Dynamical structure factors of dynamical quantum simulators

Abstract

Significance Quantum simulators promise to offer new insights into strongly correlated matter beyond what is accessible by means of classical computers. We propose dynamical quantum simulators (DQSs) as a method to simulate dynamical structure factors (DSFs) for system sizes considerably larger than what classical simulations can compute and provide complexity-theoretic evidence that they cannot be classically efficiently computed. Based on state-of-the-art experimental setups, we show how results from DQSs can be directly compared to experiments exploring properties of quantum materials. At the same time, we explore long-ranged spin systems: In particular, we show that the DSFs in DQSs can exhibit the signatures of excitation confinement in long-ranged models for which a comprehensive understanding is lacking. 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 bounded-error quantum polynomial time (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.