Low-weight high-distance error-correcting fermionic encodings

We perform an extended numerical search for practical fermion-to-qubit encodings with error-correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high minimum distance, low-weight fermionic logical operators, a s...

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Main Authors: Fedor Šimkovic IV, Martin Leib, Francisco Revson F. Pereira
Format: Article
Language:English
Published: American Physical Society 2024-11-01
Series:Physical Review Research
Online Access:http://doi.org/10.1103/PhysRevResearch.6.043123
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author Fedor Šimkovic IV
Martin Leib
Francisco Revson F. Pereira
author_facet Fedor Šimkovic IV
Martin Leib
Francisco Revson F. Pereira
author_sort Fedor Šimkovic IV
collection DOAJ
description We perform an extended numerical search for practical fermion-to-qubit encodings with error-correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high minimum distance, low-weight fermionic logical operators, a small qubit to fermionic mode ratio and a simple qubit connectivity graph including ancilla qubits for the measurement of stabilizers. Our strategy consists of a three-step procedure in which we: First generate encodings with code distances up to d≤4 by a brute-force enumeration technique; subsequently, we use these encodings as starting points and apply Clifford deformations to them which allows us to identify higher-distance codes with d≤7; finally, we optimize the hardware connectivity graphs of resulting encodings in terms of the graph thickness and the number of connections per qubit. We report multiple promising high-distance encodings which significantly improve the weights of stabilizers and logical operators compared to previously reported alternatives.
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spelling doaj-art-4b285bcb0a76439ca2b35a285d5c0b072024-11-12T15:06:21ZengAmerican Physical SocietyPhysical Review Research2643-15642024-11-016404312310.1103/PhysRevResearch.6.043123Low-weight high-distance error-correcting fermionic encodingsFedor Šimkovic IVMartin LeibFrancisco Revson F. PereiraWe perform an extended numerical search for practical fermion-to-qubit encodings with error-correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high minimum distance, low-weight fermionic logical operators, a small qubit to fermionic mode ratio and a simple qubit connectivity graph including ancilla qubits for the measurement of stabilizers. Our strategy consists of a three-step procedure in which we: First generate encodings with code distances up to d≤4 by a brute-force enumeration technique; subsequently, we use these encodings as starting points and apply Clifford deformations to them which allows us to identify higher-distance codes with d≤7; finally, we optimize the hardware connectivity graphs of resulting encodings in terms of the graph thickness and the number of connections per qubit. We report multiple promising high-distance encodings which significantly improve the weights of stabilizers and logical operators compared to previously reported alternatives.http://doi.org/10.1103/PhysRevResearch.6.043123
spellingShingle Fedor Šimkovic IV
Martin Leib
Francisco Revson F. Pereira
Low-weight high-distance error-correcting fermionic encodings
Physical Review Research
title Low-weight high-distance error-correcting fermionic encodings
title_full Low-weight high-distance error-correcting fermionic encodings
title_fullStr Low-weight high-distance error-correcting fermionic encodings
title_full_unstemmed Low-weight high-distance error-correcting fermionic encodings
title_short Low-weight high-distance error-correcting fermionic encodings
title_sort low weight high distance error correcting fermionic encodings
url http://doi.org/10.1103/PhysRevResearch.6.043123
work_keys_str_mv AT fedorsimkoviciv lowweighthighdistanceerrorcorrectingfermionicencodings
AT martinleib lowweighthighdistanceerrorcorrectingfermionicencodings
AT franciscorevsonfpereira lowweighthighdistanceerrorcorrectingfermionicencodings