Improving the speed of variational quantum algorithms for quantum error correction

Abstract

We consider the problem of devising a suitable Quantum Error Correction (QEC) procedures for a generic quantum noise acting on a quantum circuit. In general, there is no analytic universal procedure to obtain the encoding and correction unitary gates, and the problem is even harder if the noise is unknown and has to be reconstructed. The existing procedures rely on Variational Quantum Algorithms (VQAs) and are very difficult to train since the size of the gradient of the cost function decays exponentially with the number of qubits. We address this problem using a cost function based on the Quantum Wasserstein distance of order 1 ($Q{W}_1$). At variance with other quantum distances typically adopted in quantum information processing, $Q{W}_1$ lacks the unitary invariance property which makes it a suitable tool to avoid to get trapped in local minima. Focusing on a simple noise model for which an exact QEC solution is known and can be used as a theoretical benchmark, we run a series of numerical tests that show how, guiding the VQA search through the $Q{W}_1$, can indeed significantly increase both the probability of a successful training and the fidelity of the recovered state, with respect to the results one obtains when using conventional approaches.

References in corpus (7)

• Charge insensitive qubit design derived from the Cooper pair box
• Secure Quantum Key Distribution
• Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
• Coherence and Decay of Higher Energy Levels of a Superconducting Transmon Qubit
• Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
• Robust Quantum Error Correction via Convex Optimization
• Short Codes for Quantum Channels with One Prevalent Pauli Error Type

Cited by in corpus (5)

• Alleviating Barren Plateaus in Parameterized Quantum Machine Learning Circuits: Investigating Advanced Parameter Initialization Strategies
• Hückel Molecular Orbital Theory on a Quantum Computer: A Scalable System-Agnostic Variational Implementation with Compact Encoding
• Spanning Tree Matching Decoder for Quantum Surface Codes
• Quantum codes for asymmetric channels: ZZZY surface codes
• Critical Scaling of the Quantum Wasserstein Distance