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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  
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

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

Hayato Goto, Hironori Uchikawa
2013 Scientific Reports  
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

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

Ben W. Reichardt
2006 arXiv   pre-print
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

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

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

Noise Threshold of Quantum Supremacy [article]

Keisuke Fujii
2016 arXiv   pre-print
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

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

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

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

Keisuke Fujii, Katsuji Yamamoto
2006 arXiv   pre-print
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

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

Keisuke Fujii, Yuuki Tokunaga
2010 Physical Review Letters  
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

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

John M. Martinis
2015 arXiv   pre-print
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

Qubit metrology for building a fault-tolerant quantum computer

John M Martinis
2015 npj Quantum Information  
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

Measurement-free error correction with coherent ancillas [article]

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

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

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

Postselection threshold against biased noise

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

Blueprint for fault-tolerant quantum computation with Rydberg atoms

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

Fibonacci schemes of fault-tolerant quantum computation [article]

Panos Aliferis
2008 arXiv   pre-print
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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