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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| Format: | Article |
| Language: | English |
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American Physical Society
2024-11-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.6.043123 |
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| _version_ | 1846169607194279936 |
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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. |
| format | Article |
| id | doaj-art-4b285bcb0a76439ca2b35a285d5c0b07 |
| institution | Kabale University |
| issn | 2643-1564 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| 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 |