Entanglement Diagnostics for Efficient Quantum Computation

TL;DR

This paper introduces entanglement diagnostics to evaluate and optimize the performance of variational quantum circuits, linking entanglement measures to optimization accuracy and identifying effective circuit depths.

Contribution

It establishes a connection between entanglement diagnostics and optimization success, providing insights into circuit depth and parameter requirements for different Hamiltonian problems.

Findings

Entanglement diagnostics can identify optimal circuit depths for local Hamiltonian problems.

High entanglement alone is insufficient for approximating volume-law entangled states.

A large number of parameters are necessary for effective optimization of highly entangled target states.

Abstract

We consider information spreading measures in randomly initialized variational quantum circuits and introduce entanglement diagnostics for efficient variational quantum/classical computations. We establish a robust connection between entanglement measures and optimization accuracy by solving two eigensolver problems for Ising Hamiltonians with nearest-neighbor and long-range spin interactions. As the circuit depth affects the average entanglement of random circuit states, the entanglement diagnostics can identify a high-performing depth range for optimization tasks encoded in local Hamiltonians. We argue, based on an eigensolver problem for the Sachdev-Ye-Kitaev model, that entanglement alone is insufficient as a diagnostic to the approximation of volume-law entangled target states and that a large number of circuit parameters is needed for such an optimization task.