Finding good quantum codes using the Cartan form

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.

arXiv comment11 pages, 5 figures, v2: published version, minor changes

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Cited by in corpus (8)

• Fixed Depth Hamiltonian Simulation via Cartan Decomposition
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution
• Quantum variational learning for quantum error-correcting codes
• Achieving fault tolerance against amplitude-damping noise
• The Near-optimal Performance of Quantum Error Correction Codes
• Noise-adapted recovery circuits for quantum error correction
• Noise-adapted qudit codes for amplitude-damping noise
• Smallest quantum codes for amplitude damping noise