Abstract: A computer-implemented method for determining a measurement value for each operator of a plurality of operators. The method comprises grouping the plurality of operators into one or more sets of mutually commuting operators, each set comprising one or more of the plurality of operators. Determining, for each set of operators: a subset of transformed operators based on the set of operators, such that the set of operators are equal to products of the subset of transformed operators; a mapping circuit based on the subset of transformed operators, wherein the mapping circuit comprises an arrangement of quantum gates configured to operate on a plurality of qubits in a quantum computer.

Abstract: A computing device is provided, including a processor configured to transmit, to a quantum coprocessor, instructions to encode a Markov decision process (MDP) model as a quantum oracle. The processor may be further configured to train a reinforcement learning model at least in part by transmitting a plurality of superposition queries to the quantum oracle encoded at the quantum coprocessor. Training the reinforcement learning model may further include receiving, from the quantum coprocessor, one or more measurement results in response to the plurality of superposition queries. Training the reinforcement learning model may further include updating a policy function of the reinforcement learning model based at least in part on the one or more measurement results.

Abstract: A method comprises performing an iterative optimisation procedure. Each iteration of the optimisation procedure comprises: preparing a first ansatz trial state using a first arrangement of quantum gates, the first ansatz trial state having a first state energy which is dependent on a trial state variable; performing an energy estimation routine to determine and output a value associated with an estimate for the first ansatz trial state energy; performing an overlap estimation routine to determine and output a degree of overlap between a first prepared state corresponding with or based on the first ansatz trial state, and a second prepared state corresponding with or based on a known state; determining the value of an optimisation function based on the outputs of the energy estimation routine and the overlap estimation routine; and updating the trial state variable.

Abstract: A method for determining an energy level of a physical system using a quantum computer, wherein the energy level of the physical system is described by the summation of a plurality of summands. The method comprises performing an energy estimation routine which comprises preparing an ansatz trial state, and estimating an expectation value of each summand respectively. The estimating comprises constructing, based on the arrangement of quantum gates, an initial quantum circuit to operate on the ansatz trial state and further comprises performing a summand expectation value determination sub-routine a plurality of times in an iterative process. The energy estimation routine further comprises summing the expectation value estimates of each summand to determine an estimate for the trial state energy. The method further comprises determining the energy level of the physical system by applying an optimisation procedure to the energy estimation routine.