Automated discovery of logical gates for quantum error correction

Hongxiang Chen; Michael Vasmer; Nikolas P. Breuckmann; Edward Grant

doi:10.26421/QIC22.11-12-3

Automated discovery of logical gates for quantum error correction

Hongxiang Chen, Michael Vasmer, Nikolas P. Breuckmann, Edward Grant

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

132 Downloads (Pure)

Abstract

Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure which generates logical operations given known encoding and correcting procedures. Our technique is to use variational circuits for learning both the logical gates and the physical operations implementing them. This procedure can be implemented on near-term quantum computers via quantum process tomography. It enables automatic discovery of logical gates from analytically designed error correcting codes and can be extended to error correcting codes found by numerical optimizations. We test the procedure by simulation on classical computers on small quantum codes of four qubits to fifteen qubits and show that it finds most logical gates known in the current literature. Additionally, it generates logical gates not found in the current literature for the [[5,1,2]] code, the [[6,3,2]] code, and the [[8,3,2]] code.

Original language	English
Pages (from-to)	947-964
Number of pages	18
Journal	Quantum Information and Computation
Volume	22
Issue number	11-12
DOIs	https://doi.org/10.26421/QIC22.11-12-3
Publication status	Published - 4 Aug 2022

Bibliographical note

Funding Information:
We wish to acknowledge the usage of high performance computing cluster from Department of Computer Science, University College London in completion of this project. H.C. acknowledges the support through a Teaching Fellowship from UCL. E.G. is supported by the UK Engineering and Physical Sciences Research Council (EPSRC) [EP/P510270/1] M.V. at the Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Economic Development, Job Creation and Trade. N.P.B. is supported by the UCLQ Fellowship.

Publisher Copyright:
© Rinton Press.

Keywords

Error correction
Machine learning
Quantum computation

Access to Document

10.26421/QIC22.11-12-3

Full-text PDF (accepted manuscript)
This is the accepted author manuscript (AAM). The final published version (version of record) is available online via Rinton Press athttps://doi.org/10.26421/QIC22.11-12-3. Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 503 KB

Handle.net

Persistent link

Cite this

@article{7b6b046b703d4f27885f2311060f5e23,

title = "Automated discovery of logical gates for quantum error correction",

abstract = "Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure which generates logical operations given known encoding and correcting procedures. Our technique is to use variational circuits for learning both the logical gates and the physical operations implementing them. This procedure can be implemented on near-term quantum computers via quantum process tomography. It enables automatic discovery of logical gates from analytically designed error correcting codes and can be extended to error correcting codes found by numerical optimizations. We test the procedure by simulation on classical computers on small quantum codes of four qubits to fifteen qubits and show that it finds most logical gates known in the current literature. Additionally, it generates logical gates not found in the current literature for the [[5,1,2]] code, the [[6,3,2]] code, and the [[8,3,2]] code.",

keywords = "Error correction, Machine learning, Quantum computation",

author = "Hongxiang Chen and Michael Vasmer and Breuckmann, {Nikolas P.} and Edward Grant",

note = "Funding Information: We wish to acknowledge the usage of high performance computing cluster from Department of Computer Science, University College London in completion of this project. H.C. acknowledges the support through a Teaching Fellowship from UCL. E.G. is supported by the UK Engineering and Physical Sciences Research Council (EPSRC) [EP/P510270/1] M.V. at the Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Economic Development, Job Creation and Trade. N.P.B. is supported by the UCLQ Fellowship. Publisher Copyright: {\textcopyright} Rinton Press.",

year = "2022",

month = aug,

day = "4",

doi = "10.26421/QIC22.11-12-3",

language = "English",

volume = "22",

pages = "947--964",

journal = "Quantum Information and Computation",

issn = "1533-7146",

publisher = "Rinton Press Inc.",

number = "11-12",

}

TY - JOUR

T1 - Automated discovery of logical gates for quantum error correction

AU - Chen, Hongxiang

AU - Vasmer, Michael

AU - Breuckmann, Nikolas P.

AU - Grant, Edward

N1 - Funding Information: We wish to acknowledge the usage of high performance computing cluster from Department of Computer Science, University College London in completion of this project. H.C. acknowledges the support through a Teaching Fellowship from UCL. E.G. is supported by the UK Engineering and Physical Sciences Research Council (EPSRC) [EP/P510270/1] M.V. at the Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Economic Development, Job Creation and Trade. N.P.B. is supported by the UCLQ Fellowship. Publisher Copyright: © Rinton Press.

PY - 2022/8/4

Y1 - 2022/8/4

N2 - Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure which generates logical operations given known encoding and correcting procedures. Our technique is to use variational circuits for learning both the logical gates and the physical operations implementing them. This procedure can be implemented on near-term quantum computers via quantum process tomography. It enables automatic discovery of logical gates from analytically designed error correcting codes and can be extended to error correcting codes found by numerical optimizations. We test the procedure by simulation on classical computers on small quantum codes of four qubits to fifteen qubits and show that it finds most logical gates known in the current literature. Additionally, it generates logical gates not found in the current literature for the [[5,1,2]] code, the [[6,3,2]] code, and the [[8,3,2]] code.

AB - Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure which generates logical operations given known encoding and correcting procedures. Our technique is to use variational circuits for learning both the logical gates and the physical operations implementing them. This procedure can be implemented on near-term quantum computers via quantum process tomography. It enables automatic discovery of logical gates from analytically designed error correcting codes and can be extended to error correcting codes found by numerical optimizations. We test the procedure by simulation on classical computers on small quantum codes of four qubits to fifteen qubits and show that it finds most logical gates known in the current literature. Additionally, it generates logical gates not found in the current literature for the [[5,1,2]] code, the [[6,3,2]] code, and the [[8,3,2]] code.

KW - Error correction

KW - Machine learning

KW - Quantum computation

UR - http://www.scopus.com/inward/record.url?scp=85137259026&partnerID=8YFLogxK

U2 - 10.26421/QIC22.11-12-3

DO - 10.26421/QIC22.11-12-3

M3 - Article (Academic Journal)

SN - 1533-7146

VL - 22

SP - 947

EP - 964

JO - Quantum Information and Computation

JF - Quantum Information and Computation

IS - 11-12

ER -

Automated discovery of logical gates for quantum error correction

Abstract

Bibliographical note

Keywords

Access to Document

Handle.net

Other files and links

Fingerprint

Cite this