Finding good quantum codes using the Cartan form
We present a simple and fast numerical procedure to search for good quantum codes for storing logical qubits in the presence of independent per-qubit noise. In a key departure from past work, we use the worst-case fidelity as the figure of merit for quantifying code performance, a much better indica...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2021
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| Online Access: | https://hdl.handle.net/10356/147495 |
| _version_ | 1811685129619243008 |
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| author | Jayashankar, Akshaya Babu, Anjala, M. Ng, Hui Khoon Mandayam, Prabha |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Jayashankar, Akshaya Babu, Anjala, M. Ng, Hui Khoon Mandayam, Prabha |
| author_sort | Jayashankar, Akshaya |
| collection | NTU |
| description | We present a simple and fast numerical procedure to search for good quantum codes for storing logical qubits in the presence of independent per-qubit noise. In a key departure from past work, we use the worst-case fidelity as the figure of merit for quantifying code performance, a much better indicator of code quality than, say, entanglement fidelity. Yet, our algorithm does not suffer from inefficiencies usually associated with the use of worst-case fidelity. Specifically, using a near-optimal recovery map, we are able to reduce the triple numerical optimization needed for the search to a single optimization over the encoding map. We can further reduce the search space using the Cartan decomposition, focusing our search over the nonlocal degrees of freedom resilient against independent per-qubit noise, while not suffering much in code performance. |
| first_indexed | 2024-10-01T04:39:37Z |
| format | Journal Article |
| id | ntu-10356/147495 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:39:37Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | ntu-10356/1474952023-02-28T19:30:03Z Finding good quantum codes using the Cartan form Jayashankar, Akshaya Babu, Anjala, M. Ng, Hui Khoon Mandayam, Prabha School of Physical and Mathematical Sciences Science::Physics Quantum Channels Quantum Error Correction We present a simple and fast numerical procedure to search for good quantum codes for storing logical qubits in the presence of independent per-qubit noise. In a key departure from past work, we use the worst-case fidelity as the figure of merit for quantifying code performance, a much better indicator of code quality than, say, entanglement fidelity. Yet, our algorithm does not suffer from inefficiencies usually associated with the use of worst-case fidelity. Specifically, using a near-optimal recovery map, we are able to reduce the triple numerical optimization needed for the search to a single optimization over the encoding map. We can further reduce the search space using the Cartan decomposition, focusing our search over the nonlocal degrees of freedom resilient against independent per-qubit noise, while not suffering much in code performance. Published version 2021-04-06T04:11:34Z 2021-04-06T04:11:34Z 2019 Journal Article Jayashankar, A., Babu, A. M., Ng, H. K. & Mandayam, P. (2019). Finding good quantum codes using the Cartan form. Physical Review A, 101(4). https://dx.doi.org/10.1103/PhysRevA.101.042307 2469-9926 https://hdl.handle.net/10356/147495 10.1103/PhysRevA.101.042307 2-s2.0-85084935045 4 101 en Physical Review A © 2020 American Physical Society. All rights reserved. This paper was published in Physical Review A and is made available with permission of American Physical Society. application/pdf |
| spellingShingle | Science::Physics Quantum Channels Quantum Error Correction Jayashankar, Akshaya Babu, Anjala, M. Ng, Hui Khoon Mandayam, Prabha Finding good quantum codes using the Cartan form |
| title | Finding good quantum codes using the Cartan form |
| title_full | Finding good quantum codes using the Cartan form |
| title_fullStr | Finding good quantum codes using the Cartan form |
| title_full_unstemmed | Finding good quantum codes using the Cartan form |
| title_short | Finding good quantum codes using the Cartan form |
| title_sort | finding good quantum codes using the cartan form |
| topic | Science::Physics Quantum Channels Quantum Error Correction |
| url | https://hdl.handle.net/10356/147495 |
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