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arXiv · 2307.13583

Calculating the Single-Particle Many-body Green's Functions via the Quantum Singular Value Transform Algorithm

Alexis Ralli·Gabriel Greene-Diniz·David Muñoz Ramo·Nathan Fitzpatrick
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Abstract

The Quantum Singular Value Transformation (QSVT) is a technique that provides a unified framework for describing many of the quantum algorithms discovered to date. We implement a noise-free simulation of the technique to investigate how it can be used to perform matrix inversion, which is an important step in calculating the single-particle Green's function in the Lehmann representation. Due to the inverse function not being defined at zero, we explore the effect of approximating f(x)=1/x with a polynomial. This is carried out by calculating the single-particle Green's function of the two-site single-impurity Anderson model. We also propose a new circuit construction for the linear combination of unitaries block encoding technique, that reduces the number of single and two-qubit gates required.

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Alexis Ralli, Gabriel Greene-Diniz, David Muñoz Ramo, Nathan Fitzpatrick. 2023-07-25. Calculating the Single-Particle Many-body Green's Functions via the Quantum Singular Value Transform Algorithm. https://arxiv.org/abs/2307.13583

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