Simulating hydrodynamics on noisy intermediate-scale quantum devices with random circuits

Abstract

In a recent milestone experiment, Google's processor Sycamore heralded the era of "quantum supremacy" by sampling from the output of (pseudo-)random circuits. We show that such random circuits provide tailor-made building blocks for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. Specifically, we propose an algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution to study hydrodynamics and to extract transport coefficients in the linear response regime. We numerically demonstrate the algorithm by simulating the buildup of spatiotemporal correlation functions in one-and twodimensional quantum spin systems, where we particularly scrutinize the inevitable impact of errors present in any realistic implementation. Importantly, we find that the hydrodynamic scaling of the correlations is highly robust with respect to the size of the Trotter step, which opens the door to reach nontrivial time scales with a small number of gates. While errors within the random circuit are shown to be irrelevant, we furthermore unveil that meaningful results can be obtained for noisy time evolutions with error rates achievable on near-term hardware. Our work emphasizes the practical relevance of random circuits on NISQ devices beyond the abstract sampling task.

Strong quantum computational advantage using a superconducting quantum processor

“…To characterize the overall performance of the quantum processor, we employ the task of random quantum circuit sampling for benchmarking. Random quantum circuit is outstanding candidate to demonstrate quantum computational advantages, and has potential applications in certified random bits [41], error correction [42], and hydrodynamics simulation [43].…”

Quantum versus Classical Dynamics in Spin Models: Chains, Ladders, and Square Lattices

“…5 the decay of C (M) (t) for the same values of ∆ and a fixed edge length L x = L y = 5. The overall situation appears to be similar to the one for the quasi-1D two-leg ladder, e.g., the relaxation is well described by a power law t −α with a diffusive exponent α, which is α = 1 in this 2D case 7 . For ∆ = 0.5 in Fig.…”

“…( 22) and the constant c is chosen in such a way that ρ r +c has nonnegative eigenvalues. Then, the correlation function can be rewritten as a standard expectation value 7,56,78 ,…”

“…Understanding the properties of quantum many-body systems out of equilibrium is a notoriously difficult but highly desired question in various disciplines of modern physics, ranging from fundamental aspects of statistical mechanics 1,2 to more applied issues in material science and quantum information technology. Quantum spin systems are of particular importance in this context, since they are directly relevant to the magnetism of compounds in nature 3 , can be realized in new experimental platforms 4,5 , or can be simulated on already available or future quantum computers 6,7 .…”