Dynamical structure factors of dynamical quantum simulators

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 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.

Simulating Hydrodynamics on Noisy Intermediate-Scale Quantum Devices with Random Circuits

“…Complementary to well-known approaches to obtain correlation functions such as Eq. (1) on a quantum computer [60][61][62] (see also [63]), the scheme proposed in this Letter operates without requiring an overhead of bath or ancilla qubits for initial-state preparation and measurement. Rather, it combines the random-circuit technology already realized on NISQ devices [24] with "quantum parallelism" [53,64], as the time evolution of a single random state jψ R;l 0 i suffices to capture the full ensemble average (1).…”

Quantum simulation and ground state preparation for the honeycomb Kitaev model

“…Then, preparing the Kitaev GS at zero field, simulation of dynamics for h = 0 opens the route to quench studies of strongly correlated spins [18]. Let us define bond-bond correlations functions [108,109] using time-dependent expectations of two-body operators m kk (t) = ψ θ | Û † (t) Ẑk Ẑk Û (t)|ψ θ and four-body operators c kk ll (t) = ψ θ | Û † (t) Ẑk Ẑk Û (t) Ẑl Ẑl |ψ θ . We define the static correlator as C ii jj = c ii jj (0) − m ii (0)m jj (0), and the dynamics correlator as S ii jj (t) = c ii jj (t) − m ii (t)m jj (0).…”

“…We define the static correlator as C ii jj = c ii jj (0) − m ii (0)m jj (0), and the dynamics correlator as S ii jj (t) = c ii jj (t) − m ii (t)m jj (0). Such correlations can be accessed by dynamical QS with a proven advantage over classical computation [109].…”

Nuclear two point correlation functions on a quantum-computer

“…The linear response of quantum systems is a promising candidate for early applications of quantum computers [3]. Linear response, as measured for example in neutron scattering from materials or electron and neutrino scattering from nuclei directly probes the structure and dynamics of the underlying system.…”