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- TL;DR Summary
- Google has publically claimed to have achieved quantum supremacy using their 53 qubit quantum computer. They have just posted a video on this alongside their publication in Nature.

Here is the paper, published today in Nature:

Arute et al. 2019, Quantum supremacy using a programmable superconducting processor

Abstract said:The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor##^1##. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits##^{2,3,4,5,6,7}## to create quantum states on 53 qubits, corresponding to a computational state-space of dimension ##2^{53}## (about ##10^{16}##). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times—our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy##^{8,9,10,11,12,13,14}## for this specific computational task, heralding a much-anticipated computing paradigm.