Abstract: A method for error correction in a quantum computing device that can significantly improve the quantum error correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be gained. A method for decoding which uses this information to improve performance is also provided.

Abstract: A method for error correction in a quantum computing device that can significantly improve the quantum error correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be gained. A method for decoding which uses this information to improve performance is also provided.

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.