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It should be needed to sample one million samples, achieving the required XEB. Figure 1 shows a corresponding circuit example. The sampling process using the quantum circuit is computed as follows, 1. Quantum circuits: There have been many quantum circuits proposed as follows, Sycamore quantum [3]: It consists of 53 qubits and 20 cycles. For the Boson sampling problem, it only needs 200 seconds to finish this task, while it needs 10, 000 years for classical simulation. For the Gaussian Boson Sampling problem, it can use 200s to finish up to a million times compared with classical simulations.

Google's "quantum supremacy" announcement [3] has received broad questions from academia and industry due to the debatable estimate of 10, 000 years' running time for the classical simulation task on the Summit supercomputer. Has "quantum supremacy" already come? Or will it come in one or two decades later? To avoid hasty advertisements of "quantum supremacy" by tech giants or quantum startups and eliminate the cost of dedicating a team to the classical simulation task, we advocate an open-source approach to maintain a trustable benchmark performance. In this paper, we take a reinforcement learning approach for the classical simulation of quantum circuits and demonstrate its great potential by reporting an estimated simulation time of less than 4 days, a speedup of 5.40 over the state-of-the-art method. Specifically, we formulate the classical simulation task as a tensor network contraction ordering problem using the K-spin Ising model and employ a novel Hamiltonian-based reinforcement learning algorithm. Then, we evaluate the performance of classical simulation of quantum circuits. We develop a dozen of massively parallel environments to simulate quantum circuits.

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Outer products are indicated by the notation |ψ ϕ|. Pure states correspond to rank 1 mixed states. We will often label the mixed state corresponding to a pure state |ψ by ψ (instead of |ψ ψ|). Note that this is defined up to an absolute phase, i.e. |ψ and e The expectation value of an observable is given by Tr[M ρ]. Let binary random variable b {0, 1} be uniformly distributed. Similarly, let |ψ and |ϕ be arbitrary quantum states and M an obervable on their Hilbert space. Proof. 1. Choose ϕ = δ(p(x) > q(x)) δ(q(x) p(x)), where δ() is an indicator function from boolean clauses to {1, 0} which evaluates to 1 if its argument evaluates to true and evaluates to 0 if its argument is false.

In this work we make progress in understanding the relationship between learning models when given access to entangled measurements, separable measurements and statistical measurements in the quantum statistical query (QSQ) model. To this end we prove the following results 1. For learning Boolean concept classes, we show that the entangled and separable sample complexity are polynomially related.

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Quantum computing pioneer D-Wave Quantum on Tuesday announced the general availability of its sixth-generation quantum computer, the Advantage2. The company said the Advantage2 offers orders-of-magnitude greater performance compared to its prior system, expanding the tasks the company can accomplish in optimization problems. The machine even achieves the long-sought goal of quantum "supremacy," says the company, despite that term's highly controversial past. "This is a really historic moment for both D-Wave and the quantum computing industry," said D-Wave CEO Alan Baratz in an interview via Zoom. "Fundamentally, our technology is doing something that can't be touched classically."