Quantifying the Sensitivity to Errors in Analog Quantum Simulation

Abstract

Quantum simulators are widely seen as one of the most promising near-term applications of quantum technologies. However, it remains unclear to what extent a noisy device can output reliable results in the presence of unavoidable imperfections. Here we propose a framework to characterize the performance of quantum simulators by linking the robustness of measured quantum expectation values to the spectral properties of the output observable, which in turn can be associated with its macroscopic or microscopic character. We show that, under general assumptions and on average over all states, imperfect devices are able to reproduce the dynamics of macroscopic observables accurately, while the relative error in the expectation value of microscopic observables is much larger on average. We experimentally demonstrate the universality of these features in a state-of-the-art quantum simulator and show that the predicted behavior is generic for a highly accurate device, without assuming any detailed knowledge about the nature of the imperfections.

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

“…In the experiment, the Josephson junction-based quantum processor was used to sample from the output distribution of (pseudo-)random circuits involving up to 53 qubits, thereby going beyond the capacities of modern supercomputers. As this sampling task may appear rather abstract, it is crucial to identify a wider range of relevant applications of near-term NISQ devices that can be performed despite their imperfect fidelities of one-and two-qubit gates and the lack of error correction [25][26][27][28].…”

Analog quantum simulation of chemical dynamics

“…In general, errors in analog simulation depend strongly on the observable, with global properties being more robust. 68,69 For example, in Fig. 5 with a Trotter step of 0.5 fs (blue lines), the population deviates by at most 0.05 in 300 fs, whereas the delity rapidly decays to less than 0.6 in the same time.…”

The effect of chaos on the simulation of quantum critical phenomena in analog quantum simulators

“…Errors arise from a variety of causes, which are typically characterized as control errors due to miscalibration or inhomogeneities, uncontrolled classical noise, and decoherence due to entanglement with a quantum reservoir. Recently there have been various studies about the reliability and quantum advantage of NISQ devices in the presence of such errors for applications including simulation [10][11][12][13][14], optimizations [16], and random sampling [17].…”