Measurement Cost of Metric-Aware Variational Quantum Algorithms

2020/05/31 by Barnaby van Straaten, Bálint Koczor · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Computer science #Fisher information #Mathematics #Matrix (chemical analysis) #Metric (unit) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum circuit #Quantum computer #Quantum error correction #Quantum information #Quantum many-body systems #Quantum mechanics #Quantum phase estimation algorithm #Qubit #Statistics #Theoretical computer science #quant-ph

paper · pdf · doi:10.1103/prxquantum.2.030324

published in PRX Quantum 2(3) (American Physical Society) · 17 pages, 3 figures

openalex publication_date 2021/08/10 · arxiv created 2021/09/09 · arxiv updated 2021/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider metric-aware quantum algorithms that use a quantum computer to efficiently estimate both a matrix and a vector object. For example, the recently introduced quantum natural gradient approach uses the Fisher matrix as a metric tensor to correct the gradient vector for the codependence of the circuit parameters. We rigorously characterize and upper bound the number of measurements required to determine an iteration step to a fixed precision, and propose a general approach for optimally distributing samples between matrix and vector entries. Finally, we establish that the number of circuit repetitions needed for estimating the quantum Fisher information matrix is asymptotically negligible for an increasing number of iterations and qubits.

Citations

• Quantum implementation of the unitary coupled cluster for simulating molecular electronic structure
• A Quantum Approximate Optimization Algorithm
• Quantum Simulation of Helium Hydride Cation in a Solid-State Spin Register
• A variational eigenvalue solver on a photonic quantum processor
• Quantum Computing in the NISQ era and beyond
• Quantum computational chemistry
• Pauli Partitioning with Respect to Gate Sets
• Minimizing State Preparations in Variational Quantum Eigensolver by Partitioning into Commuting Families
• Quantum Natural Gradient
• Operator Sampling for Shot-frugal Optimization in Variational Algorithms
• Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer