as a strategy for demonstrating supremacy. Boson sampling This computing paradigm based upon sending identical photons through a linear-optical network can solve certain sampling and search problems that, assuming a few complexity-theoretical conjectures (that calculating the permanent of Gaussian matrices is #P-Hard and that the polynomial hierarchy does not collapse) are intractable for classical computers. However, it has been shown that boson sampling in a system with large enough loss and noise can be simulated efficiently. The largest experimental implementation of boson sampling to date had 6 modes so could handle up to 6 photons at a time. The best proposed classical algorithm for simulating boson sampling runs in time for a system with n photons and m output modes. BosonSampling is an open-source implementation in R. The algorithm leads to an estimate of 50 photons required to demonstrate quantum supremacy with boson sampling. Sampling the output distribution of random quantum circuits The best known algorithm for simulating an arbitrary random quantum circuit requires an amount of time that scales exponentially with the number of qubits, leading one group to estimate that around 50 qubits could be enough to demonstrate quantum supremacy. Bouland, Fefferman, Nirkhe and Vazirani gave, in 2018, theoretical evidence that efficiently simulating a random quantum circuit would require a collapse of the computational polynomial hierarchy. Google had announced its intention to demonstrate quantum supremacy by the end of 2017 by constructing and running a 49-qubit chip that would be able to sample distributions inaccessible to any current classical computers in a reasonable amount of time. The largest universal quantum circuit simulator running on classical supercomputers at the time was able to simulate 48 qubits. But for particular kinds of circuits, larger quantum circuit simulations with 56 qubits are possible. This may require increasing the number of qubits to demonstrate quantum supremacy. On October 23, 2019, Google published the results of this quantum supremacy experiment in the Nature article, “Quantum Supremacy Using a Programmable Superconducting Processor” in which they developed a new 53-qubit processor, named “Sycamore”, that is capable of fast, high-fidelity quantum logic gates, in order to perform the benchmark testing. Google claims that their machine performed the target computation in 200 seconds, and estimated that their classical algorithm would take 10,000 years in the world's fastest supercomputer to solve the same problem. IBM disputed this claim, saying that an improved classical algorithm should be able to