Abstract: A method and system for estimating the ground state energy of a quantum Hamiltonian. The disclosed algorithm may run on any hardware and is suited for early fault tolerant quantum computers. The algorithm employs low-depth quantum circuits with one ancilla qubit with classical post-processing. The algorithm first draws samples from Hadamard tests in which the unitary is a controlled time evolution of the Hamiltonian. The samples are used for evaluating the convolution of the spectral measure and a filter function, and then inferring the ground state energy from this convolution. Quantum circuit depth is linear in the inverse spectral gap and poly-logarithmic in the inverse target accuracy and inverse initial overlap. Runtime is polynomial in the inverse spectral gap, inverse target accuracy, and inverse initial overlap. The algorithm produces a highly-accurate estimate of the ground state energy with reasonable runtime using low-depth quantum circuits.

Abstract: An angle grinder includes a housing, an output shaft at least partially extending out of the housing and being rotatable about a first axis relative to the housing, a sleeve fixedly connected to the housing, a first shield surrounding the output shaft and detachably connected to the sleeve, a second shield surrounding at least a part of the first shield and detachably connected to the first shield, and a connector configured for connecting the second shield to the first shield. The second shield is formed or connected with a mounting element for cooperating with the connector, and the connector and the mounting element are separately formed.

Abstract: A hybrid quantum-classical (HQC) computer takes advantage of the available quantum coherence to maximally enhance the power of sampling on noisy quantum devices, reducing measurement number and runtime compared to VQE. The HQC computer derives inspiration from quantum metrology, phase estimation, and the more recent “alpha-VQE” proposal, arriving at a general formulation that is robust to error and does not require ancilla qubits. The HQC computer uses the “engineered likelihood function” (ELF)to carry out Bayesian inference. The ELF formalism enhances the quantum advantage in sampling as the physical hardware transitions from the regime of noisy intermediate-scale quantum computers into that of quantum error corrected ones. This technique speeds up a central component of many quantum algorithms, with applications including chemistry, materials, finance, and beyond.

Abstract: A method and system are provided for solving combinatorial optimization problems. A classical algorithm provides an approximate or “seed” solution which is then used by a quantum circuit to search its “neighborhood” for higher-quality feasible solutions. A continuous-time quantum walk (CTQW) is implemented on a weighted, undirected graph that connects the feasible solutions. An iterative optimizer tunes the quantum circuit parameters to maximize the probability of obtaining high-quality solutions from the final state. The ansatz circuit design ensures that only feasible solutions are obtained from the measurement. The disclosed method solves constrained problems without modifying their cost functions, confines the evolution of the quantum state to the feasible subspace, and does not rely on efficient indexing of the feasible solutions as some previous methods require.

Abstract: A method and system are provided for solving combinatorial optimization problems. A classical algorithm provides an approximate or “seed” solution which is then used by a quantum circuit to search its “neighborhood” for higher-quality feasible solutions. A continuous-time quantum walk (CTQW) is implemented on a weighted, undirected graph that connects the feasible solutions. An iterative optimizer tunes the quantum circuit parameters to maximize the probability of obtaining high-quality solutions from the final state. The ansatz circuit design ensures that only feasible solutions are obtained from the measurement. The disclosed method solves constrained problems without modifying their cost functions, confines the evolution of the quantum state to the feasible subspace, and does not rely on efficient indexing of the feasible solutions as some previous methods require.

Abstract: A hybrid quantum-classical (HQC) computer takes advantage of the available quantum coherence to maximally enhance the power of sampling on noisy quantum devices, reducing measurement number and runtime compared to VQE. The HQC computer derives inspiration from quantum metrology, phase estimation, and the more recent “alpha-VQE” proposal, arriving at a general formulation that is robust to error and does not require ancilla qubits. The HQC computer uses the “engineered likelihood function” (ELF) to carry out Bayesian inference. The ELF formalism enhances the quantum advantage in sampling as the physical hardware transitions from the regime of noisy intermediate-scale quantum computers into that of quantum error corrected ones. This technique speeds up a central component of many quantum algorithms, with applications including chemistry, materials, finance, and beyond.

Abstract: A method and apparatus are disclosed for estimating ground state properties of molecules and materials with high accuracy on a hybrid quantum-classical computer using low-depth quantum circuits. The ground stat energy is estimated for a Hamiltonian (H) matrix characterizes a physical system. For an observable (O), samples are run on a parameterized Hadamard test circuit, the outcomes are evaluated, and the expectation value (p0) of the observable (O) is estimated with respect to the ground state energy. A weighted expectation value p0O0 is estimated, and the ground state property ?0|O|?0 is calculated. Applications include Green's functions used to compute electron transport in materials, and the one-particle reduced density matrices used to compute electric dipoles of molecules. In another aspect, the disclosed technology is applicable to early fault-tolerant quantum computers for carrying out molecular-level and materials-level calculations.

Abstract: A hybrid quantum-classical (HQC) computer takes advantage of the available quantum coherence to maximally enhance the power of sampling on noisy quantum devices, reducing measurement number and runtime compared to VQE. The HQC computer derives inspiration from quantum metrology, phase estimation, and the more recent “alpha-VQE” proposal, arriving at a general formulation that is robust to error and does not require ancilla qubits. The HQC computer uses the “engineered likelihood function” (ELF) to carry out Bayesian inference. The ELF formalism enhances the quantum advantage in sampling as the physical hardware transitions from the regime of noisy intermediate-scale quantum computers into that of quantum error corrected ones. This technique speeds up a central component of many quantum algorithms, with applications including chemistry, materials, finance, and beyond.