Abstract: Methods and systems perform conversion of time signals to frequency spectra. Such methods and systems facilitate a simple analysis of robustness under various algorithmic noise models. While a robustness analysis can be carried out for other methods of quantum phase estimation, the methods and systems provide a foundation for the robustness analysis beyond quantum phase estimation.

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: A quantum optimization system and method estimate, on a classical computer and for a quantum state, an expectation value of a Hamiltonian, expressible as a linear combination of observables, based on expectation values of the observables; and transform, on the classical computer, one or both of the Hamiltonian and the quantum state to reduce the expectation value of the Hamiltonian.