Abstract: A method includes configuring a quantum annealer based on a parameter of a Hamiltonian and performing annealing using the configured quantum annealer to obtain output samples, wherein each sample of the output samples indicates state values of elements of the quantum annealer for a set of indices of the output samples. The method also includes providing, to an oracle, the output samples to obtain a set of oracle outputs. The method also includes determining an expectation based on the set of oracle outputs and updating a parameter indexed by the set of indices based on the expectation and a learning rate parameter.

Abstract: Some embodiments include a process, including obtaining, with a classical computer system, a mathematical problem to be solved by a quantum computing system, wherein: the quantum computing system comprises one or more quantum computers, the mathematical problem involves more variables than any of the one or more quantum computers have logical qubits, and solving the mathematical problem entails determining values of the variables; decomposing, with the classical computer system, the mathematical problem into a plurality of sub-problems, wherein decomposing the mathematical problem into the plurality of sub-problems comprises decomposing the mathematical problem with machine learning into quantum circuits; causing, with the classical computer system, the quantum computing system to solve each of the sub-problems and aggregate solutions to the sub-problems to determine a solution to the mathematical problem; and storing, with the classical computer system, the solution to the mathematical problem in memory.

Abstract: Some embodiments include a process, including obtaining, with a classical computer system, a mathematical problem to be solved by a quantum computing system, wherein: the quantum computing system comprises one or more quantum computers, the mathematical problem involves more variables than any of the one or more quantum computers have logical qubits, and solving the mathematical problem entails determining values of the variables; decomposing, with the classical computer system, the mathematical problem into a plurality of sub-problems, wherein decomposing the mathematical problem into the plurality of sub-problems comprises decomposing the mathematical problem with machine learning into quantum circuits; causing, with the classical computer system, the quantum computing system to solve each of the sub-problems and aggregate solutions to the sub-problems to determine a solution to the mathematical problem; and storing, with the classical computer system, the solution to the mathematical problem in memory.