Flag Gadgets Based on Classical Codes
Fault-tolerant syndrome extraction is a key ingredient in implementing fault-tolerant quantum computation. While conventional methods use a number of extra qubits that are linear in the weight of the syndrome, several improvements have been introduced using flag gadgets. In this work, we develop a f...
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American Physical Society
2024-12-01
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| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/PRXQuantum.5.040340 |
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| author | Benjamin Anker Milad Marvian |
| author_facet | Benjamin Anker Milad Marvian |
| author_sort | Benjamin Anker |
| collection | DOAJ |
| description | Fault-tolerant syndrome extraction is a key ingredient in implementing fault-tolerant quantum computation. While conventional methods use a number of extra qubits that are linear in the weight of the syndrome, several improvements have been introduced using flag gadgets. In this work, we develop a framework to design flag gadgets using classical codes. Using this framework, we show how to perform fault-tolerant syndrome extraction for any stabilizer code with arbitrary distance using exponentially fewer qubits than conventional methods when qubit measurement and reset are relatively slow compared to a round of error correction. In particular, our method requires only (2t+1)t⌈log_{2}(w)⌉ flag qubits to fault-tolerantly measure a weight-w stabilizer. We further take advantage of the saving provided by our construction to fault-tolerantly measure multiple stabilizers using a single gadget and show that it maintains the same exponential advantage when it is used to fault-tolerantly extract the syndromes of quantum low-density parity-check codes. Using the developed framework, we perform computer-assisted search to find several small examples where our constructions reduce the number of qubits required. These small examples may be relevant to near-term experiments on small-scale quantum computers. |
| format | Article |
| id | doaj-art-e05f909b7a074591a8232140632691b9 |
| institution | OA Journals |
| issn | 2691-3399 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj-art-e05f909b7a074591a8232140632691b92025-08-20T01:59:14ZengAmerican Physical SocietyPRX Quantum2691-33992024-12-015404034010.1103/PRXQuantum.5.040340Flag Gadgets Based on Classical CodesBenjamin AnkerMilad MarvianFault-tolerant syndrome extraction is a key ingredient in implementing fault-tolerant quantum computation. While conventional methods use a number of extra qubits that are linear in the weight of the syndrome, several improvements have been introduced using flag gadgets. In this work, we develop a framework to design flag gadgets using classical codes. Using this framework, we show how to perform fault-tolerant syndrome extraction for any stabilizer code with arbitrary distance using exponentially fewer qubits than conventional methods when qubit measurement and reset are relatively slow compared to a round of error correction. In particular, our method requires only (2t+1)t⌈log_{2}(w)⌉ flag qubits to fault-tolerantly measure a weight-w stabilizer. We further take advantage of the saving provided by our construction to fault-tolerantly measure multiple stabilizers using a single gadget and show that it maintains the same exponential advantage when it is used to fault-tolerantly extract the syndromes of quantum low-density parity-check codes. Using the developed framework, we perform computer-assisted search to find several small examples where our constructions reduce the number of qubits required. These small examples may be relevant to near-term experiments on small-scale quantum computers.http://doi.org/10.1103/PRXQuantum.5.040340 |
| spellingShingle | Benjamin Anker Milad Marvian Flag Gadgets Based on Classical Codes PRX Quantum |
| title | Flag Gadgets Based on Classical Codes |
| title_full | Flag Gadgets Based on Classical Codes |
| title_fullStr | Flag Gadgets Based on Classical Codes |
| title_full_unstemmed | Flag Gadgets Based on Classical Codes |
| title_short | Flag Gadgets Based on Classical Codes |
| title_sort | flag gadgets based on classical codes |
| url | http://doi.org/10.1103/PRXQuantum.5.040340 |
| work_keys_str_mv | AT benjaminanker flaggadgetsbasedonclassicalcodes AT miladmarvian flaggadgetsbasedonclassicalcodes |