Finding good quantum codes using the Cartan form

• Main Authors: Jayashankar, Akshaya, Babu, Anjala, M., Ng, Hui Khoon, Mandayam, Prabha
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2021
• Subjects: Science::Physics; Quantum Channels; Quantum Error Correction
• Online Access: https://hdl.handle.net/10356/147495
• Institution: Nanyang Technological University

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.