Evaluating energy differences on a quantum computer with robust phase estimation

Abstract

We adapt the robust phase estimation algorithm to the evaluation of energy differences between two eigenstates using a quantum computer. This approach does not require controlled unitaries between auxiliary and system registers or even a single auxiliary qubit. As a proof of concept, we calculate the energies of the ground state and low-lying electronic excitations of a hydrogen molecule in a minimal basis on a cloud quantum computer. The denominative robustness of our approach is then quantified in terms of a high tolerance to coherent errors in the state preparation and measurement. Conceptually, we note that all quantum phase estimation algorithms ultimately evaluate eigenvalue differences.

15 pages, 6 figures (including supplemental material)

References in corpus (7)

• Simulated Quantum Computation of Molecular Energies
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Entanglement-free Heisenberg-limited phase estimation
• Characterization of addressability by simultaneous randomized benchmarking
• Optimal Quantum Measurements of Expectation Values of Observables
• Constructive Quantum Shannon Decomposition from Cartan Involutions
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