Fault-tolerant quantum memory using low-depth random circuit codes
Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless. In this work, we design a fault-tolerant distillation protoco...
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-01-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.013040 |
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| author | Jon Nelson Gregory Bentsen Steven T. Flammia Michael J. Gullans |
| author_facet | Jon Nelson Gregory Bentsen Steven T. Flammia Michael J. Gullans |
| author_sort | Jon Nelson |
| collection | DOAJ |
| description | Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless. In this work, we design a fault-tolerant distillation protocol for preparing encoded states of one-dimensional random circuit codes even when all gates and measurements are subject to noise. This is sufficient for fault-tolerant quantum memory since these encoded states can then be used as ancillas for Steane error correction. We show through numerical simulations that our protocol can correct erasure errors up to an error rate of 2%. In addition, we also extend results in the code capacity setting by developing a maximum likelihood marginal decoder for depolarizing noise similar to work by Darmawan et al. [Phys. Rev. Res. 6, 023055 (2024)2643-156410.1103/PhysRevResearch.6.023055]. As in their work, we formulate the decoding problem as a tensor network contraction and show how to contract the network efficiently by exploiting the low-depth structure. Replacing the tensor network with a so-called “tropical” tensor network, we also show how to perform minimum weight decoding. With these decoders, we are able to numerically estimate the depolarizing error threshold of finite-rate random circuit codes and show that this threshold closely matches the hashing bound even when the decoding is suboptimal. |
| format | Article |
| id | doaj-art-bb7bb9c9284c4b86b917ff8948dbff15 |
| institution | Kabale University |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-bb7bb9c9284c4b86b917ff8948dbff152025-01-10T15:07:46ZengAmerican Physical SocietyPhysical Review Research2643-15642025-01-017101304010.1103/PhysRevResearch.7.013040Fault-tolerant quantum memory using low-depth random circuit codesJon NelsonGregory BentsenSteven T. FlammiaMichael J. GullansLow-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless. In this work, we design a fault-tolerant distillation protocol for preparing encoded states of one-dimensional random circuit codes even when all gates and measurements are subject to noise. This is sufficient for fault-tolerant quantum memory since these encoded states can then be used as ancillas for Steane error correction. We show through numerical simulations that our protocol can correct erasure errors up to an error rate of 2%. In addition, we also extend results in the code capacity setting by developing a maximum likelihood marginal decoder for depolarizing noise similar to work by Darmawan et al. [Phys. Rev. Res. 6, 023055 (2024)2643-156410.1103/PhysRevResearch.6.023055]. As in their work, we formulate the decoding problem as a tensor network contraction and show how to contract the network efficiently by exploiting the low-depth structure. Replacing the tensor network with a so-called “tropical” tensor network, we also show how to perform minimum weight decoding. With these decoders, we are able to numerically estimate the depolarizing error threshold of finite-rate random circuit codes and show that this threshold closely matches the hashing bound even when the decoding is suboptimal.http://doi.org/10.1103/PhysRevResearch.7.013040 |
| spellingShingle | Jon Nelson Gregory Bentsen Steven T. Flammia Michael J. Gullans Fault-tolerant quantum memory using low-depth random circuit codes Physical Review Research |
| title | Fault-tolerant quantum memory using low-depth random circuit codes |
| title_full | Fault-tolerant quantum memory using low-depth random circuit codes |
| title_fullStr | Fault-tolerant quantum memory using low-depth random circuit codes |
| title_full_unstemmed | Fault-tolerant quantum memory using low-depth random circuit codes |
| title_short | Fault-tolerant quantum memory using low-depth random circuit codes |
| title_sort | fault tolerant quantum memory using low depth random circuit codes |
| url | http://doi.org/10.1103/PhysRevResearch.7.013040 |
| work_keys_str_mv | AT jonnelson faulttolerantquantummemoryusinglowdepthrandomcircuitcodes AT gregorybentsen faulttolerantquantummemoryusinglowdepthrandomcircuitcodes AT steventflammia faulttolerantquantummemoryusinglowdepthrandomcircuitcodes AT michaeljgullans faulttolerantquantummemoryusinglowdepthrandomcircuitcodes |