Simulating quantum many-body dynamics on noisy intermediate-scale quantum devices with typicality

In a recent milestone experiment, Google's processor Sycamore heralded the era of "quantum supremacy" by sampling from the output of (pseudo-)random circuits. By leveraging the concept of quantum typicality (QT), we show that such random circuits provide tailor-made building blocks for simulating the dynamics of quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. QT can be understood as a form of quantum parallelism and asserts that even a single quantum state, drawn at random from a high-dimensional Hilbert space, can mimic the properties of the full statistical ensemble. Here, we propose a QT-based algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution to simulate hydrodynamics and study transport properties in the linear response regime, which we numerically exemplify for one- and two-dimensional quantum spin systems. While the algorithm operates without an overhead of bath or ancilla qubits for initial-state preparation and measurement, our numerics further suggest that it is comparatively robust against systematic Trotter errors and noisy gates. Our work emphasizes the practical relevance of random circuits on NISQ devices beyond the abstract sampling task.