Abstract: The present invention provides methods and apparatuses for approximating a ground state or a Gibbs state of a k-local Hamiltonian using a quantum computer system. The procedure begins by providing a set of local generalised measurements corresponding to the terms of the k-local Hamiltonian. A set of data qudits is initialised into an initial state and a local generalised measurement is subsequently performed to perturb a subset of the data qudits from an initial state to a perturbed state. The perturbation is accepted or rejected based on a measurement outcome of the local generalised measurement. The perturbation and accept/reject steps are repeated unless or until a stopping condition is met. The result of the procedure is to provably drive the encoded Hamiltonian toward or even into a ground state or a Gibbs state, a useful starting point in many quantum algorithms, such as those relating to materials simulation.

Abstract: A method of simulating condensed matter systems on quantum computers includes reducing the Hamiltonian of the system to adapt it to being implementable on a given quantum computer. Part of this adaptation is identifying an active space and associated degrees of freedom within the active space. This effective Hamiltonian is provided a localised representation to assist in reducing the depth of the quantum circuit which used to simulate the system. The quadratic and quartic interaction matrix and coefficients between modes of the localised Hamiltonian are calculated and the modes of the localised Hamiltonian are encoded onto the qubits of the quantum computer. Qubit interactions corresponding to interactions between modes of the localised Hamiltonian are implemented between the qubits and the resulting state is measured to extract a simulation of the active space of the effective Hamiltonian.

Abstract: A method is provided for determining a control sequence for performing a multiqudit algorithm on a quantum computer, the multiqudit algorithm expressible as a series of one or more k-qudit interactions. The method comprises, for each of the k-qudit interactions, decomposing the k-qudit interaction into a sequence of single-qudit unitary rotations and/or two-qudit unitary rotations from the continuous family of controllable unitary rotations generated by underlying physical interactions in the hardware of the quantum computer subject to a specified minimum interaction time, said sequence being physically implementable on the quantum computer. The method further comprises combining the sequences to form a combined interaction sequence. The method further comprises determining, based on the combined interaction sequence, the control sequence for performing the multiqudit algorithm on the quantum computer.