Characterizing quantum supremacy in near-term devices

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. arXiv:1608.00263v3 [quant-ph]

Classical boson sampling algorithms with superior performance to near-term experiments

“…Compared to a universal digital quantum computer, the resources required for experimental boson sampling appear much less demanding. This approach of designing quantum algorithms to demonstrate computational supremacy with nearterm experimental capabilities has inspired a raft of proposals suited to different hardware platforms [18][19][20] .Based on a simple architecture, the boson sampling problem is similarly straightforward to state. A number n of indistinguishable noninteracting bosons (for example, photons) should be injected into n input ports of a circuit comprised of a number m of linearly coupled bosonic modes.…”

“…Compared to a universal digital quantum computer, the resources required for experimental boson sampling appear much less demanding. This approach of designing quantum algorithms to demonstrate computational supremacy with nearterm experimental capabilities has inspired a raft of proposals suited to different hardware platforms [18][19][20] .…”

Discrepancies between asymptotic and exact spectral-gap analyses of quantum adiabatic barrier tunneling

“…Despite the simplicity of one-dimensional positionspace tunneling, we find that an asymptotic analysis of QAO spectral gaps for n → ∞, which give bounds on the adiabatic run time, fail to accurately describe the behavior of the tunneling for moderately large n. We find that n > 10 12 is needed to ensure that asymptotic expressions accurately describe behavior, to the point where polynomial and exponential run time scaling can be confused for lower n. Given the current and near-term sizes of quantum computer implementations [18], this failure of asymptotics casts doubt on the efficacy of using asymptotics to analyze the output of these systems or to predict their capabilities.…”

Quantum Mechanics, vacuum, particles, Gödel-Cohen incompleteness and the Universe

“…The origin of Quantum Mechanics is a crucial issue, not only for fundamental Physics but also for several fields of high-technology applications (electronics, computers [113,114], telecommunications [115,116]...). If conventional particles are actually excitations of a preonic vacuum, standard laws like Quantum Mechanics and relativity are expected to be low-energy approximations to a more fundamental (preonic) dynamics.…”