Dynamical structure factors of dynamical quantum simulators

TL;DR

This paper explores the computational complexity of dynamical structure factors in quantum systems, demonstrating their potential for quantum simulation and proposing practical measurement methods across various quantum architectures.

Contribution

It establishes the BQP-hardness of accessible dynamical structure factors and introduces improved measurement setups for different quantum hardware.

Findings

Dynamical structure factors are computationally hard to simulate classically.

Quantum simulators can observe complex dynamical features beyond classical capabilities.

Proposed measurement methods are feasible in current quantum hardware architectures.

Abstract

The dynamical structure factor is one of the experimental quantities crucial in scrutinizing the validity of the microscopic description of strongly correlated systems. However, despite its long-standing importance, it is exceedingly difficult in generic cases to numerically calculate it, ensuring that the necessary approximations involved yield a correct result. Acknowledging this practical difficulty, we discuss in what way results on the hardness of classically tracking time evolution under local Hamiltonians are precisely inherited by dynamical structure factors; and hence offer in the same way the potential computational capabilities that dynamical quantum simulators do: We argue that practically accessible variants of the dynamical structure factors are BQP-hard for general local Hamiltonians. Complementing these conceptual insights, we improve upon a novel, readily available, measurement setup allowing for the determination of the dynamical structure factor in different architectures, including arrays of ultra-cold atoms, trapped ions, Rydberg atoms, and superconducting qubits. Our results suggest that quantum simulations employing near-term noisy intermediate scale quantum devices should allow for the observation of features of dynamical structure factors of correlated quantum matter in the presence of experimental imperfections, for larger system sizes than what is achievable by classical simulation.