Finding good quantum codes using the Cartan form
| Autor: | Jayashankar, Akshaya, Babu, Anjala M, Ng, Hui Khoon, Mandayam, Prabha |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Phys. Rev. A 101, 042307 (2020) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevA.101.042307 |
| Popis: | 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. Comment: 11 pages, 5 figures, v2: published version, minor changes |
| Databáze: | arXiv |
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