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arXiv · 1911.02965

Finding good quantum codes using the Cartan form

Akshaya Jayashankar·Anjala M Babu·Hui Khoon Ng·Prabha Mandayam
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Abstract

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.

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Akshaya Jayashankar, Anjala M Babu, Hui Khoon Ng, Prabha Mandayam. 2019-11-07. Finding good quantum codes using the Cartan form. https://doi.org/10.1103/physreva.101.042307

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