Scaling adaptive quantum simulation algorithms via operator pool tiling

TL;DR

This paper introduces operator pool tiling, a method to create problem-specific pools for adaptive quantum simulation, enabling efficient scaling to larger systems by leveraging insights from smaller instances.

Contribution

The paper presents a novel operator pool tiling technique that constructs tailored pools for large quantum systems based on smaller problem instances, improving efficiency.

Findings

Effective operator pools for large systems derived from smaller instances.

Demonstrated success on 1D and 2D strongly correlated quantum spin models.

Pool tiling is broadly applicable to lattice-structured problems.

Abstract

Adaptive variational quantum simulation algorithms use information from the quantum computer to dynamically create optimal trial wavefunctions for a given problem Hamiltonian. A key ingredient in these algorithms is a predefined operator pool from which trial wavefunctions are constructed. Finding suitable pools is critical for the efficiency of the algorithm as the problem size increases. Here, we present a technique called operator pool tiling that facilitates the construction of problem-tailored pools for arbitrarily large problem instances. By first performing an ADAPT-VQE calculation on a smaller instance of the problem using a large, but computationally inefficient operator pool, we extract the most relevant operators and use them to design more efficient pools for larger instances. We demonstrate the method here on strongly correlated quantum spin models in one and two dimensions, finding that ADAPT automatically finds a highly effective ansatz for these systems. Given that many problems, such as those arising in condensed matter physics, have a naturally repeating lattice structure, we expect the pool tiling method to be a widely applicable technique apt for such systems.