanno
,
J.
Burguet-Castell
,
O.
Burmeister
,
R. L.
Byer
,
L.
Cadonati
,
J. B.
Camp
,
P.
Campsie
,
J.
Cannizzo
,
K.
Cannon
,
J.
Cao
,
C. D.
Capano
,
S.
Caride
,
S.
Caudill
,
M.
Cavagliá
,
C.
Cepeda
,
T.
Chalermsongsak
,
E.
Chalkley
,
P.
Charlton
,
S.
Chelkowski
,
Y.
Chen
,
N.
Christensen
,
H.
Cho
,
S. S. Y.
Chua
,
S.
Chung
,
C. T. Y.
Chung
,
G.
Ciani
,
F.
Clara
,
D. E.
Clark
,
J.
Clark
,
J. H.
Clayton
,
R.
Conte
,
D.
Cook
,
T. R.
Corbitt
,
M.
Cordier
,
N.
Cornish
,
A.
Corsi
,
C. A.
Costa
,
M.
Coughlin
,
P.
Couvares
,
D. M.
Coward
,
D. C.
Coyne
,
J. D. E.
Creighton
,
T. D.
Creighton
,
A. M.
Cruise
,
A.
Cumming
,
L.
Cunningham
,
R. M.
Cutler
,
K.
Dahl
,
S. L.
Danilishin
,
R.
Dannenberg
,
K.
Danzmann
,
B.
Daudert
,
H.
Daveloza
,
G.
Davies
,
E. J.
Daw
,
T.
Dayanga
,
D.
DeBra
,
J.
Degallaix
,
T.
Dent
,
V.
Dergachev
,
R.
DeRosa
,
R.
DeSalvo
,
S.
Dhurandhar
,
J.
DiGuglielmo
,
I.
Di Palma
,
M.
Díaz
,
F.
Donovan
,
K. L.
Dooley
,
S.
Dorsher
,
R. W. P.
Drever
,
J. C.
Driggers
,
Z.
Du
,
J.-C.
Dumas
,
S.
Dwyer
,
T.
Eberle
,
M.
Edgar
,
M.
Edwards
,
A.
Effler
,
P.
Ehrens
,
R.
Engel
,
T.
Etzel
,
K.
Evans
,
M.
Evans
,
T.
Evans
,
M.
Factourovich
,
S.
Fairhurst
,
Y.
Fan
,
B. F.
Farr
,
W.
Farr
,
D.
Fazi
,
H.
Fehrmann
,
D.
Feldbaum
,
L. S.
Finn
,
R. P.
Fisher
,
M.
Flanigan
,
S.
Foley
,
E.
Forsi
,
N.
Fotopoulos
,
M.
Frede
,
M.
Frei
,
Z.
Frei
,
A.
Freise
,
R.
Frey
,
T. T.
Fricke
,
D.
Friedrich
,
P.
Fritschel
,
V. V.
Frolov
,
P. J.
Fulda
,
M.
Fyffe
,
M. R.
Ganija
,
J.
Garcia
,
J. A.
Garofoli
,
R.
Geng
,
L. Á.
Gergely
,
I.
Gholami
,
S.
Ghosh
,
J. A.
Giaime
,
S.
Giampanis
,
K. D.
Giardina
,
C.
Gill
,
E.
Goetz
,
L. M.
Goggin
,
G.
González
,
M. L.
Gorodetsky
,
S.
Goßler
,
C.
Graef
,
A.
Grant
,
S.
Gras
,
C.
Gray
,
N.
Gray
,
R. J. S.
Greenhalgh
,
A. M.
Gretarsson
,
R.
Grosso
,
H.
Grote
,
S.
Grunewald
,
C.
Guido
,
R.
Gupta
,
E. K.
Gustafson
,
R.
Gustafson
,
T.
Ha
,
B.
Hage
,
J. M.
Hallam
,
D.
Hammer
,
G.
Hammond
,
J.
Hanks
,
C.
Hanna
,
J.
Hanson
,
J.
Harms
,
G. M.
Harry
,
I. W.
Harry
,
E. D.
Harstad
,
M. T.
Hartman
,
K.
Haughian
,
K.
Hayama
,
J.
Heefner
,
M. C.
Heintze
,
M. A.
Hendry
,
I. S.
Heng
,
A. W.
Heptonstall
,
V.
Herrera
,
M.
Hewitson
,
S.
Hild
,
D.
Hoak
,
K. A.
Hodge
,
K.
Holt
,
T.
Hong
,
S.
Hooper
,
D. J.
Hosken
,
J.
Hough
,
E. J.
Howell
,
B.
Hughey
,
T.
Huynh-Dinh
,
S.
Husa
,
S. H.
Huttner
,
D. R.
Ingram
,
R.
Inta
,
T.
Isogai
,
A.
Ivanov
,
K.
Izumi
,
M.
Jacobson
,
H.
Jang
,
W. W.
Johnson
,
D. I.
Jones
,
G.
Jones
,
R.
Jones
,
L.
Ju
,
P.
Kalmus
,
V.
Kalogera
,
I.
Kamaretsos
,
S.
Kandhasamy
,
G.
Kang
,
J. B.
Kanner
,
E.
Katsavounidis
,
W.
Katzman
,
H.
Kaufer
,
K.
Kawabe
,
S.
Kawamura
,
F.
Kawazoe
,
W.
Kells
,
D. G.
Keppel
,
Z.
Keresztes
,
A.
Khalaidovski
,
F. Y.
Khalili
,
E. A.
Khazanov
,
B.
Kim
,
C.
Kim
,
D.
Kim
,
H.
Kim
,
K.
Kim
,
N.
Kim
,
Y.-M.
Kim
,
P. J.
King
,
M.
Kinsey
,
D. L.
Kinzel
,
J. S.
Kissel
,
S.
Klimenko
,
K.
Kokeyama
,
V.
Kondrashov
,
R.
Kopparapu
,
S.
Koranda
,
W. Z.
Korth
,
D.
Kozak
,
V.
Kringel
,
S.
Krishnamurthy
,
B.
Krishnan
,
G.
Kuehn
,
R.
Kumar
,
P.
Kwee
, and LIGO Scientific Collaboration
, “
A gravitational wave observatory operating beyond the quantum shot-noise limit
,” Nat. Phys.
7
, 962
(2011
).116.
S.
Danilin
,
A. V.
Lebedev
,
A.
Vepsäläinen
,
G. B.
Lesovik
,
G.
Blatter
, and
G. S.
Paraoanu
, “
Quantum-enhanced magnetometry by phase estimation algorithms with a single artificial atom
,” npj Quantum Inf.
4
(1
), 29
(2018
).117.
W.
Wang
,
Y.
Wu
,
Y.
Ma
,
W.
Cai
,
L.
Hu
,
X.
Mu
,
Y.
Xu
,
Z.-J.
Chen
,
H.
Wang
,
Y. P.
Song
,
H.
Yuan
,
C.-L.
Zou
,
L.-M.
Duan
, and
L.
Sun
, “
Heisenberg-limited single-mode quantum metrology in a superconducting circuit
,” Nat. Commun.
10
, 4382
(2019
).118.
M.
Penasa
,
S.
Gerlich
,
T.
Rybarczyk
,
V.
Métillon
,
M.
Brune
,
J. M.
Raimond
,
S.
Haroche
,
L.
Davidovich
, and
I.
Dotsenko
, “
Measurement of a microwave field amplitude beyond the standard quantum limit
,” Phys. Rev. A
94
, 022313
(2016
).119.
W. J.
Munro
,
K.
Nemoto
,
G. J.
Milburn
, and
S. L.
Braunstein
, “
Weak-force detection with superposed coherent states
,” Phys. Rev. A
66
, 023819
(2002
).120.
K.
Duivenvoorden
,
B. M.
Terhal
, and
D.
Weigand
, “
Single-mode displacement sensor
,” Phys. Rev. A
95
, 012305
(2017
).121.
J.
Braumüller
,
M.
Marthaler
,
A.
Schneider
,
A.
Stehli
,
H.
Rotzinger
,
M.
Weides
, and
A. V.
Ustinov
, “
Analog quantum simulation of the Rabi model in the ultra-strong coupling regime
,” Nat. Commun.
8
, 779
(2017
).122.
C. S.
Wang
,
J. C.
Curtis
,
B. J.
Lester
,
Y.
Zhang
,
Y. Y.
Gao
,
J.
Freeze
,
V. S.
Batista
,
P. H.
Vaccaro
,
I. L.
Chuang
,
L.
Frunzio
,
L.
Jiang
,
S. M.
Girvin
, and
R. J.
Schoelkopf
, “
Efficient multiphoton sampling of molecular vibronic spectra on a superconducting bosonic processor
,” Phys. Rev. X
10
, 021060
(2020
).123.
L.
Hu
,
Y.-C.
Ma
,
Y.
Xu
,
W.-T.
Wang
,
Y.-W.
Ma
,
K.
Liu
,
H.-Y.
Wang
,
Y.-P.
Song
,
M.-H.
Yung
, and
L.-Y.
Sun
, “
Simulation of molecular spectroscopy with circuit quantum electrodynamics
,” Sci. Bull.
63
, 293
(2018
).124.
A. A.
Houck
,
H. E.
Türeci
, and
J.
Koch
, “
On-chip quantum simulation with superconducting circuits
,” Nat. Phys.
8
, 292
(2012
).125.
A.
Kurcz
,
A.
Bermudez
, and
J. J.
García-Ripoll
, “
Hybrid quantum magnetism in circuit QED: From spin-photon waves to many-body spectroscopy
,” Phys. Rev. Lett.
112
, 180405
(2014
).126.
C. S.
Wang
,
N. E.
Frattini
,
B. J.
Chapman
,
S.
Puri
,
S. M.
Girvin
,
M. H.
Devoret
, and
R. J.
Schoelkopf
, “
Observation of wave-packet branching through an engineered conical intersection
,” Phys. Rev. X
13
, 011008
(2023
).127.
S.
Rosenblum
,
Y. Y.
Gao
,
P.
Reinhold
,
C.
Wang
,
C. J.
Axline
,
L.
Frunzio
,
S. M.
Girvin
,
L.
Jiang
,
M.
Mirrahimi
,
M. H.
Devoret
, and
R. J.
Schoelkopf
, “
A CNOT gate between multiphoton qubits encoded in two cavities
,” Nat. Commun.
9
, 652
(2018
).128.
S. K.
Lamoreaux
,
K. A.
van Bibber
,
K. W.
Lehnert
, and
G.
Carosi
, “
Analysis of single-photon and linear amplifier detectors for microwave cavity dark matter axion searches
,” Phys. Rev. D
88
, 035020
(2013
).129.
B. M.
Brubaker
,
L.
Zhong
,
Y. V.
Gurevich
,
S. B.
Cahn
,
S. K.
Lamoreaux
,
M.
Simanovskaia
,
J. R.
Root
,
S. M.
Lewis
,
S.
Al Kenany
,
K. M.
Backes
,
I.
Urdinaran
,
N. M.
Rapidis
,
T. M.
Shokair
,
K. A.
van Bibber
,
D. A.
Palken
,
M.
Malnou
,
W. F.
Kindel
,
M. A.
Anil
,
K. W.
Lehnert
, and
G.
Carosi
, “
First results from a microwave cavity axion search at 24 μeV
,” Phys. Rev. Lett.
118
, 061302
(2017
).130.
D.
Gross
,
A.
Sevrin
, and
P.
Zoller
, “The Physics of Quantum Information
” (
World Scientific
, 2023
).131.
J.
Buolamwini
and
T.
Gebru
, “
Gender Shades: Intersectional accuracy disparities in commercial gender classification
,” in Proceedings of the 1st Conference on Fairness, Accountability and Transparency
[Proc. Mach. Learn. Res.
81
, 77–91 (2018)].132.
E.
Beaunoyer
,
S.
Dupéré
, and
M. J.
Guitton
, “
COVID-19 and digital inequalities: Reciprocal impacts and mitigation strategies
,” Comput. Human Behav.
111
, 106424
(2020
).133.
O. W.
Johnson
,
J. Y.-C.
Han
,
A.-L.
Knight
,
S.
Mortensen
,
M. T.
Aung
,
M.
Boyland
, and
B. P.
Resurrección
, “
Intersectionality and energy transitions: A review of gender, social equity and low-carbon energy
,” Energy Res. Social Sci.
70
, 101774
(2020
).134.
K.
Crenshaw
, Demarginalizing The Intersection of Race and Sex: A Black Feminist Critique of Antidiscrimination Doctrine, Feminist Theory and Antiracist Politics
(
University of Chicago Legal Forum
, 1989
).135.
Y.
Zheng
and
G.
Walsham
, “
Inequality of what? An intersectional approach to digital inequality under Covid-19
,” Inf. Org.
31
, 100341
(2021
).136.
R.
de Wolf
, “
The potential impact of quantum computers on society
,” Ethics Inf. Technol.
19
, 271
(2017
).137.
C.
Ten Holter
,
P.
Inglesant
, and
M.
Jirotka
, “
Reading the road: Challenges and opportunities on the path to responsible innovation in quantum computing
,” Technol. Anal. Strategic Manage.
35
, 844
(2023
).138.
D. P.
DiVincenzo
, “
Scientists and citizens: Getting to quantum technologies
,” Ethics Inf. Technol.
19
, 247
(2017
).139.
R. B.
Freeman
and
W.
Huang
, “
Collaborating with People Like Me: Ethnic Coauthorship within the United States
,” J. Labor Econ.
33
, S289
(2015
).140.
B. K.
AlShebli
,
T.
Rahwan
, and
W. L.
Woon
, “
The preeminence of ethnic diversity in scientific collaboration
,” Nat. Commun.
9
, 5163
(2018
).141.
B.
Hofstra
,
V. V.
Kulkarni
,
S.
Munoz-Najar Galvez
,
B.
He
,
D.
Jurafsky
, and
D. A.
McFarland
, “
The diversity–innovation paradox in science
,” Proc. Natl. Acad. Sci. U. S. A.
117
, 9284
(2020
).142.
Z. C.
Seskir
,
S.
Umbrello
,
C.
Coenen
, and
P. E.
Vermaas
, “
Democratization of quantum technologies
,” Quantum Sci. Technol.
8
, 024005
(2023
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
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