Characterizing Quantum Supremacy in Near-Term Devices

TL;DR

This paper investigates the potential for near-term quantum devices without error correction to achieve quantum supremacy by sampling from complex quantum circuit distributions, supported by extensive simulations and new benchmarking methods.

Contribution

It extends complexity theory to argue that classical simulation of such quantum sampling tasks is exponentially hard and introduces cross entropy as a practical benchmark for quantum supremacy.

Findings

Simulations with up to 42 qubits approach quantum supremacy.

Cross entropy effectively benchmarks quantum circuit fidelity.

Quantum supremacy feasible with approximately fifty superconducting qubits.

Abstract

A critical question for the field of quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond the capabilities of state-of-the-art classical computers, achieving so-called quantum supremacy. We study the task of sampling from the output distributions of (pseudo-)random quantum circuits, a natural task for benchmarking quantum computers. Crucially, sampling this distribution classically requires a direct numerical simulation of the circuit, with computational cost exponential in the number of qubits. This requirement is typical of chaotic systems. We extend previous results in computational complexity to argue more formally that this sampling task must take exponential time in a classical computer. We study the convergence to the chaotic regime using extensive supercomputer simulations, modeling circuits with up to 42 qubits - the largest quantum circuits simulated to date for a computational task that approaches quantum supremacy. We argue that while chaotic states are extremely sensitive to errors, quantum supremacy can be achieved in the near-term with approximately fifty superconducting qubits. We introduce cross entropy as a useful benchmark of quantum circuits which approximates the circuit fidelity. We show that the cross entropy can be efficiently measured when circuit simulations are available. Beyond the classically tractable regime, the cross entropy can be extrapolated and compared with theoretical estimates of circuit fidelity to define a practical quantum supremacy test.