Hybrid Quantum-Classical Computer for Bayesian Inference with Engineered Likelihood Functions for Robust Amplitude Estimation

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.

1 . A method for improved quantum amplitude estimation for reducing a number of measurements to generate a statistic accurately, comprising:
 selecting, with a classical computer, a plurality of quantum-circuit-parameter values to optimize an accuracy-improvement rate of the statistic estimating an expectation value (s|P|s) of an observable p with respect to a quantum state |s);   applying, to one or more qubits of a quantum computer, a sequence of alternating first and second generalized reflection operators to transform the one or more qubits from the quantum state |s) into a reflected quantum state, each of the first and second generalized reflection operators being controlled according to a corresponding one of the plurality of quantum-circuit-parameter values;   measuring the plurality of qubits in the reflected quantum state with respect to the observable p to obtain a set of measurement outcomes; and   updating, on the classical computer, the statistic with the set of measurement outcomes.