Quantum Supremacy is Very Near

In 2016, IBM made a five-qubit quantum processor available to developers, researchers and programmers for experimentation via its cloud portal.

In May, 2017 IBM announced a 16 qubit processor for its cloud-based quantum computer and a more tightly engineered 17-qubit processor could be the basis for commercial systems. IBM is using wire-loop superconducting circuits. Google's 20-qubit processor is also using wire loop superconducting circuits. Google's Quantum Artificial Intelligence Lab expects to achieve quantum supremacy (quantum computers with a 49-qubit chip by the end of this year.

Superconducting circuits and trapped ions should both be able become larger than 50 qubits to become more powerful than any classical computer. Quantum volume measures the number and quality of calculations the machine can perform. Quantum volume includes additional factors such as how fast the qubits can perform the calculations and tolerant they are of errors. Adding more qubits can increase the rate of errors.

These IBM and Google quantum computers have universal qubits. Dwave has thousands of qubits for quantum annealing systems. Within a few years we should have universal quantum computers with thousands of qubits.

Quantum supremacy

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 - Characterizing Quantum Supremacy in Near-Term Devices