Measurement cost of metric-aware variational quantum algorithms

Abstract

Variational quantum algorithms are promising tools for near-term quantum computers as their shallow circuits are robust to experimental imperfections. Their practical applicability, however, strongly depends on how many times their circuits need to be executed for sufficiently reducing shot-noise. We consider metric-aware quantum algorithms: variational 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 quantum Fisher information matrix as a metric tensor to correct the gradient vector for the co-dependence of the circuit parameters. We rigorously characterise 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.

17 pages, 3 figures

References in corpus (9)

• A Quantum Approximate Optimization Algorithm
• Hartree-Fock on a superconducting qubit quantum computer
• Simulating chemistry using quantum computers
• Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer
• Variational Quantum State Eigensolver
• A measurement-based variational quantum eigensolver
• Quantum Analytic Descent
• Operator Sampling for Shot-frugal Optimization in Variational Algorithms
• Pauli Partitioning with Respect to Gate Sets

Cited by in corpus (24)

• Variational Quantum Algorithms
• The Variational Quantum Eigensolver: a review of methods and best practices
• Fermionic partial tomography via classical shadows
• Estimating the gradient and higher-order derivatives on quantum hardware
• Exponential Error Suppression for Near-Term Quantum Devices
• Capacity and quantum geometry of parametrized quantum circuits
• Fisher Information in Noisy Intermediate-Scale Quantum Applications
• Scalable measures of magic resource for quantum computers
• The Dominant Eigenvector of a Noisy Quantum State
• Quantum Analytic Descent
• Symmetry enhanced variational quantum spin eigensolver
• Stochastic Gradient Line Bayesian Optimization for Efficient Noise-Robust Optimization of Parameterized Quantum Circuits
• Training variational quantum circuits with CoVaR: covariance root finding with classical shadows
• Adaptive variational quantum minimally entangled typical thermal states for finite temperature simulations
• Efficient quantum imaginary time evolution by drifting real time evolution: an approach with low gate and measurement complexity
• Connecting geometry and performance of two-qubit parameterized quantum circuits
• Natural parameterized quantum circuit
• Measurement optimization of variational quantum simulation by classical shadow and derandomization
• Algorithmic Shadow Spectroscopy
• Natural Gradient Optimization for Optical Quantum Circuits
• Exploring ab initio machine synthesis of quantum circuits
• Adaptive shot allocation for fast convergence in variational quantum algorithms
• Efficient classical calculation of the Quantum Natural Gradient
• Optimized numerical gradient and Hessian estimation for variational quantum algorithms