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On the Hardnesses of Several Quantum Decoding Problems [article]

Kao-Yueh Kuo, Chung-Chin Lu
2013 arXiv   pre-print
We classify the time complexities of three important decoding problems for quantum stabilizer codes.  ...  Our results indicate that finding a polynomial-time decoding algorithm for general stabilizer codes may be impossible, but this, on the other hand, strengthens the foundation of quantum code-based cryptography  ...  In quantum cryptography, the hardnesses of QMLD and QMEPD reflect the hardness of eavesdropping on a stabilizer code-based cryptosystem over the depolarizing channel model, i.e., the artificial noise used  ... 
arXiv:1306.5173v2 fatcat:rfa57vhzlnhevaoomikmhrkh2y

Optimal and efficient decoding of concatenated quantum block codes

David Poulin
2006 Physical Review A. Atomic, Molecular, and Optical Physics  
Our Monte Carlo results using the 5 qubit and Steane's code on a depolarizing channel demonstrate significant advantages of the message passing algorithms in two respects. 1) Optimal decoding increases  ...  We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system.  ...  This work was supported, in part, by the Gordon and Betty Moore Foundation through Caltech's Center for the Physics of Information, by the National Science Foundation under Grant No.  ... 
doi:10.1103/physreva.74.052333 fatcat:vd3t3743x5dnhdafkthvhhzlrm

Enhanced Feedback Iterative Decoding of Sparse Quantum Codes

Yun-Jiang Wang, Barry C. Sanders, Bao-Ming Bai, Xin-Mei Wang
2012 IEEE Transactions on Information Theory  
In our feedback procedure, we exploit much of the information from stabilizers, not just the syndrome but also the values of the frustrated checks on individual qubits of the code and the channel model  ...  Furthermore we show that our decoding algorithm is superior to belief propagation algorithms using only the syndrome in the feedback procedure for all cases of the depolarizing channel.  ...  Acknowledgment The authors appreciate critical comments by D. Poulin  ... 
doi:10.1109/tit.2011.2169534 fatcat:mvhkhuqatfgh3kswdzdxo3vija

Hard decoding algorithm for optimizing thresholds under general Markovian noise

Christopher Chamberland, Joel Wallman, Stefanie Beale, Raymond Laflamme
2017 Physical Review A  
We use our hard decoding algorithm to study the performance of several error-correcting codes under various non-Pauli noise models by computing threshold values and failure rates for these codes.  ...  We compare the performance of our hard decoding algorithm to decoders optimized for depolarizing noise and show improvements in thresholds and reductions in failure rates by several orders of magnitude  ...  C. would like to acknowledge the support of QEII-GSST. C. C. would also like to thank Tomas Jochym-O'Connor for useful discussions and Steve Weiss for providing the necessary computational resources.  ... 
doi:10.1103/physreva.95.042332 fatcat:chzd4nszrzab5a52cuhvydew44

Soft Syndrome Decoding of Quantum LDPC Codes for Joint Correction of Data and Syndrome Errors [article]

Nithin Raveendran, Narayanan Rengaswamy, Asit Kumar Pradhan, Bane Vasić
2022 arXiv   pre-print
In this paper, we use this "soft" or analog information without the conventional discretization step to benefit the iterative decoders for decoding quantum low-density parity-check (QLDPC) codes.  ...  In particular, the new BP decoder with noisy syndrome performs as good as the standard BP decoder under ideal syndrome.  ...  Noise Model The single-qubit depolarizing channel, also known as the memoryless Pauli channel, is a widely studied error model characterized by the depolarizing probability p: the channel randomly introduces  ... 
arXiv:2205.02341v1 fatcat:exvksbvifvhupc3goyjktuugky

Stochastic resonance decoding for quantum LDPC codes

Nithin Raveendran, Priya J. Nadkarni, Shayan Srinivasa Garani, Bane Vasic
2017 2017 IEEE International Conference on Communications (ICC)  
The quantum error correction circuit is based on iterative syndrome decoding of quantum low-density parity check codes, and uses the positive effect of errors in gates to correct errors due to decoherence  ...  We introduce a stochastic resonance based decoding paradigm for quantum codes using an error correction circuit made of a combination of noisy and noiseless logic gates.  ...  Channel Model We consider a quantum depolarizing channel characterized by the depolarizing probability p.  ... 
doi:10.1109/icc.2017.7996747 dblp:conf/icc/RaveendranNGV17 fatcat:qiypns62kvcy3hpbqzowudihsm

A class of quantum LDPC codes: construction and performances under iterative decoding

Thomas Camara, Harold Ollivier, Jean-Pierre Tillich
2007 2007 IEEE International Symposium on Information Theory  
We provide several specific examples of quantum LDPC codes obtained by our method, together with numerical simulations over the depolarizing channel and the erasure channel.  ...  A generic method for constructing quantum LDPC codes is presented. We first explain how to overcome the difficulty of finding a set of low weight generators for the stabilizer group of the code.  ...  RESULTS We present simulation results of several quantum LDPC codes under iterative decoding (namely the SUM-PRODUCT algorithm applied to their Tanner Graph in their syndrome decoding form) on the depolarizing  ... 
doi:10.1109/isit.2007.4557324 dblp:conf/isit/CamaraOT07 fatcat:p7t4xtemzzeejkxa5wb56ff5dm

Error Correction for Reliable Quantum Computing [article]

Patricio Fuentes
2022 arXiv   pre-print
Stabilizer codes, a particular subclass of quantum codes, have enabled fast progress in the field of quantum error correction by allowing parallels to be drawn with the widely studied field of classical  ...  In this dissertation we study a phenomenon exclusive to the quantum paradigm, known as degeneracy, and its effects on the performance of sparse quantum codes.  ...  of QLDPC codes under BP decoding.  ... 
arXiv:2202.08599v1 fatcat:wnjowybbu5ad5m6r2nokqo43xa

On the iterative decoding of sparse quantum codes [article]

David Poulin, Yeojin Chung
2008 arXiv   pre-print
We address the problem of decoding sparse quantum error correction codes.  ...  For Pauli channels, this task can be accomplished by a version of the belief propagation algorithm used for decoding sparse classical codes. Quantum codes pose two new challenges however.  ...  DP is supported in part by the Gordon and Betty Moore Foundation through Caltech's Center for the Physics of Information, by the National Science Foundation under Grant No.  ... 
arXiv:0801.1241v2 fatcat:dc6i6kjdavdgzlvf7qxfhzufuu

The Encoding and Decoding Complexities of Entanglement-Assisted Quantum Stabilizer Codes [article]

Kao-Yueh Kuo, Ching-Yi Lai
2019 arXiv   pre-print
Finally we discuss decoding of entanglement-assisted quantum stabilizer codes and extend previously known computational hardness results on decoding quantum stabilizer codes.  ...  A raw state is mapped, by an encoding circuit, to a codeword so that the most likely quantum errors from a noisy quantum channel can be removed after a decoding process.  ...  Finally we discuss decoding of entanglement-assisted quantum stabilizer codes and extend previously known computational hardness results on decoding quantum stabilizer codes. I.  ... 
arXiv:1903.10013v2 fatcat:zfwl7fpgz5cdpmkt26lnb6zes4

Ultrahigh Error Threshold for Surface Codes with Biased Noise

David K. Tuckett, Stephen D. Bartlett, Steven T. Flammia
2018 Physical Review Letters  
The modified surface code still uses only weight-4 stabilizers on a square lattice, but merely requires measuring products of Y instead of Z around the faces, as this doubles the number of useful syndrome  ...  Our results demonstrate that large efficiency gains can be found by appropriately tailoring codes and decoders to realistic noise models, even under the locality constraints of topological codes.  ...  The proof of achievability involves using random codes, and it is generally hard to find explicit codes and decoders that perform at or above this rate for an arbitrary channel, especially if one wishes  ... 
doi:10.1103/physrevlett.120.050505 pmid:29481205 fatcat:gcsxyghqfbhkxlouqwnl45idpm

Degenerate Quantum LDPC Codes With Good Finite Length Performance

Pavel Panteleev, Gleb Kalachev
2021 Quantum  
We study the performance of medium-length quantum LDPC (QLDPC) codes in the depolarizing channel.  ...  It is shown that with the help of OSD-like post-processing the performance of the standard belief propagation (BP) decoder on many QLDPC codes can be improved by several orders of magnitude.  ...  This work was also supported by the Ministry of Science and Higher Education of the Russian Federation (Grant № 075-15-2020-801).  ... 
doi:10.22331/q-2021-11-22-585 fatcat:m4txlpstxnfexd74caawcupqly

Degenerate Quantum LDPC Codes With Good Finite Length Performance [article]

Pavel Panteleev, Gleb Kalachev
2021 arXiv   pre-print
We study the performance of medium-length quantum LDPC (QLDPC) codes in the depolarizing channel.  ...  It is shown that with the help of OSD-like post-processing the performance of the standard belief propagation (BP) decoder on many QLDPC codes can be improved by several orders of magnitude.  ...  This work was also supported by the Ministry of Science and Higher Education of the Russian Federation (Grant № 075-15-2020-801).  ... 
arXiv:1904.02703v3 fatcat:vqxddiq3urhtfo6b7pvwphibtm

Quantum Topological Error Correction Codes: The Classical-to-Quantum Isomorphism Perspective

Daryus Chandra, Zunaira Babar, Hung Viet Nguyen, Dimitrios Alanis, Panagiotis Botsinis, Soon Xin Ng, Lajos Hanzo
2018 IEEE Access  
Finally, we characterize the performance of QTECCs in the face of the quantum depolarizing channel in terms of both the quantum-bit error rate (QBER) and fidelity.  ...  Index Terms-quantum error correction codes, quantum stabilizer codes, quantum topological codes, lattice code, LDPC The authors are with the  ...  PERFORMANCE OF QUANTUM TOPOLOGICAL ERROR CORRECTION CODES In this treatise, we consider the performance of QTECCs under the popular quantum depolarizing channel.  ... 
doi:10.1109/access.2017.2784417 fatcat:qoqlrsus3be2necelaojeskwaa

On the Performance of Interleavers for Quantum Turbo Codes

Josu Etxezarreta Martinez, Pedro M. Crespo, Javier Garcia-Frías
2019 Entropy  
Consequently, inspired by the widely used classical-to-quantum isomorphism, this paper studies the integration of classical interleaving design methods into the paradigm of quantum turbo coding.  ...  Quantum turbo codes (QTC) have shown excellent error correction capabilities in the setting of quantum communication, achieving a performance less than 1 dB away from their corresponding hashing bounds  ...  The funding sponsors had no role in the design of the study; in the collection, analyses or interpretation of data; in the writing of the manuscript; nor in the decision to publish the results.  ... 
doi:10.3390/e21070633 pmid:33267346 fatcat:327qocgpmreofpsglh2xygndpm
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