Abstract: There is provided a series of steps, according to user-defined instructions, that enhance a quantum state preparation circuit encoding some multivariate probability distribution such that the circuit further includes dimensions pertaining to sums, products and maxima/minima of other dimensions, and optionally includes a further “flag” qubit that will act as a conditional control in quantum Monte Carlo integration (QMCI). The series of steps are useful for computations in many applications in science and engineering.

Abstract: There is provided a method for modifying any quantum phase-estimation-free quantum amplitude-estimation algorithm, to improve the statistical performance and robustness of the amplitude estimation. A phase-estimation-free amplitude-estimation algorithm provides an estimate for the amplitude of a desired quantum state, realised by performing classical post-processing for combined measurement data resulting from a number of different quantum circuits derived from the desired quantum state. The method for modifying any such algorithm prepares quantum circuits that each correspond to different initial states (chosen either quasi-randomly, randomly, or deterministically). These are prepared using linear combinations of unitary operations, and each initial state corresponds to a state rotated in the two-dimensional invariant subspace to a corresponding initial angle.

Abstract: A quantum computer system and a method for using such a quantum computer system are provided. The quantum computer system comprises a first register and a second register which are used to separate a quantum state into multiple subspaces of a 2n dimensional Hilbert space. The method comprises defining a quantum state comprising 2n elements on the first register, the first register comprising n qubits; defining a quantum state on the second register, the second register comprising one or more qubits; and receiving a value k, where k is a binary integer such that 0=<k=<n. The method further comprises performing a bit-wise iteration process to separate the quantum state on the first register into distinct subspaces of the Hilbert space, wherein elements of the distinct subspaces have different Hamming weights and exactly one of the subspaces contains only elements of Hamming weight k.

Abstract: A method and quantum computing system are provided for investigating quantum electrodynamic effects in a physical system containing bosonic components and spin components. The method includes defining a Hamiltonian representation of the physical system, wherein the Hamiltonian representation comprises states and operators for the bosonic components and spin components. The physical system comprises a plurality of interconnected cavities in which the bosonic and spin components of the physical system are located. The bosonic and spin components of the physical system interact with one another according to quantum electrodynamics. The bosonic components of the physical system are able to hop between the interconnected cavities. The states and operators from the Hamiltonian representation of the physical system are mapped onto a quantum circuit for execution on the quantum computing system.

Abstract: Provided are computer-implemented quantum computation methods and systems that can be used to compute a Green's function, such as for finite-sized fermionic Hubbard models and related impurity models within Dynamical Mean Field Theory. The methods are suitable for implementation using a hybrid classical-quantum computation system. The Green's function is an important quantity for describing optical and electronic responses in quantum systems, from which various properties and behaviours can be computed. Described is a quantum computational method that involves a cumulant expansion of expectation values calculated for each of a set of moments of an operator. This reduces the need for a large overhead in the number of measurements and instead measures the expectation value of the moments with one set of measurement circuits. From the measured moments, a tridiagonal matrix can be computed, which in turn yields the Green's function.

Abstract: A system and method perform machine learning using a quantum computer. A model comprises a Quantum Boltzmann machine with a Hamiltonian ansatz having a set of operators and a set of parameters. A first stage of training the model against data from a target is performed on classical computing hardware, using a selected subset of the set of operators, to obtain optimized values for a subset of the set of parameters and a partly trained model. A second stage of training the model against data from the target is performed, at least partly using quantum computer hardware, using a larger subset of the set of operators to obtain optimized values for a larger subset of the set parameters for the model. The optimized parameter values from the first stage of training are used to initialize the corresponding parameters for the second stage of training.