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arXiv · 2010.03236

Inverse iteration quantum eigensolvers assisted with a continuous variable

Min-Quan He·Dan-Bo Zhang·Z. D. Wang
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Abstract

The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse power iteration method. A key ingredient is constructing an inverse Hamiltonian as a linear combination of coherent Hamiltonian evolution. We first consider a continuous-variable quantum mode (qumode) for realizing such a linear combination as an integral, with weights being encoded into a qumode resource state. We demonstrate the quantum algorithm with numerical simulations under finite squeezing for various physical systems, including molecules and quantum many-body models. We also discuss a hybrid quantum-classical algorithm that directly sums up Hamiltonian evolution with different durations for comparison. It is revealed that continuous-variable resources are valuable for reducing the coherent evolution time of Hamiltonians in quantum algorithms.

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Min-Quan He, Dan-Bo Zhang, Z. D. Wang. 2022-03-08. Inverse iteration quantum eigensolvers assisted with a continuous variable. https://doi.org/10.1088/2058-9565%2Fac5b30

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