Abstract: A method for machine learning using a quantum system is provided. A neural network is associated with the quantum system. The method includes initializing the quantum system in an initial quantum state, and, for each configuration of a number of configurations taken from the training data set, encoding the configuration in input qubits that form a subset of the set of primary qubits, and, for each configuration of the number of configurations, performing N rounds of operations. Each round includes applying a sequence of unitary operators acting on at least a portion of the quantum system, and performing a measurement of at least a portion of the quantum system. The method includes performing a measurement of one or more ancillary qubits. The method includes, based at least on the measurement of the one or more ancillary qubits, determining at least one weight of a connection of the plurality of connections.

Abstract: A method of determining a quantum operation control layout for a quantum computation on a quantum system is provided. The quantum computation is to be carried out on constituents of the quantum system arranged in accordance with a mesh. Vertices of the mesh represent possible sites for the constituents of the quantum system. Each cell of the mesh indicates that quantum interactions between constituents of the quantum system arranged in that cell are possible during the quantum computation. The method includes providing a data set including data representing hyperedges of a hypergraph. The method includes determining a set of generalized cycles. The method includes determining a mesh mapping that maps data representing the hyperedges of the hypergraph or of the enlarged hypergraph to the vertices of the mesh. The method includes generating the quantum operation control layout. The quantum operation control layout includes data indicating layout vertices of the mesh.

Abstract: A method of computing a solution to a computational problem using a quantum system comprising a plurality of qubits includes encoding the computational problem into a single-body problem Hamiltonian comprising a plurality of adjustable parameters, and encoding comprises determining a problem-encoding configuration for the plurality of adjustable parameters.

Abstract: This application concerns methods and apparatus for performing a quantum algorithm of logical qubits. The quantum algorithm is performed on a quantum system of physical qubits. The method includes providing a quantum system comprising a plurality of physical qubits in a spatial arrangement. The number of physical qubits is larger than the number of logical qubits. The logical qubits are encoded into physical qubits. A physical qubit represents either the parity of two or more logical qubits or a single logical qubit. Constraint-fulfilling sets of physical qubits fulfil constraints and each constraint-fulfilling set comprises a number of physical qubits such that every logical qubit is represented by zero or an even number of physical qubits in that set. The method includes enabling quantum interactions between logical qubits by performing quantum interactions on physical qubits. Further, at least a portion of the physical qubits is measured to obtain a readout.

Abstract: A method of computing a solution to a computational problem using a quantum system comprising a plurality of qubits is provided. The method includes encoding the computational problem into a problem Hamiltonian of the quantum system, wherein the problem Hamiltonian is a single-body Hamiltonian including a plurality of adjustable parameters, and wherein the encoding includes determining, from the computational problem, a problem-encoding configuration for the plurality of adjustable parameters. The method further includes evolving the quantum system from an initial quantum state towards a ground state of a final Hamiltonian of the quantum system, wherein the final Hamiltonian is the sum of the problem Hamiltonian and a short-range Hamiltonian, wherein the plurality of adjustable parameters of the problem Hamiltonian are in the problem-encoding configuration and wherein the short-range Hamiltonian is a d-body Hamiltonian, wherein d is independent of the computational problem.