Accelerating quantum imaginary-time evolution with random measurements

Abstract

Quantum imaginary-time evolution (QITE) is a promising tool to prepare thermal or ground states of Hamiltonians, as convergence is guaranteed when the evolved state overlaps with the ground state. However, its implementation using a a hybrid quantum/classical approach, where the dynamics of the parameters of the quantum circuit are derived by McLachlan's variational principle is impractical as the number of parameters $m$ increases, since each step in the evolution takes $\Theta (m^2)$ state preparations to calculate the quantum Fisher information matrix (QFIM). In this work, we accelerate QITE by rapid estimation of the QFIM, while conserving the convergence guarantees to the extent possible. To this end, we prove that if a parameterized state is rotated by a 2-design and measured in the computational basis, then the QFIM can be inferred from partial derivative cross correlations of the probability outcomes. One sample estimate costs only $\Theta (m)$ state preparations, leading to rapid QFIM estimation when a few samples suffice. The second family of estimators take greater liberties and replace QFIMs with averaged classical Fisher information matrices (CFIMs). In an extreme special case optimized for rapid (over accurate) descent, just one CFIM sample is drawn. We justify the second estimator family by proving rapid descent. Guided by these results, we propose the random-measurement imaginary-time evolution (RMITE) algorithm, which we showcase and test in several molecular systems, with the goal of preparing ground states.

21 pages, 8 figures; v2 published version

References in corpus (7)

• Simulated Quantum Computation of Molecular Energies
• Logical quantum processor based on reconfigurable atom arrays
• Bounds for the adiabatic approximation with applications to quantum computation
• Exact Parameterization of Fermionic Wave Functions via Unitary Coupled Cluster Theory
• A general framework for active space embedding methods: applications in quantum computing
• Random coordinate descent: a simple alternative for optimizing parameterized quantum circuits
• Random Natural Gradient

Cited by in corpus (7)

• Measurement-Induced Entanglement Phase Transition in Free Fermion Systems
• Adaptive variational quantum dynamics simulations with compressed circuits and fewer measurements
• Quantum simulation of the phase transition of the massive Thirring model
• Stochastic Schrödinger Equations for Quantum Reverse Diffusion
• Error and Resource Estimates of Variational Quantum Algorithms for Solving Differential Equations Based on Runge-Kutta Methods
• Adaptive time Compressed QITE (ACQ) and its geometrical interpretation
• Quantum imaginary time evolution and UD-MIS problem