Evidence for the utility of quantum computing before fault tolerance

Quantum computing promises to offer substantial speed-ups over its classical counterpart for certain problems. However, the greatest impediment to realizing its full potential is noise that is inherent to these systems. The widely accepted solution to this challenge is the implementation of fault-to...

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Published inNature (London) Vol. 618; no. 7965; pp. 500 - 505
Main Authors Kim, Youngseok, Eddins, Andrew, Anand, Sajant, Wei, Ken Xuan, van den Berg, Ewout, Rosenblatt, Sami, Nayfeh, Hasan, Wu, Yantao, Zaletel, Michael, Temme, Kristan, Kandala, Abhinav
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LanguageEnglish
Published London Nature Publishing Group UK 15.06.2023
Nature Publishing Group
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Abstract Quantum computing promises to offer substantial speed-ups over its classical counterpart for certain problems. However, the greatest impediment to realizing its full potential is noise that is inherent to these systems. The widely accepted solution to this challenge is the implementation of fault-tolerant quantum circuits, which is out of reach for current processors. Here we report experiments on a noisy 127-qubit processor and demonstrate the measurement of accurate expectation values for circuit volumes at a scale beyond brute-force classical computation. We argue that this represents evidence for the utility of quantum computing in a pre-fault-tolerant era. These experimental results are enabled by advances in the coherence and calibration of a superconducting processor at this scale and the ability to characterize 1 and controllably manipulate noise across such a large device. We establish the accuracy of the measured expectation values by comparing them with the output of exactly verifiable circuits. In the regime of strong entanglement, the quantum computer provides correct results for which leading classical approximations such as pure-state-based 1D (matrix product states, MPS) and 2D (isometric tensor network states, isoTNS) tensor network methods 2 , 3 break down. These experiments demonstrate a foundational tool for the realization of near-term quantum applications 4 , 5 . Experiments on a noisy 127-qubit superconducting quantum processor report the accurate measurement of expectation values beyond the reach of current brute-force classical computation, demonstrating evidence for the utility of quantum computing before fault tolerance.
AbstractList Quantum computing promises to offer substantial speed-ups over its classical counterpart for certain problems. However, the greatest impediment to realizing its full potential is noise that is inherent to these systems. The widely accepted solution to this challenge is the implementation of fault-tolerant quantum circuits, which is out of reach for current processors. Here we report experiments on a noisy 127-qubit processor and demonstrate the measurement of accurate expectation values for circuit volumes at a scale beyond brute-force classical computation. We argue that this represents evidence for the utility of quantum computing in a pre-fault-tolerant era. These experimental results are enabled by advances in the coherence and calibration of a superconducting processor at this scale and the ability to characterize 1 and controllably manipulate noise across such a large device. We establish the accuracy of the measured expectation values by comparing them with the output of exactly verifiable circuits. In the regime of strong entanglement, the quantum computer provides correct results for which leading classical approximations such as pure-state-based 1D (matrix product states, MPS) and 2D (isometric tensor network states, isoTNS) tensor network methods 2,3 break down. These experiments demonstrate a foundational tool for the realization of near-term quantum applications 4,5 .
Quantum computing promises to offer substantial speed-ups over its classical counterpart for certain problems. However, the greatest impediment to realizing its full potential is noise that is inherent to these systems. The widely accepted solution to this challenge is the implementation of fault-tolerant quantum circuits, which is out of reach for current processors. Here we report experiments on a noisy 127-qubit processor and demonstrate the measurement of accurate expectation values for circuit volumes at a scale beyond brute-force classical computation. We argue that this represents evidence for the utility of quantum computing in a pre-fault-tolerant era. These experimental results are enabled by advances in the coherence and calibration of a superconducting processor at this scale and the ability to characterize 1 and controllably manipulate noise across such a large device. We establish the accuracy of the measured expectation values by comparing them with the output of exactly verifiable circuits. In the regime of strong entanglement, the quantum computer provides correct results for which leading classical approximations such as pure-state-based 1D (matrix product states, MPS) and 2D (isometric tensor network states, isoTNS) tensor network methods 2 , 3 break down. These experiments demonstrate a foundational tool for the realization of near-term quantum applications 4 , 5 . Experiments on a noisy 127-qubit superconducting quantum processor report the accurate measurement of expectation values beyond the reach of current brute-force classical computation, demonstrating evidence for the utility of quantum computing before fault tolerance.
Quantum computing promises to offer substantial speed-ups over its classical counterpart for certain problems. However, the greatest impediment to realizing its full potential is noise that is inherent to these systems. The widely accepted solution to this challenge is the implementation of fault-tolerant quantum circuits, which is out of reach for current processors. Here we report experiments on a noisy 127-qubit processor and demonstrate the measurement of accurate expectation values for circuit volumes at a scale beyond brute-force classical computation. We argue that this represents evidence for the utility of quantum computing in a pre-fault-tolerant era. These experimental results are enabled by advances in the coherence and calibration of a superconducting processor at this scale and the ability to characterize and controllably manipulate noise across such a large device. We establish the accuracy of the measured expectation values by comparing them with the output of exactly verifiable circuits. In the regime of strong entanglement, the quantum computer provides correct results for which leading classical approximations such as pure-state-based 1D (matrix product states, MPS) and 2D (isometric tensor network states, isoTNS) tensor network methods break down. These experiments demonstrate a foundational tool for the realization of near-term quantum applications.
Quantum computing promises to offer substantial speed-ups over its classical counterpart for certain problems. However, the greatest impediment to realizing its full potential is noise that is inherent to these systems. The widely accepted solution to this challenge is the implementation of fault-tolerant quantum circuits, which is out of reach for current processors. Here we report experiments on a noisy 127-qubit processor and demonstrate the measurement of accurate expectation values for circuit volumes at a scale beyond brute-force classical computation. We argue that this represents evidence for the utility of quantum computing in a pre-fault-tolerant era. These experimental results are enabled by advances in the coherence and calibration of a superconducting processor at this scale and the ability to characterize1 and controllably manipulate noise across such a large device. We establish the accuracy of the measured expectation values by comparing them with the output of exactly verifiable circuits. In the regime of strong entanglement, the quantum computer provides correct results for which leading classical approximations such as pure-state-based 1D (matrix product states, MPS) and 2D (isometric tensor network states, isoTNS) tensor network methods2,3 break down. These experiments demonstrate a foundational tool for the realization of near-term quantum applications4,5.Quantum computing promises to offer substantial speed-ups over its classical counterpart for certain problems. However, the greatest impediment to realizing its full potential is noise that is inherent to these systems. The widely accepted solution to this challenge is the implementation of fault-tolerant quantum circuits, which is out of reach for current processors. Here we report experiments on a noisy 127-qubit processor and demonstrate the measurement of accurate expectation values for circuit volumes at a scale beyond brute-force classical computation. We argue that this represents evidence for the utility of quantum computing in a pre-fault-tolerant era. These experimental results are enabled by advances in the coherence and calibration of a superconducting processor at this scale and the ability to characterize1 and controllably manipulate noise across such a large device. We establish the accuracy of the measured expectation values by comparing them with the output of exactly verifiable circuits. In the regime of strong entanglement, the quantum computer provides correct results for which leading classical approximations such as pure-state-based 1D (matrix product states, MPS) and 2D (isometric tensor network states, isoTNS) tensor network methods2,3 break down. These experiments demonstrate a foundational tool for the realization of near-term quantum applications4,5.
Quantum computing promises to offer substantial speed-ups over its classical counterpart for certain problems. However, the greatest impediment to realizing its full potential is noise that is inherent to these systems. The widely accepted solution to this challenge is the implementation of fault-tolerant quantum circuits, which is out of reach for current processors. Here we report experiments on a noisy 127-qubit processor and demonstrate the measurement of accurate expectation values for circuit volumes at a scale beyond brute-force classical computation. We argue that this represents evidence for the utility of quantum computing in a pre-fault-tolerant era. These experimental results are enabled by advances in the coherence and calibration of a superconducting processor at this scale and the ability to characterize and controllably manipulate noise across such a large device. We establish the accuracy of the measured expectation values by comparing them with the output of exactly verifiable circuits. In the regime of strong entanglement, the quantum computer provides correct results for which leading classical approximations such as pure-state-based 1D (matrix product states, MPS) and 2D (isometric tensor network states, isoTNS) tensor network methods break down. These experiments demonstrate a foundational tool for the realization of near-term quantum applications .
Quantum computing promises to offer substantial speed-ups over its classical counterpart for certain problems. However, the greatest impediment to realizing its full potential is noise that is inherent to these systems. The widely accepted solution to this challenge is the implementation of fault-tolerant quantum circuits, which is out of reach for current processors. Here we report experiments on a noisy 127-qubit processor and demonstrate the measurement of accurate expectation values for circuit volumes at a scale beyond brute-force classical computation. We argue that this represents evidence for the utility of quantum computing in a pre-fault-tolerant era. These experimental results are enabled by advances in the coherence and calibration of a superconducting processor at this scale and the ability to characterize1 and controllably manipulate noise across such a large device. We establish the accuracy of the measured expectation values by comparing them with the output of exactly verifiable circuits. In the regime of strong entanglement, the quantum computer provides correct results for which leading classical approximations such as pure-state-based 1D (matrix product states, MPS) and 2D (isometric tensor network states, isoTNS) tensor network methods2,3 break down. These experiments demonstrate a foundational tool for the realization of near-term quantum applications4,5.
Author Wei, Ken Xuan
Nayfeh, Hasan
van den Berg, Ewout
Rosenblatt, Sami
Zaletel, Michael
Kim, Youngseok
Anand, Sajant
Eddins, Andrew
Wu, Yantao
Temme, Kristan
Kandala, Abhinav
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  orcidid: 0000-0002-8486-9162
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  organization: IBM Quantum, IBM Thomas J. Watson Research Center
– sequence: 2
  givenname: Andrew
  orcidid: 0000-0001-5088-4711
  surname: Eddins
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  givenname: Ken Xuan
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  fullname: Wei, Ken Xuan
  organization: IBM Quantum, IBM Thomas J. Watson Research Center
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  organization: IBM Quantum, IBM Thomas J. Watson Research Center
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  organization: IBM Quantum, IBM Thomas J. Watson Research Center
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  fullname: Nayfeh, Hasan
  organization: IBM Quantum, IBM Thomas J. Watson Research Center
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  surname: Wu
  fullname: Wu, Yantao
  organization: Department of Physics, University of California, Berkeley, RIKEN iTHEMS
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  givenname: Michael
  surname: Zaletel
  fullname: Zaletel, Michael
  organization: Department of Physics, University of California, Berkeley, Materials Sciences Division, Lawrence Berkeley National Laboratory
– sequence: 10
  givenname: Kristan
  orcidid: 0000-0002-4195-0569
  surname: Temme
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  organization: IBM Quantum, IBM Thomas J. Watson Research Center
BackLink https://www.ncbi.nlm.nih.gov/pubmed/37316724$$D View this record in MEDLINE/PubMed
https://www.osti.gov/servlets/purl/2229295$$D View this record in Osti.gov
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DumitrescuEFCloud quantum computing of an atomic nucleusPhys. Rev. Lett.20181202105012018PhRvL.120u0501D1:CAS:528:DC%2BC1MXltVygtrs%3D10.1103/PhysRevLett.120.21050129883142
LiYBenjaminSCEfficient variational quantum simulator incorporating active error minimizationPhys. Rev. X20177021050
StehlikJTunable coupling architecture for fixed-frequency transmon superconducting qubitsPhys. Rev. Lett.20211270805052021PhRvL.127h0505S1:CAS:528:DC%2BB3MXhvFGhsr7L10.1103/PhysRevLett.127.08050534477428
SchöllwockUThe density-matrix renormalization group in the age of matrix product statesAnn. Phys.2011326961922011AnPhy.326...96S276967010.1016/j.aop.2010.09.0121213.81178
Ferracin, S. et al. Efficiently improving the performance of noisy quantum computers. Preprint at https://arxiv.org/abs/2201.10672 (2022).
PreskilljQuantum computing in the NISQ era and beyondQuantum201827910.22331/q-2018-08-06-79
Giurgica-Tiron, T., Hindy, Y., Larose, R., Mari, A. & Zeng, W. J. digital zero noise extrapolation for quantum error mitigation. in 2020 IEEE International Conference on Quantum Computing and Engineering (QCE) 306–316 (IEEE, 2020).
Shor, P. W. in Proc. 35th Annual Symposium on Foundations of Computer Science 124–134 (IEEE, 1994).
BravyiSSimulation of quantum circuits by low-rank stabilizer decompositionsQuantum2019318110.22331/q-2019-09-02-181
HeANachmanBde JongWABauerCWZero-noise extrapolation for quantum-gate error mitigation with identity insertionsPhys. Rev. A20201020124262020PhRvA.102a2426H41316961:CAS:528:DC%2BB3cXhs1emsbfI10.1103/PhysRevA.102.012426
TemmeKBravyiSGambettaJMError mitigation for short-depth quantum circuitsPhys. Rev. Lett.20171191805092017PhRvL.119r0509T373072410.1103/PhysRevLett.119.18050929219599
CiracJIPérez-GarcíaDSchuchNVerstraeteFMatrix product states and projected entangled pair states: concepts, symmetries, theoremsRev. Mod. Phys.2021930450032021RvMP...93d5003C43699101:CAS:528:DC%2BB38Xhsl2jsbo%3D10.1103/RevModPhys.93.045003
ZhangEJHigh-performance superconducting quantum processors via laser annealing of transmon qubitsSci. Adv.20228eabi66901:CAS:528:DC%2BB38XhsV2rurnL10.1126/sciadv.abi6690355596839106287
RakovszkyTvon KeyserlingkCWPollmannFDissipation-assisted operator evolution method for capturing hydrodynamic transportPhys. Rev. B20221050751312022PhRvB.105g5131R1:CAS:528:DC%2BB38Xmsleht78%3D10.1103/PhysRevB.105.075131
KandalaAError mitigation extends the computational reach of a noisy quantum processorNature20195674914952019Natur.567..491K1:CAS:528:DC%2BC1MXosVSjur0%3D10.1038/s41586-019-1040-730918370
McDonough, B. et al. Automated quantum error mitigation based on probabilistic error reduction. In IEEE/ACM Third International Workshop on Quantum Computing Software(QCS) 83–93 (IEEE/ACM, 2022).
BennettCHPurification of noisy entanglement and faithful teleportation via noisy channelsPhys. Rev. Lett.1996767227251996PhRvL..76..722B1:CAS:528:DyaK28XntVCktA%3D%3D10.1103/PhysRevLett.76.72210061534
CaiZMulti-exponential error extrapolation and combining error mitigation techniques for NISQ applicationsnpj Quantum Inf.20217802021npjQI...7...80C10.1038/s41534-021-00404-3
FreyPRachelSRealization of a discrete time crystal on 57 qubits of a quantum computerSci. Adv.20228eabm765210.1126/sciadv.abm7652352353478890700
WhiteCDZaletelMMongRSKRefaelGQuantum dynamics of thermalizing systemsPhys. Rev. B2018970351272018PhRvB..97c5127W1:CAS:528:DC%2BC1MXlt1ersL0%3D10.1103/PhysRevB.97.035127
KochJCharge-insensitive qubit design derived from the Cooper pair boxPhys. Rev. A2007760423192007PhRvA..76d2319K10.1103/PhysRevA.76.042319
CarrollMRosenblattSJurcevicPIauerIKandalaADynamics of superconducting qubit relaxation timesnpj Quantum Inf.202292022npjQI...8..132C10.1038/s41534-022-00643-y
BhartiKNoisy intermediate-scale quantum algorithmsRev. Mod. Phys.2022940150042022RvMP...94a5004B44220441:CAS:528:DC%2BB38XhtVOnsLrE10.1103/RevModPhys.94.015004
Tran, M. C., Sharma, K. & Temme, K. Locality and error mitigation of quantum circuits. Preprint at https://arxiv.org/abs/2303.06496 (2023).
van den Berg, E., Minev, Z.K., Kandala, A. et al. Probabilistic error cancellation with sparse Pauli–Lindblad models on noisy quantum processors. Nat. Phys.https://doi.org/10.1038/s41567-023-02042-2 (2023).
AaronsonSGottesmanDImproved simulation of stabilizer circuitsPhys. Rev. A2004700523282004PhRvA..70e2328A10.1103/PhysRevA.70.052328
WeiKXHamiltonian engineering with multicolor drives for fast entangling gates and quantum crosstalk cancellationPhys. Rev. Lett.20221290605012022PhRvL.129f0501W1:CAS:528:DC%2BB38Xit1antb7M10.1103/PhysRevLett.129.06050136018659
ChowJMSimple all-microwave entangling gate for fixed-frequency superconducting qubitsPhys. Rev. Lett.20111070805022011PhRvL.107h0502C10.1103/PhysRevLett.107.08050221929152
Hauschild, J. & Pollmann, F. Efficient numerical simulations with tensor networks: Tensor Network Python (TeNPy). SciPost Phys. Lect. Noteshttps://doi.org/10.21468/SciPostPhysLectNotes.5 (2018).
ZhouYStoudenmireEMWaintalXWhat limits the simulation of quantum computers?Phys. Rev. X2020100410381:CAS:528:DC%2BB3MXjtFSktLo%3D
Kim, Y. et al. Scalable error mitigation for noisy quantum circuits produces competitive expectation values. Nat. Phys.https://doi.org/10.1038/s41567-022-01914-3 (2023).
ChenI-CBurdickBYaoYOrthPPIadecolaTError-mitigated simulation of quantum many-body scars on quantum computers with pulse-level controlPhys. Rev. Res.202240430271:CAS:528:DC%2BB3sXhsVGgtLc%3D10.1103/PhysRevResearch.4.043027
MariAShammahNZengWJExtending quantum probabilistic error cancellation by noise scalingPhys. Rev. A20211040526072021PhRvA.104e2607M43524811:CAS:528:DC%2BB3MXislagtr%2FM10.1103/PhysRevA.104.052607
PaeckelSTime-evolution methods for matrix-product statesAnn. Phys.201941116799840313741:CAS:528:DC%2BC1MXitFOjt73N10.1016/j.aop.2019.1679981433.81170
MiXTime-crystalline eigenstate order on a quantum processorNature20226015315362022Natur.601..531M1:CAS:528:DC%2BB38XhslCns7Y%3D10.1038/s41586-021-04257-w34847568
EndoSBenjaminSCLiYPractical quantum error mitigation for near-future applicationsPhys. Rev. X201880310271:CAS:528:DC%2BC1MXltFSnsLw%3D
GuoCGeneral-purpose quantum circuit simulator with projected entangled-pair states and the quantum supremacy frontierPhys. Rev. Lett.20191231905012019PhRvL.123s0501G1:CAS:528:DC%2BB3cXhvFyksbY%3D10.1103/PhysRevLett.123.19050131765197
CalabresePCardyJEvolution of entanglement entropy in one-dimensional systemsJ. Stat. Mech. Theory Exp.20052005P04010214103310.1088/1742-5468/2005/04/P040101456.82578
HubigCHaegemanJSchollwöckUError estimates for extrapolations with matrix-product statesPhys. Rev. B2018970451252018PhRvB..97d5125H10.1103/PhysRevB.97.045125
ZaletelMPPollmannFIsometric tensor network states in two dimensionsPhys. Rev. Lett.20201240372012020PhRvL.124c7201Z40565941:CAS:528:DC%2BB3cXmslygsr0%3D10.1103/PhysRevLett.124.03720132031848
AruteFQuantum supremacy using a programmable superconducting processorNature20195745055102019Natur.574..505A1:CAS:528:DC%2BC1MXitVagsb3I10.1038/s41586-019-1666-531645734
MiXNoise-resilient edge modes on a chain of superconducting qubitsScience20223787857902022Sci...378..785M1:CAS:528:DC%2BB38XivFensbvF10.1126/science.abq576936395220
Knill, E. Fault-tolerant postselected quantum computation: threshold analysis. Preprint at https://arxiv.org/abs/quant-ph/0404104 (2004).
AyralTDensity-matrix renormalization group algorithm for simulating quantum circuits with a finite fidelityPRX Quantum202340203042023PRXQ....4b0304A10.1103/PRXQuantum.4.020304
S Aaronson (6096_CR29) 2004; 70
EF Dumitrescu (6096_CR20) 2018; 120
KX Wei (6096_CR44) 2022; 129
JI Cirac (6096_CR45) 2021; 93
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CH Bennett (6096_CR23) 1996; 76
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C Guo (6096_CR35) 2019; 123
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K Bharti (6096_CR5) 2022; 94
S Paeckel (6096_CR2) 2019; 411
I-C Chen (6096_CR13) 2022; 4
References_xml – reference: Kitaev, A. Y. Quantum measurements and the Abelian Stabilizer Problem. Preprint at https://arxiv.org/abs/quant-ph/9511026 (1995).
– reference: AruteFQuantum supremacy using a programmable superconducting processorNature20195745055102019Natur.574..505A1:CAS:528:DC%2BC1MXitVagsb3I10.1038/s41586-019-1666-531645734
– reference: ChowJMSimple all-microwave entangling gate for fixed-frequency superconducting qubitsPhys. Rev. Lett.20111070805022011PhRvL.107h0502C10.1103/PhysRevLett.107.08050221929152
– reference: KandalaAError mitigation extends the computational reach of a noisy quantum processorNature20195674914952019Natur.567..491K1:CAS:528:DC%2BC1MXosVSjur0%3D10.1038/s41586-019-1040-730918370
– reference: ZaletelMPPollmannFIsometric tensor network states in two dimensionsPhys. Rev. Lett.20201240372012020PhRvL.124c7201Z40565941:CAS:528:DC%2BB3cXmslygsr0%3D10.1103/PhysRevLett.124.03720132031848
– reference: CarrollMRosenblattSJurcevicPIauerIKandalaADynamics of superconducting qubit relaxation timesnpj Quantum Inf.202292022npjQI...8..132C10.1038/s41534-022-00643-y
– reference: StehlikJTunable coupling architecture for fixed-frequency transmon superconducting qubitsPhys. Rev. Lett.20211270805052021PhRvL.127h0505S1:CAS:528:DC%2BB3MXhvFGhsr7L10.1103/PhysRevLett.127.08050534477428
– reference: TemmeKBravyiSGambettaJMError mitigation for short-depth quantum circuitsPhys. Rev. Lett.20171191805092017PhRvL.119r0509T373072410.1103/PhysRevLett.119.18050929219599
– reference: DumitrescuEFCloud quantum computing of an atomic nucleusPhys. Rev. Lett.20181202105012018PhRvL.120u0501D1:CAS:528:DC%2BC1MXltVygtrs%3D10.1103/PhysRevLett.120.21050129883142
– reference: CalabresePCardyJEvolution of entanglement entropy in one-dimensional systemsJ. Stat. Mech. Theory Exp.20052005P04010214103310.1088/1742-5468/2005/04/P040101456.82578
– reference: BennettCHPurification of noisy entanglement and faithful teleportation via noisy channelsPhys. Rev. Lett.1996767227251996PhRvL..76..722B1:CAS:528:DyaK28XntVCktA%3D%3D10.1103/PhysRevLett.76.72210061534
– reference: CiracJIPérez-GarcíaDSchuchNVerstraeteFMatrix product states and projected entangled pair states: concepts, symmetries, theoremsRev. Mod. Phys.2021930450032021RvMP...93d5003C43699101:CAS:528:DC%2BB38Xhsl2jsbo%3D10.1103/RevModPhys.93.045003
– reference: McDonough, B. et al. Automated quantum error mitigation based on probabilistic error reduction. In IEEE/ACM Third International Workshop on Quantum Computing Software(QCS) 83–93 (IEEE/ACM, 2022).
– reference: van den Berg, E., Minev, Z.K., Kandala, A. et al. Probabilistic error cancellation with sparse Pauli–Lindblad models on noisy quantum processors. Nat. Phys.https://doi.org/10.1038/s41567-023-02042-2 (2023).
– reference: EndoSBenjaminSCLiYPractical quantum error mitigation for near-future applicationsPhys. Rev. X201880310271:CAS:528:DC%2BC1MXltFSnsLw%3D
– reference: RakovszkyTvon KeyserlingkCWPollmannFDissipation-assisted operator evolution method for capturing hydrodynamic transportPhys. Rev. B20221050751312022PhRvB.105g5131R1:CAS:528:DC%2BB38Xmsleht78%3D10.1103/PhysRevB.105.075131
– reference: Knill, E. Fault-tolerant postselected quantum computation: threshold analysis. Preprint at https://arxiv.org/abs/quant-ph/0404104 (2004).
– reference: PaeckelSTime-evolution methods for matrix-product statesAnn. Phys.201941116799840313741:CAS:528:DC%2BC1MXitFOjt73N10.1016/j.aop.2019.1679981433.81170
– reference: BravyiSSimulation of quantum circuits by low-rank stabilizer decompositionsQuantum2019318110.22331/q-2019-09-02-181
– reference: Giurgica-Tiron, T., Hindy, Y., Larose, R., Mari, A. & Zeng, W. J. digital zero noise extrapolation for quantum error mitigation. in 2020 IEEE International Conference on Quantum Computing and Engineering (QCE) 306–316 (IEEE, 2020).
– reference: AaronsonSGottesmanDImproved simulation of stabilizer circuitsPhys. Rev. A2004700523282004PhRvA..70e2328A10.1103/PhysRevA.70.052328
– reference: WhiteCDZaletelMMongRSKRefaelGQuantum dynamics of thermalizing systemsPhys. Rev. B2018970351272018PhRvB..97c5127W1:CAS:528:DC%2BC1MXlt1ersL0%3D10.1103/PhysRevB.97.035127
– reference: MariAShammahNZengWJExtending quantum probabilistic error cancellation by noise scalingPhys. Rev. A20211040526072021PhRvA.104e2607M43524811:CAS:528:DC%2BB3MXislagtr%2FM10.1103/PhysRevA.104.052607
– reference: CaiZMulti-exponential error extrapolation and combining error mitigation techniques for NISQ applicationsnpj Quantum Inf.20217802021npjQI...7...80C10.1038/s41534-021-00404-3
– reference: HubigCHaegemanJSchollwöckUError estimates for extrapolations with matrix-product statesPhys. Rev. B2018970451252018PhRvB..97d5125H10.1103/PhysRevB.97.045125
– reference: LiYBenjaminSCEfficient variational quantum simulator incorporating active error minimizationPhys. Rev. X20177021050
– reference: WeiKXHamiltonian engineering with multicolor drives for fast entangling gates and quantum crosstalk cancellationPhys. Rev. Lett.20221290605012022PhRvL.129f0501W1:CAS:528:DC%2BB38Xit1antb7M10.1103/PhysRevLett.129.06050136018659
– reference: Tran, M. C., Sharma, K. & Temme, K. Locality and error mitigation of quantum circuits. Preprint at https://arxiv.org/abs/2303.06496 (2023).
– reference: FreyPRachelSRealization of a discrete time crystal on 57 qubits of a quantum computerSci. Adv.20228eabm765210.1126/sciadv.abm7652352353478890700
– reference: MiXNoise-resilient edge modes on a chain of superconducting qubitsScience20223787857902022Sci...378..785M1:CAS:528:DC%2BB38XivFensbvF10.1126/science.abq576936395220
– reference: ChenI-CBurdickBYaoYOrthPPIadecolaTError-mitigated simulation of quantum many-body scars on quantum computers with pulse-level controlPhys. Rev. Res.202240430271:CAS:528:DC%2BB3sXhsVGgtLc%3D10.1103/PhysRevResearch.4.043027
– reference: ZhangEJHigh-performance superconducting quantum processors via laser annealing of transmon qubitsSci. Adv.20228eabi66901:CAS:528:DC%2BB38XhsV2rurnL10.1126/sciadv.abi6690355596839106287
– reference: BhartiKNoisy intermediate-scale quantum algorithmsRev. Mod. Phys.2022940150042022RvMP...94a5004B44220441:CAS:528:DC%2BB38XhtVOnsLrE10.1103/RevModPhys.94.015004
– reference: KochJCharge-insensitive qubit design derived from the Cooper pair boxPhys. Rev. A2007760423192007PhRvA..76d2319K10.1103/PhysRevA.76.042319
– reference: Ferracin, S. et al. Efficiently improving the performance of noisy quantum computers. Preprint at https://arxiv.org/abs/2201.10672 (2022).
– reference: GuoCGeneral-purpose quantum circuit simulator with projected entangled-pair states and the quantum supremacy frontierPhys. Rev. Lett.20191231905012019PhRvL.123s0501G1:CAS:528:DC%2BB3cXhvFyksbY%3D10.1103/PhysRevLett.123.19050131765197
– reference: Kim, Y. et al. Scalable error mitigation for noisy quantum circuits produces competitive expectation values. Nat. Phys.https://doi.org/10.1038/s41567-022-01914-3 (2023).
– reference: HeANachmanBde JongWABauerCWZero-noise extrapolation for quantum-gate error mitigation with identity insertionsPhys. Rev. A20201020124262020PhRvA.102a2426H41316961:CAS:528:DC%2BB3cXhs1emsbfI10.1103/PhysRevA.102.012426
– reference: PreskilljQuantum computing in the NISQ era and beyondQuantum201827910.22331/q-2018-08-06-79
– reference: MiXTime-crystalline eigenstate order on a quantum processorNature20226015315362022Natur.601..531M1:CAS:528:DC%2BB38XhslCns7Y%3D10.1038/s41586-021-04257-w34847568
– reference: ZhouYStoudenmireEMWaintalXWhat limits the simulation of quantum computers?Phys. Rev. X2020100410381:CAS:528:DC%2BB3MXjtFSktLo%3D
– reference: Shor, P. W. in Proc. 35th Annual Symposium on Foundations of Computer Science 124–134 (IEEE, 1994).
– reference: AyralTDensity-matrix renormalization group algorithm for simulating quantum circuits with a finite fidelityPRX Quantum202340203042023PRXQ....4b0304A10.1103/PRXQuantum.4.020304
– reference: SchöllwockUThe density-matrix renormalization group in the age of matrix product statesAnn. Phys.2011326961922011AnPhy.326...96S276967010.1016/j.aop.2010.09.0121213.81178
– reference: Hauschild, J. & Pollmann, F. Efficient numerical simulations with tensor networks: Tensor Network Python (TeNPy). SciPost Phys. Lect. Noteshttps://doi.org/10.21468/SciPostPhysLectNotes.5 (2018).
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Snippet Quantum computing promises to offer substantial speed-ups over its classical counterpart for certain problems. However, the greatest impediment to realizing...
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SubjectTerms 639/705/258
639/766/483/3926
639/766/483/481
Approximation
Circuits
Estimates
Fault tolerance
Humanities and Social Sciences
Information technology
Isometric
Mathematical analysis
MATHEMATICS AND COMPUTING
Microprocessors
multidisciplinary
Quantum computers
Quantum computing
Quantum entanglement
Quantum information
Quantum simulation
Qubits (quantum computing)
Science
Science (multidisciplinary)
Tensors
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Title Evidence for the utility of quantum computing before fault tolerance
URI https://link.springer.com/article/10.1038/s41586-023-06096-3
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Volume 618
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