Noise-Resilient Variational Hybrid Quantum-Classical Optimization

Abstract

Variational hybrid quantum-classical optimization represents one of the most promising avenue to show the advantage of nowadays noisy intermediate-scale quantum computers in solving hard problems, such as finding the minimum-energy state of a Hamiltonian or solving some machine-learning tasks. In these devices noise is unavoidable and impossible to error-correct, yet its role in the optimization process is not well understood, especially from the theoretical viewpoint. Here we consider a minimization problem with respect to a variational state, iteratively obtained via a parametric quantum circuit, taking into account both the role of noise and the stochastic nature of quantum measurement outcomes. We show that the accuracy of the result obtained for a fixed number of iterations is bounded by a quantity related to the Quantum Fisher Information of the variational state. Using this bound, we study the convergence property of the quantum approximate optimization algorithm under realistic noise models, showing the robustness of the algorithm against different noise strengths.

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• Variational Quantum Algorithms
• The Variational Quantum Eigensolver: a review of methods and best practices
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• A Review on Quantum Approximate Optimization Algorithm and its Variants
• Robust data encodings for quantum classifiers
• Hybrid Quantum-Classical Convolutional Neural Networks
• Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation
• Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule
• Measurement cost of metric-aware variational quantum algorithms
• Training Saturation in Layerwise Quantum Approximate Optimisation
• Fast and reliable entanglement distribution with quantum repeaters: principles for improving protocols using reinforcement learning
• Stochastic noise can be helpful for variational quantum algorithms
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• Ability of error correlations to improve the performance of variational quantum algorithms
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• How to enhance quantum generative adversarial learning of noisy information
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• Evaluating the Resilience of Variational Quantum Algorithms to Leakage Noise
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