1.CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China
2.CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
3.Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China
Jin-Shi Xu (jsxu@ustc.edu.cn)
Yong-Jian Han (smhan@ustc.edu.cn)
Chuan-Feng Li (cfli@ustc.edu.cn)
纸质出版日期:2022-08-31,
网络出版日期:2022-07-05,
收稿日期:2022-03-30,
修回日期:2022-06-08,
录用日期:2022-06-10
Scan for full text
Kai Sun, Ze-Yan Hao, Yan Wang, 等. Optical demonstration of quantum fault-tolerant threshold[J]. Light: Science & Applications, 2022,11(8):1834-1842.
Sun, K. et al. Optical demonstration of quantum fault-tolerant threshold. Light: Science & Applications, 11, 1834-1842 (2022).
Kai Sun, Ze-Yan Hao, Yan Wang, 等. Optical demonstration of quantum fault-tolerant threshold[J]. Light: Science & Applications, 2022,11(8):1834-1842. DOI: 10.1038/s41377-022-00891-9.
Sun, K. et al. Optical demonstration of quantum fault-tolerant threshold. Light: Science & Applications, 11, 1834-1842 (2022). DOI: 10.1038/s41377-022-00891-9.
A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes
in which logical qubits are encoded by several physical qubits
enable to the output of a higher probability of correct logical qubits under the presence of errors. However
strict requirements to encode qubits and operators render the implementation of a full fault-tolerant computation challenging even for the achievable noisy intermediate-scale quantum technology. Especially the threshold for fault-tolerant computation still lacks experimental verification. Here
based on an all-optical setup
we experimentally demonstrate the existence of the threshold for the fault-tolerant protocol. Four physical qubits are represented as the spatial modes of two entangled photons
which are used to encode two logical qubits. The experimental results clearly show that when the error rate is below the threshold
the probability of correct output in the circuit
formed with fault-tolerant gates
is higher than that in the corresponding non-encoded circuit. In contrast
when the error rate is above the threshold
no advantage is observed in the fault-tolerant implementation. The developed high-accuracy optical system may provide a reliable platform to investigate error propagation in more complex circuits with fault-tolerant gates.
D. G. Cory, 等. Experimental quantum error correction. Phys. Rev. Lett., 1998. 812152-2155. DOI:10.1103/PhysRevLett.81.2152http://doi.org/10.1103/PhysRevLett.81.2152.
E. Knill, 等. Benchmarking quantum computers: the five-qubit error correcting code. Phys. Rev. Lett., 2001. 865811-5814. DOI:10.1103/PhysRevLett.86.5811http://doi.org/10.1103/PhysRevLett.86.5811.
J. Chiaverini, 等. Realization of quantum error correction. Nature, 2004. 432602-605. DOI:10.1038/nature03074http://doi.org/10.1038/nature03074.
P. Schindler, 等. Experimental repetitive quantum error correction. Science, 2011. 3321059-1061. DOI:10.1126/science.1203329http://doi.org/10.1126/science.1203329.
M. D. Reed, 等. Realization of three-qubit quantum error correction with superconducting circuits. Nature, 2012. 482382-385. DOI:10.1038/nature10786http://doi.org/10.1038/nature10786.
D. Nigg, 等. Quantum computations on a topologically encoded qubit. Science, 2014. 345302-305. DOI:10.1126/science.1253742http://doi.org/10.1126/science.1253742DOI:10.1126/science.1253742http://doi.org/10.1126/science.1253742.
G. Waldherr, 等. Quantum error correction in a solid-state hybrid spin register. Nature, 2014. 506204-207. DOI:10.1038/nature12919http://doi.org/10.1038/nature12919.
B. A. Bell, 等. Experimental demonstration of a graph state quantum error-correction code. Nat. Commun., 2014. 53658DOI:10.1038/ncomms4658http://doi.org/10.1038/ncomms4658.
M. Gong, 等. Experimental exploration of five-qubit quantum error-correcting code with superconducting qubits. Natl Sci. Rev., 2022. 9nwab011DOI:10.1093/nsr/nwab011http://doi.org/10.1093/nsr/nwab011.
C. K. Andersen, 等. Repeated quantum error detection in a surface code. Nat. Phys., 2020. 16875-880. DOI:10.1038/s41567-020-0920-yhttp://doi.org/10.1038/s41567-020-0920-y.
L. Egan, 等. Fault-tolerant control of an error-corrected qubit. Nature, 2021. 598281-286. DOI:10.1038/s41586-021-03928-yhttp://doi.org/10.1038/s41586-021-03928-y.
Zhao, Y. W. et al. Realization of an error-correcting surface code with superconducting qubits. Preprint at https://arxiv.org/abs/2112.13505https://arxiv.org/abs/2112.13505 (2021).
A. Noiri, 等. Fast universal quantum gate above the fault-tolerance threshold in silicon. Nature, 2022. 601338-342. DOI:10.1038/s41586-021-04182-yhttp://doi.org/10.1038/s41586-021-04182-y.
X. Xue, 等. Quantum logic with spin qubits crossing the surface code threshold. Nature, 2022. 601343-347. DOI:10.1038/s41586-021-04273-whttp://doi.org/10.1038/s41586-021-04273-w.
M. T. Mądzik, 等. Precision tomography of a three-qubit donor quantum processor in silicon. Nature, 2022. 601348-353. DOI:10.1038/s41586-021-04292-7http://doi.org/10.1038/s41586-021-04292-7.
P. W. Shor. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A, 1995. 52R2493-R2496. DOI:10.1103/PhysRevA.52.R2493http://doi.org/10.1103/PhysRevA.52.R2493.
A. M. Steane. Error correcting codes in quantum theory. Phys. Rev. Lett., 1996. 77793-797. DOI:10.1103/PhysRevLett.77.793http://doi.org/10.1103/PhysRevLett.77.793.
A. R. Calderbank, P. W. Shor. Good quantum error-correcting codes exist. Phys. Rev. A, 1996. 541098-1105. DOI:10.1103/PhysRevA.54.1098http://doi.org/10.1103/PhysRevA.54.1098.
M. Grassl, T. Beth, T. Pellizzari. Codes for the quantum erasure channel. Phys. Rev. A, 1997. 5633-38. DOI:10.1103/PhysRevA.56.33http://doi.org/10.1103/PhysRevA.56.33.
D. Bacon, 等. Universal fault-tolerant quantum computation on decoherence-free subspaces. Phys. Rev. Lett., 2000. 851758-1761. DOI:10.1103/PhysRevLett.85.1758http://doi.org/10.1103/PhysRevLett.85.1758.
Gottesman, D. Quantum fault tolerance in small experiments. Preprint at https://arxiv.org/abs/1610.03507https://arxiv.org/abs/1610.03507 (2016).
Knill, E., Laflamme, R. & Zurek, W. H. Threshold accuracy for quantum computation. Preprint at https://arxiv.org/abs/quant-ph/9610011https://arxiv.org/abs/quant-ph/9610011 (1996).
D. Aharonov, M. Ben-Or. Fault-tolerant quantum computation with constant error rate. SIAM J. Comput., 2008. 381207-1282. DOI:10.1137/S0097539799359385http://doi.org/10.1137/S0097539799359385.
D. Gottesman. Fault-tolerant quantum computation with local gates. J. Mod. Opt., 2000. 47333-345. DOI:10.1080/09500340008244046http://doi.org/10.1080/09500340008244046.
R. Raussendorf, J. Harrington. Fault-tolerant quantum computation with high threshold in two dimensions. Phys. Rev. Lett., 2007. 98190504DOI:10.1103/PhysRevLett.98.190504http://doi.org/10.1103/PhysRevLett.98.190504.
J. M. Auger, 等. Fault-tolerance thresholds for the surface code with fabrication errors. Phys. Rev. A, 2017. 96042316DOI:10.1103/PhysRevA.96.042316http://doi.org/10.1103/PhysRevA.96.042316.
K. Fukui, 等. High-threshold fault-tolerant quantum computation with analog quantum error correction. Phys. Rev. X, 2018. 8021054.
Gottesman, D. An introduction to quantum error correction and fault-tolerant quantum computation. Preprint at https://arxiv.org/abs/0904.2557https://arxiv.org/abs/0904.2557 (2009).
A. Bermudez, 等. Assessing the progress of trapped-ion processors towards fault-tolerant quantum computation. Phys. Rev. X, 2017. 7041061.
J. Preskill. Quantum computing in the NISQ era and beyond. Quantum, 2018. 279DOI:10.22331/q-2018-08-06-79http://doi.org/10.22331/q-2018-08-06-79.
S. Rosenblum, 等. Fault-tolerant detection of a quantum error. Science, 2018. 361266-270. DOI:10.1126/science.aat3996http://doi.org/10.1126/science.aat3996.
S. Puri, 等. Stabilized cat in a driven nonlinear cavity: a fault-tolerant error syndrome detector. Phys. Rev. X, 2019. 9041009.
S. Bravyi, 等. Quantum advantage with noisy shallow circuits. Nat. Phys., 2020. 161040-1045. DOI:10.1038/s41567-020-0948-zhttp://doi.org/10.1038/s41567-020-0948-z.
N. M. Linke, 等. Fault-tolerant quantum error detection. Sci. Adv., 2017. 3e1701074DOI:10.1126/sciadv.1701074http://doi.org/10.1126/sciadv.1701074.
M. Takita, 等. Experimental demonstration of fault-tolerant state preparation with superconducting qubits. Phys. Rev. Lett., 2017. 119180501DOI:10.1103/PhysRevLett.119.180501http://doi.org/10.1103/PhysRevLett.119.180501.
C. Vuillot. Is error detection helpful on IBM 5Q chips?. Quantum Inf. Comput., 2018. 18949-964. .
R. Harper, S. T. Flammia. Fault-tolerant logical gates in the IBM quantum experience. Phys. Rev. Lett., 2019. 122080504DOI:10.1103/PhysRevLett.122.080504http://doi.org/10.1103/PhysRevLett.122.080504.
R. Cane, 等. Experimental characterization of fault-tolerant circuits in small-scale quantum processors. IEEE Access, 2021. 9162996-163011. DOI:10.1109/ACCESS.2021.3133483http://doi.org/10.1109/ACCESS.2021.3133483.
P. Kok, 等. Linear optical quantum computing with photonic qubits. Rev. Mod. Phys., 2007. 79135-174. DOI:10.1103/RevModPhys.79.135http://doi.org/10.1103/RevModPhys.79.135.
J. S. Xu, 等. Simulating the exchange of Majorana zero modes with a photonic system. Nat. Commun., 2016. 713194DOI:10.1038/ncomms13194http://doi.org/10.1038/ncomms13194.
J. S. Xu, 等. Photonic implementation of majorana-based berry phases. Sci. Adv., 2018. 4eaat6533DOI:10.1126/sciadv.aat6533http://doi.org/10.1126/sciadv.aat6533.
F. Töppel, 等. Classical entanglement in polarization metrology. N. J. Phys., 2014. 16073019DOI:10.1088/1367-2630/16/7/073019http://doi.org/10.1088/1367-2630/16/7/073019.
T. Kim, M. Fiorentino, F. N. C. Wong. Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer. Phys. Rev. A, 2006. 73012316DOI:10.1103/PhysRevA.73.012316http://doi.org/10.1103/PhysRevA.73.012316.
J. L. O'Brien, 等. Quantum process tomography of a controlled-NOT gate. Phys. Rev. Lett., 2004. 93080502DOI:10.1103/PhysRevLett.93.080502http://doi.org/10.1103/PhysRevLett.93.080502.
P. F. Wang, 等. Single ion qubit with estimated coherence time exceeding one hour. Nat. Commun., 2021. 12233DOI:10.1038/s41467-020-20330-whttp://doi.org/10.1038/s41467-020-20330-w.
D. Kielpinski, C. Monroe, D. J. Wineland. Architecture for a large-scale ion-trap quantum computer. Nature, 2002. 417709-711. DOI:10.1038/nature00784http://doi.org/10.1038/nature00784.
R. Barends, 等. Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature, 2014. 508500-503. DOI:10.1038/nature13171http://doi.org/10.1038/nature13171.
J. Kelly, 等. State preservation by repetitive error detection in a superconducting quantum circuit. Nature, 2015. 51966-69. DOI:10.1038/nature14270http://doi.org/10.1038/nature14270.
F. Arute, 等. Quantum supremacy using a programmable superconducting processor. Nature, 2019. 574505-510. DOI:10.1038/s41586-019-1666-5http://doi.org/10.1038/s41586-019-1666-5.
B. Yang, 等. Cooling and entangling ultracold atoms in optical lattices. Science, 2020. 369550-553. DOI:10.1126/science.aaz6801http://doi.org/10.1126/science.aaz6801.
C. X. Huang, 等. Experimental one-step deterministic polarization entanglement purification. Sci. Bull., 2022. 67593-597. DOI:10.1016/j.scib.2021.12.018http://doi.org/10.1016/j.scib.2021.12.018.
S. Ecker, 等. Remotely establishing polarization entanglement over noisy polarization channels. Phys. Rev. Appl., 2022. 17034009DOI:10.1103/PhysRevApplied.17.034009http://doi.org/10.1103/PhysRevApplied.17.034009.
H. X. Yan, 等. Entanglement purification and protection in a superconducting quantum network. Phys. Rev. Lett., 2022. 128080504DOI:10.1103/PhysRevLett.128.080504http://doi.org/10.1103/PhysRevLett.128.080504.
L. Zhou, Y. B. Sheng. Purification of logic-qubit entanglement. Sci. Rep., 2016. 628813DOI:10.1038/srep28813http://doi.org/10.1038/srep28813.
L. Zhou, Y. B. Sheng. Polarization entanglement purification for concatenated Greenberger-Horne-Zeilinger state. Ann. Phys., 2017. 38510-35. DOI:10.1016/j.aop.2017.07.012http://doi.org/10.1016/j.aop.2017.07.012.
W. J. Munro, 等. Quantum communication without the necessity of quantum memories. Nat. Photonics, 2012. 6777-781. DOI:10.1038/nphoton.2012.243http://doi.org/10.1038/nphoton.2012.243.
S. Muralidharan, 等. Ultrafast and fault-tolerant quantum communication across long distances. Phys. Rev. Lett., 2014. 112250501DOI:10.1103/PhysRevLett.112.250501http://doi.org/10.1103/PhysRevLett.112.250501.
F. Ewert, M. Bergmann, P. van Loock. Ultrafast long-distance quantum communication with static linear optics. Phys. Rev. Lett., 2016. 117210501DOI:10.1103/PhysRevLett.117.210501http://doi.org/10.1103/PhysRevLett.117.210501.
A. Peruzzo, 等. Quantum walks of correlated photons. Science, 2010. 3291500-1503. DOI:10.1126/science.1193515http://doi.org/10.1126/science.1193515.
Z. Q. Jiao, 等. Two-dimensional quantum walks of correlated photons. Optica, 2021. 81129-1135. DOI:10.1364/OPTICA.425879http://doi.org/10.1364/OPTICA.425879.
0
浏览量
0
Downloads
0
CSCD
关联资源
相关文章
相关作者
相关机构
京公网安备11010802024621