Estimating the gradient and higher-order derivatives on quantum hardware

2020/08/31 by Andrea Mari, Thomas R. Bromley, Nathan Killoran · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Computer science #Divergence (linguistics) #Estimator #Hessian matrix #Hyperparameter #Mathematical optimization #Mathematics #Metric (unit) #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum circuit #Quantum computer #Quantum error correction #Quantum mechanics #Quantum phase estimation algorithm #Quantum-Dot Cellular Automata #Simple (philosophy) #Statistics #Tensor (intrinsic definition) #quant-ph

paper · pdf · doi:10.1103/physreva.103.012405

published as Phys. Rev. A 103, 012405 (2021) · Source code for the numerics in this paper can be found at https://github.com/XanaduAI/derivatives-of-variational-circuits (v2) updated Fubini-Study metric definition and corrected typo in resulting equations

openalex publication_date 2021/01/11 · arxiv created 2021/02/26 · arxiv updated 2021/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

The authors show how to evaluate, with near-term quantum computers, high-order derivatives of expectation values with respect to the variational parameters of quantum circuits. The authors also study how such derivatives are affected by statistical noise. Their theoretical results are then tested with both numerical simulations and experiments.

Citations

• A Quantum Approximate Optimization Algorithm
• Quantum Geometric Tensor (Fubini-Study Metric) in Simple Quantum System: A pedagogical Introduction
• A variational eigenvalue solver on a photonic quantum processor
• Hybrid Quantum-Classical Approach to Quantum Optimal Control
• Evaluating analytic gradients on quantum hardware
• Quantum Natural Gradient
• Operator Sampling for Shot-frugal Optimization in Variational Algorithms
• Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer
• PennyLane: Automatic differentiation of hybrid quantum-classical computations

Cited by

• LogosQ: A High-Performance and Type-Safe Quantum Computing Library in Rust
• Preconditioning Natural and Second Order Gradient Descent in Quantum Optimization: A Performance Benchmark