Abstract: A quantum computer and methods of operating the quantum computer, such that the quantum computer is enabled to fully simulate molecular chemistry, are described. The circuit depth of the quantum computer is reduced by at least an order of magnitude, as compared to conventional quantum computing methods. Parallelized qubit or fermionic swap networks are employed to render the non-local terms of the second quantized Hamiltonian, as local on consecutive qubits of the computer. Thus, non-local quantum dynamics are rendered local. By localizing the non-local interactions, the quantum computations may be significantly parallelized and a single template circuit, simulating the time-evolution operator for 4-qubit interactions, may be applied to the localized groupings of four qubits.

Abstract: Boltzmann machines are trained using an objective function that is evaluated by sampling quantum states that approximate a Gibbs state. Classical processing is used to produce the objective function, and the approximate Gibbs state is based on weights and biases that are refined using the sample results. In some examples, amplitude estimation is used. A combined classical/quantum computer produces suitable weights and biases for classification of shapes and other applications.

Abstract: Examples are disclosed relating to obtaining a solution to a multiproduct formula of order m to solve a quantum computing problem comprising a product formula. One example provides a method comprising selecting a set of exponents kj, wherein each kj is a real number and is an exponent in a linear combination of product formulas. Based on the set of exponents kj, a set of pre-factors aj is determined based on an underdetermined solution to an m×M system of linear equations, where M is a number of lower-order product formulas in the linear combination of product formulas. The set of exponents kj and the set of pre-factors aj are used to solve the quantum computing problem comprising the product formula. By minimizing the set of exponents kj and the set of pre-factors aj, sparse solutions to the multiproduct formula are generated, reducing computational time and scaling.

Abstract: Methods and apparatus are provided that permit estimation of eigenphase or eigenvalue gaps in which random or pseudo-random unitaries are applied to a selected initial quantum state to produce a random quantum state. A target unitary is then applied to the random quantum state one or more times, or an evolution time is allowed to elapse after application of the target unitary. An inverse of the pseudo-random unitary used to produce the random quantum state is applied, and the resultant state is measured with respect to the initial quantum state. Measured values are used to produce Bayesian updates, and eigenvalue/eigenvector gaps are estimated. In some examples, the disclosed methods are used in amplitude estimate and control map determinations. Eigenvalue gaps for time-dependent Hamiltonians can be evaluated by adiabatic evolution of the Hamiltonian from an initial Hamiltonian to a final Hamiltonian.

Abstract: Examples are disclosed relating to obtaining a solution to a multiproduct formula of order m to solve a quantum computing problem comprising a product formula. One example provides a method comprising selecting a set of exponents kj, wherein each kj is a real number and is an exponent in a linear combination of product formulas. Based on the set of exponents kj, a set of pre-factors aj is determined based on an underdetermined solution to an m×M system of linear equations, where M is a number of lower-order product formulas in the linear combination of product formulas. The set of exponents kj and the set of pre-factors aj are used to solve the quantum computing problem comprising the product formula. By minimizing the set of exponents kj and the set of pre-factors aj, sparse solutions to the multiproduct formula are generated, reducing computational time and scaling.

Abstract: A quantum computer and methods of operating the quantum computer, such that the quantum computer is enabled to fully simulate molecular chemistry, are described. The circuit depth of the quantum computer is reduced by at least an order of magnitude, as compared to conventional quantum computing methods. Parallelized qubit or fermionic swap networks are employed to render the non-local terms of the second quantized Hamiltonian, as local on consecutive qubits of the computer. Thus, non-local quantum dynamics are rendered local. By localizing the non-local interactions, the quantum computations may be significantly parallelized and a single template circuit, simulating the time-evolution operator for 4-qubit interactions, may be applied to the localized groupings of four qubits.

Abstract: Nearest neighbor distances are obtained by coherent majority voting based on a plurality of available distance estimates produced using amplitude estimation without measurement in a quantum computer. In some examples, distances are Euclidean distances or are based on inner products of a target vector with vectors from a training set of vectors. Distances such as mean square distances and distances from a data centroid can also be obtained.

Abstract: Methods and apparatus are provided that permit estimation of eigenphase or eigenvalue gaps in which random or pseudo-random unitaries are applied to a selected initial quantum state to produce a random quantum state. A target unitary is then applied to the random quantum state one or more times, or an evolution time is allowed to elapse after application of the target unitary. An inverse of the pseudo-random unitary used to produce the random quantum state is applied, and the resultant state is measured with respect to the initial quantum state. Measured values are used to produce Bayesian updates, and eigenvalue/eigenvector gaps are estimated. In some examples, the disclosed methods are used in amplitude estimate and control map determinations. Eigenvalue gaps for time-dependent Hamiltonians can be evaluated by adiabatic evolution of the Hamiltonian from an initial Hamiltonian to a final Hamiltonian.

Abstract: Quantum circuits and associated methods use Repeat-Until-Success (RUS) circuits to perform approximate multiplication and approximate squaring of input values supplied as rotations encoded on ancilla qubits. So-called gearbox and programmable ancilla circuits are coupled to encode even or odd products of input values as a rotation of a target qubit. In other examples, quantum RUS circuits provide target qubit rotations that are associated with reciprocals using series expansion representations.

Abstract: Quantum methods for Bayesian inference represent prior or current posterior distributions with a series of qubits. A rotation gate defined by a rotation angle based on the prior or current posterior is applied to a selected qubit of the series. The selected qubit is measured, and if measurement is successful, the state of the series of qubits represents a posterior or updated posterior. If the measurement is unsuccessful, the representation of the prior or current posterior in the series of qubits, the rotation operation, and the measurement operations are repeated until success. A sinc2 based model distribution is obtained using a quantum Fourier transform (QFT), and, in some cases, a QFT is also used to implement convolution in a filtering operation for inference with time-dependent systems.

Abstract: Methods of training Boltzmann machines include rejection sampling to approximate a Gibbs distribution associated with layers of the Boltzmann machine. Accepted sample values obtained using a set of training vectors and a set of model values associate with a model distribution are processed to obtain gradients of an objective function so that the Boltzmann machine specification can be updated. In other examples, a Gibbs distribution is estimated or a quantum circuit is specified so at to produce eigenphases of a unitary.

Abstract: Boltzmann machines are trained using an objective function that is evaluated by sampling quantum states that approximate a Gibbs state. Classical processing is used to produce the objective function, and the approximate Gibbs state is based on weights and biases that are refined using the sample results. In some examples, amplitude estimation is used. A combined classical/quantum computer produces suitable weights and biases for classification of shapes and other applications.

Abstract: Quantum circuits and associated methods use Repeat-Until-Success (RUS) circuits to perform approximate multiplication and approximate squaring of input values supplied as rotations encoded on ancilla qubits. So-called gearbox and programmable ancilla circuits are coupled to encode even or odd products of input values as a rotation of a target qubit. In other examples, quantum RUS circuits provide target qubit rotations that are associated with reciprocals using series expansion representations.

Abstract: In some examples, techniques and architectures for solving combinatorial optimization or statistical sampling problems use a recursive hierarchical approach that involves reinitializing various subsets of a set of variables. The entire set of variables may correspond to a first level of a hierarchy. In individual steps of the recursive process of solving an optimization problem, the set of variables may be partitioned into subsets corresponding to higher-order levels of the hierarchy, such as a second level, a third level, and so on. Variables of individual subsets may be randomly initialized. Based on the objective function, a combinatorial optimization operation may be performed on the individual subsets to modify variables of the individual subsets. Reinitializing subsets of variables instead of reinitializing the entire set of variables may allow for preservation of information gained in previous combinatorial optimization operations.

Abstract: Nearest neighbor distances are obtained by coherent majority voting based on a plurality of available distance estimates produced using amplitude estimation without measurement in a quantum computer. In some examples, distances are Euclidean distances or are based on inner products of a target vector with vectors from a training set of vectors. Distances such as mean square distances and distances from a data centroid can also be obtained.

Abstract: A transformer based inverter system comprises a transformer core, a secondary winding wound around the transformer core, a plurality of primary winding circuits each comprising a clockwise or counterclockwise winding wound around the transformer core and a switch operative to selectively open and close to allow current to flow through the winding. Each primary winding circuit is connected to terminals of a DC generator to drive current around the transformer core in a clockwise or counterclockwise direction. A control system is operative to open and close the switches such that an input DC voltage from a generator is transformed and inverted into an AC voltage that has a frequency and voltage equal to a desired frequency and voltage, and such that as the input DC voltage varies within a range, the AC voltage at the terminal ends of the secondary winding remains substantially constant.