Importance

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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 ψ₀|O|ψ₀ 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.

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First Claim