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Microscopic quantum dynamics study on the noise threshold of fault-tolerant quantum error correction

Y. C. Cheng, R. J. Silbey
2005 Physical Review A. Atomic, Molecular, and Optical Physics  

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2004 pre-print arXiv:quant-ph/0412168v1 fatcat:adda6degjreezokhzpyxbs6bvu
Quantum circuits implementing fault-tolerant quantum error correction (QEC) for the three qubit bit-flip code and five-qubit code are studied.  ...  These results provide insights into the fault-tolerant QEC process as well as useful information for designing the optimal fault-tolerant QEC circuit for particular physical implementation of quantum computer  ...  To combat the inevitable errors and decoherence of quantum states during the process of computation, quantum error correction (QEC) and fault-tolerant methods of quantum computation have to be applied  ... 
doi:10.1103/physreva.72.012320 fatcat:spqlaror5ncghcmoeqrq6rcvzi
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Y. C. Cheng, R. J. Silbey. "Microscopic quantum dynamics study on the noise threshold of fault-tolerant quantum error correction." Physical Review A. Atomic, Molecular, and Optical Physics 72.1 (2005)

Fault-tolerant quantum computation with a soft-decision decoder for error correction and detection by teleportation

Hayato Goto, Hironori Uchikawa
2013 Scientific Reports  

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For further improvement of fault-tolerant quantum computation, here we propose a softdecision decoder for quantum error correction and detection by teleportation.  ...  Fault-tolerant quantum computation with quantum error-correcting codes has been considerably developed over the past decade.  ...  G. proposed and devised the soft-decision decoding for quantum error correction and detection by teleportation, performed all the simulations, and wrote the paper. H.  ... 
doi:10.1038/srep02044 pmid:23784512 pmcid:PMC3687222 fatcat:bgcanhzncnhanakayfinop6keu
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Hayato Goto, Hironori Uchikawa. "Fault-tolerant quantum computation with a soft-decision decoder for error correction and detection by teleportation." Scientific Reports 3.1 (2013)

Error-detection-based quantum fault tolerance against discrete Pauli noise [article]

Ben W. Reichardt
2006 arXiv   pre-print

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Developed over the last couple of years, new schemes for achieving fault tolerance based on error detection, rather than error correction, appear to tolerate as much as 3-6% noise per gate -- an order  ...  With an analysis based on decomposing complicated probability distributions into mixtures of simpler ones, we rigorously prove the existence of constant tolerable noise rates ("noise thresholds") for error-detection-based  ...  I will sketch here a proof of a threshold for error-detection-based fault-tolerance schemes.  ... 
arXiv:quant-ph/0612004v1 fatcat:opygot5mizbptemae3j3kkauni
Citation

Ben W. Reichardt. "Error-detection-based quantum fault tolerance against discrete Pauli noise." arXiv (2006)

Fault-tolerant linear optics quantum computation by error-detecting quantum state transfer

Jaeyoon Cho
2007 Physical Review A. Atomic, Molecular, and Optical Physics  

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2006 pre-print
arXiv:quant-ph/0612073v1 fatcat:lklre5ehyvdatc57l2kofpm6cq
2007 accepted
arXiv:quant-ph/0612073v3 fatcat:xspw45fg3ze67ocjnqjjvnh2cu
2007 pre-print
arXiv:quant-ph/0612073v2 fatcat:xhgkd2dvlbcpjffjm26nhe3b4y
A scheme for linear optical implementation of fault-tolerant quantum computation is proposed, which is based on an error-detecting code.  ...  Each computational step is mediated by transfer of quantum information into an ancilla system embedding error-detection capability.  ...  Fault-tolerant threshold and resource consumption.  ... 
doi:10.1103/physreva.76.042311 fatcat:l7g63hcpqrdjhop5qnwko4ecuu
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Jaeyoon Cho. "Fault-tolerant linear optics quantum computation by error-detecting quantum state transfer." Physical Review A. Atomic, Molecular, and Optical Physics 76.4 (2007)

Noise Threshold of Quantum Supremacy [article]

Keisuke Fujii
2016 arXiv   pre-print

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fault-tolerant quantum computation with the same circuit-level noise model.  ...  By applying this to fault-tolerant quantum computation with the surface codes, we obtain the threshold value 2.84% for quantum supremacy, which is much higher than the standard threshold 0.75% for universal  ...  Therefore the threshold is given not by the error correction property of quantum error correction codes but by the error detection property.  ... 
arXiv:1610.03632v1 fatcat:hfhatfdxsvcyxa4vhtsgefub2i
Citation

Keisuke Fujii. "Noise Threshold of Quantum Supremacy." arXiv (2016)

Towards Demonstrating Fault Tolerance in Small Circuits Using Bacon-Shor Codes [article]

Ariel Shlosberg, Anthony M. Polloreno, Graeme Smith
2021 arXiv   pre-print

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In this work we study a next step - fault-tolerantly implementing quantum circuits. We choose the [[4, 1, 2]] Bacon-Shor subsystem code, which has a particularly simple error-detection circuit.  ...  This provides a concrete suggestion for a small-scale fault-tolerant demonstration of a quantum algorithm that could be accessible with existing hardware.  ...  ACKNOWLEDGEMENTS This material is based upon work supported by the U.S.  ... 
arXiv:2108.02079v1 fatcat:qjuceffeebg57a537d57fqspti
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Ariel Shlosberg, Anthony M. Polloreno, Graeme Smith. "Towards Demonstrating Fault Tolerance in Small Circuits Using Bacon-Shor Codes." arXiv (2021)

Fault-tolerant Quantum Computation with Highly Verified Logical Cluster States [article]

Keisuke Fujii, Katsuji Yamamoto
2006 arXiv   pre-print

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We investigate a scheme of fault-tolerant quantum computation based on the cluster model. Logical qubits are encoded by a suitable code such as the Steane's 7-qubit code.  ...  The noise threshold is improved significantly by making the high fidelity preparation and transversal measurement. It is estimated to be about 3% by a numerical simulation.  ...  Then, fault-tolerant quantum computation with error correction has been investigated in the literature [1, 2, 3, 4, 5, 6, 7] .  ... 
arXiv:quant-ph/0611160v1 fatcat:vow47dpevngxpfbpbqfbqvmy4m
Citation

Keisuke Fujii, Katsuji Yamamoto. "Fault-tolerant Quantum Computation with Highly Verified Logical Cluster States." arXiv (2006)

Fault-Tolerant Topological One-Way Quantum Computation with Probabilistic Two-Qubit Gates

Keisuke Fujii, Yuuki Tokunaga
2010 Physical Review Letters  

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2010 pre-print arXiv:1008.3752v1 fatcat:svo6gtlsbrddxbfvcnfyp42zla

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2010 accepted
arXiv:1008.3752v2 fatcat:27u4ewedl5dzpjdqmmclwm5omy
It is shown that fault-tolerant TOWC can be performed with the success probability of the two-qubit gate such as 0.5 (0.1) provided that the conditional error probability of the two-qubit gate is less  ...  Furthermore, the resource usage is considerably suppressed compared to the conventional fault-tolerant schemes with probabilistic two-qubit gates.  ...  We explore fault-tolerant quantum computation with such probabilistic two-qubit gates.  ... 
doi:10.1103/physrevlett.105.250503 pmid:21231570 fatcat:zaxgi7lupbgwjos2vy7mxtzq2e
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Keisuke Fujii, Yuuki Tokunaga. "Fault-Tolerant Topological One-Way Quantum Computation with Probabilistic Two-Qubit Gates." Physical Review Letters 105.25 (2010)

Qubit metrology for building a fault-tolerant quantum computer [article]

John M. Martinis
2015 arXiv   pre-print

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In a fault-tolerant quantum computer the qubits and their logic interactions must have errors below a threshold: scaling up with more and more qubits then brings the net error probability down to appropriate  ...  This challenge arises from the fundamental fragility of quantum information, which can only be overcome with quantum error correction.  ...  When Λ < 1 error detection fails, and even billions of bad qubits do not help. A key focus for fault tolerance is making qubit errors less than the threshold.  ... 
arXiv:1510.01406v1 fatcat:nbvxnnunoffvponqfroooyq45a
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John M. Martinis. "Qubit metrology for building a fault-tolerant quantum computer." arXiv (2015)

Qubit metrology for building a fault-tolerant quantum computer

John M Martinis
2015 npj Quantum Information  

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When Λo 1 error detection fails, and even billions of bad qubits do not help. A key focus for fault tolerance is making qubit errors less than the threshold.  ...  In conclusion, progress in making a fault-tolerant quantum computer must be closely tied to error metrology, as improvements with scaling will only occur when errors are below threshold.  ...  Quantum error correction takes advantage of an interesting property of qubitsXẐ ¼ -ẐX, so that a change in sequence just produces a minus sign.  ... 
doi:10.1038/npjqi.2015.5 fatcat:3dgcqkxkajc7vlmabwro2yv2ru
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John M Martinis. "Qubit metrology for building a fault-tolerant quantum computer." npj Quantum Information 1.1 (2015)

Measurement-free error correction with coherent ancillas [article]

Vickram N. Premakumar, M. Saffman, Robert Joynt
2020 arXiv   pre-print

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This is done by means of a fault-tolerant circuit that has a favorable error threshold for a conservative error model.  ...  The possibility of coherent error correction is important for those quantum computing platforms in which measurements in the course of the computation are undesirable.  ...  Generally speaking, the overhead involved in fault-tolerant CEC has been thought to be greater than in fault-tolerant measurement-based error correction (MEC) [7] .  ... 
arXiv:2007.09804v1 fatcat:c6wwfqxzgjbqzn6piqaipxsy4u
Citation

Vickram N. Premakumar, M. Saffman, Robert Joynt. "Measurement-free error correction with coherent ancillas." arXiv (2020)

Fault-Tolerant Quantum Computation for Local Leakage Faults [article]

Panos Aliferis, Barbara M. Terhal
2006 arXiv   pre-print

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2005 pre-print
arXiv:quant-ph/0511065v1 fatcat:nbksxyr66bhbxgceh7ss3ym6ei
2006 pre-print
arXiv:quant-ph/0511065v3 fatcat:rmwph7kolrcsteyepnn7babknq
2006 pre-print
arXiv:quant-ph/0511065v4 fatcat:4i45qjhyrvhqvn4p6bbukqvxjm
2005 pre-print
arXiv:quant-ph/0511065v2 fatcat:mqzq2txozfcmhnc3nztjeta4sm
We provide a rigorous analysis of fault-tolerant quantum computation in the presence of local leakage faults.  ...  We describe ways to limit the use of leakage-reduction units while keeping the quantum circuits fault-tolerant and we also discuss how leakage reduction by teleportation is naturally achieved in measurement-based  ...  Our quantum circuit diagrams were drawn using the Q-circuit L A T E X macro package by Steve Flammia and Bryan Eastin.  ... 
arXiv:quant-ph/0511065v5 fatcat:ad3oivargzfupe5uc4ywq7hor4
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Panos Aliferis, Barbara M. Terhal. "Fault-Tolerant Quantum Computation for Local Leakage Faults." arXiv (2006)

Postselection threshold against biased noise

Ben Reichardt
2006 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)  

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2006 accepted
arXiv:quant-ph/0608018v2 fatcat:chk3ryhtfzan5grjy6gjxxcljm
2006 pre-print
arXiv:quant-ph/0608018v1 fatcat:yjp3khlyurgnnhfxez2dcpfczy
The highest current estimates for the amount of noise a quantum computer can tolerate are based on fault-tolerance schemes relying heavily on postselecting on no detected errors.  ...  The main idea is to maintain strong control over the distribution of errors in the quantum state at all times.  ...  Can a postselection-based fault-tolerance scheme be concatenated on top of, or below, other fault-tolerance schemes? This changes the base error model. Numerics.  ... 
doi:10.1109/focs.2006.64 dblp:conf/focs/Reichardt06 fatcat:lolorxneyreapdlhln5tbchklm
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Ben Reichardt. "Postselection threshold against biased noise." 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06) (2006) 420-428

Blueprint for fault-tolerant quantum computation with Rydberg atoms

James M. Auger, Silvia Bergamini, Dan E. Browne
2017 Physical Review A  

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2017 pre-print
arXiv:1707.06498v1 fatcat:jxp5hfzfcbapnoogiq3em5fdea
2017 accepted
arXiv:1707.06498v2 fatcat:cjxivk2etzh7fi75da6agbimsq
We present a blueprint for building a fault-tolerant universal quantum computer with Rydberg atoms.  ...  We discuss the advantages and challenges of using Rydberg atoms to build such a quantum computer, and we perform error correction simulations to obtain an error threshold for our scheme.  ...  fault-tolerant quantum computer with Rydberg atoms.  ... 
doi:10.1103/physreva.96.052320 fatcat:ndvbmvl6urcovn756xkzzsxjci
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James M. Auger, Silvia Bergamini, Dan E. Browne. "Blueprint for fault-tolerant quantum computation with Rydberg atoms." Physical Review A 96.5 (2017)

Fibonacci schemes of fault-tolerant quantum computation [article]

Panos Aliferis
2008 arXiv   pre-print

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2008 pre-print
arXiv:0709.3603v2 fatcat:qe3ccbsmyrfgzmzpz7s3zs7qhm
2007 pre-print
arXiv:0709.3603v1 fatcat:yyhv6qypuffbbf7wdz3hpmq6dm
The threshold estimate derived in previous versions of this paper was incorrect; this note explains the flaw. A new proof is discussed in arXiv:0809.5063.  ...  As in earlier proofs of the quantum threshold theorem, previous versions of this paper [1] analyzed a scheme for fault-tolerant quantum computation which had a self-similar structure: logical qubits  ...  errors at level j of the concatenated code become located errors that can be corrected at level j+1.  ... 
arXiv:0709.3603v3 fatcat:fzbqkhpa3zgj5g57ka74kdivzi
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Panos Aliferis. "Fibonacci schemes of fault-tolerant quantum computation." arXiv (2008)

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