AQC 2016 - Towards Quantum Supremacy with Pre-Fault-Tolerant Devices

A Google TechTalk, June 28, 2016, presented by Sergio Boixo (Google) 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 random quantum circuits, a natural task for benchmarking quantum computers. Crucially this requires a direct numerical simulation to solve classically, with computational time and space cost exponential in the size of Hilbert space. This requirement is typical of chaotic systems. 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 show that while chaotic states are extremely sensitive to errors, quantum supremacy can be achieved in the near-term with approximately fifty superconducting qubits. We extend previous results to argue that performing this task with a fault tolerant quantum computer would have strong implications in computational complexity theory. 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. Presented at the Adiabatic Quantum Computing Conference, June 26-29, 2016, at Google's Los Angeles office.