Variational quantum amplitude estimation

Abstract

We propose to perform amplitude estimation with the help of constant-depth quantum circuits that variationally approximate states during amplitude amplification. In the context of Monte Carlo (MC) integration, we numerically show that shallow circuits can accurately approximate many amplitude amplification steps. We combine the variational approach with maximum likelihood amplitude estimation [Y. Suzuki et al., Quantum Inf. Process. 19, 75 (2020)] in variational quantum amplitude estimation (VQAE). VQAE typically has larger computational requirements than classical MC sampling. To reduce the variational cost, we propose adaptive VQAE and numerically show in 6 to 12 qubit simulations that it can outperform classical MC sampling.

11 pages, 5 figures

References in corpus (18)

• Variational Quantum Algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• Polynomial-time quantum algorithm for the simulation of chemical dynamics
• Quantum Computing for Finance: State of the Art and Future Prospects
• Optimal Quantum Measurements of Expectation Values of Observables
• Hardware-efficient variational quantum algorithms for time evolution
• Filtering variational quantum algorithms for combinatorial optimization
• Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule
• Minimizing estimation runtime on noisy quantum computers
• Low depth algorithms for quantum amplitude estimation
• Variational inference with a quantum computer
• Prospects and challenges of quantum finance
• Amplitude estimation via maximum likelihood on noisy quantum computer
• Quantum Monte Carlo Integration: The Full Advantage in Minimal Circuit Depth
• A Jacobi Diagonalization and Anderson Acceleration Algorithm For Variational Quantum Algorithm Parameter Optimization
• Calculus on parameterized quantum circuits
• A Quantum Algorithm for the Sensitivity Analysis of Business Risks
• Normalized Gradient Descent for Variational Quantum Algorithms

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• Barren plateaus in quantum tensor network optimization
• Quantum algorithms for anomaly detection using amplitude estimation
• Quantum Dimensionality Reduction by Linear Discriminant Analysis
• Multivariate trace estimation in constant quantum depth
• Noisy quantum amplitude estimation without noise estimation
• Time-Optimal Quantum Driving by Variational Circuit Learning
• Noise tailoring for Robust Amplitude Estimation