Quantum Error Correction via Convex Optimization

Abstract

We show that the problem of designing a quantum information error correcting procedure can be cast as a bi-convex optimization problem, iterating between encoding and recovery, each being a semidefinite program. For a given encoding operator the problem is convex in the recovery operator. For a given method of recovery, the problem is convex in the encoding scheme. This allows us to derive new codes that are locally optimal. We present examples of such codes that can handle errors which are too strong for codes derived by analogy to classical error correction techniques.

16 pages

References in corpus (9)

• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Distance measures to compare real and ideal quantum processes
• Internal Consistency of Fault-Tolerant Quantum Error Correction in Light of Rigorous Derivations of the Quantum Markovian Limit
• Optimum Quantum Error Recovery using Semidefinite Programming
• Iterative Optimization of Quantum Error Correcting Codes
• Robust Quantum Error Correction via Convex Optimization
• Purity and State Fidelity of Quantum Channels via Hamiltonians
• Empirical Determination of Bang-Bang Operations
• Suboptimal quantum-error-correcting procedure based on semidefinite programming

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