Quantum Computed Green’s Functions Using A Cumulant Expansion Of The Lanczos Method

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Gabriel Greene-Diniz¹, David Zsolt Manrique¹, Kentaro Yamamoto², Evgeny Plekhanov¹, Nathan Fitzpatrick¹, Michal Krompiec¹, Rei Sakuma³, and David Muñoz Ramo¹

¹Quantinuum, Terrington House, 13-15 Hills Road, Cambridge CB2 1NL, UK
²Quantinuum K.K., Otemachi Financial City Grand Cube 3F, 1-9-2 Otemachi, Chiyoda-ku, Tokyo, Japan
³Materials Informatics Initiative, RD Technology & Digital Transformation Center, JSR Corporation, 3-103-9, Tonomachi, Kawasaki-ku, Kawasaki, 210-0821, Kanagawa, Japan.

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Abstract

In this paper, we present a quantum computational method to calculate the many-body Green’s function matrix in a spin orbital basis. We apply our approach to finite-sized fermionic Hubbard models and related impurity models within Dynamical Mean Field Theory, and demonstrate the calculation of Green’s functions on Quantinuum’s H1-1 trapped-ion quantum computer. Our approach involves a cumulant expansion of the Lanczos method, using Hamiltonian moments as measurable expectation values. This bypasses the need for a large overhead in the number of measurements due to repeated applications of the variational quantum eigensolver (VQE), and instead measures the expectation value of the moments with one set of measurement circuits. From the measured moments, the tridiagonalised Hamiltonian matrix can be computed, which in turn yields the Green’s function via continued fractions. While we use a variational algorithm to prepare the ground state in this work, we note that the modularity of our implementation allows for other (non-variational) approaches to be used for the ground state.

► BibTeX data

@article{GreeneDiniz2024quantumcomputed, doi = {10.22331/q-2024-06-20-1383}, url = {https://doi.org/10.22331/q-2024-06-20-1383}, title = {Quantum {C}omputed {G}reen’s {F}unctions using a {C}umulant {E}xpansion of the {L}anczos {M}ethod}, author = {Greene-Diniz, Gabriel and Manrique, David Zsolt and Yamamoto, Kentaro and Plekhanov, Evgeny and Fitzpatrick, Nathan and Krompiec, Michal and Sakuma, Rei and Ramo, David Mu{~{n}}oz}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {8}, pages = {1383}, month = jun, year = {2024} }

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Cited by

[1] Reinis Irmejs and Raul A. Santos, “Approximating dynamical correlation functions with constant depth quantum circuits”, arXiv:2406.03204, (2024).

[2] Lorenzo Del Re, Brian Rost, Michael Foss-Feig, A. F. Kemper, and J. K. Freericks, “Robust Measurements of n -Point Correlation Functions of Driven-Dissipative Quantum Systems on a Digital Quantum Computer”, Physical Review Letters 132 10, 100601 (2024).

[3] Michael A. Jones, Harish J. Vallury, and Lloyd C. L. Hollenberg, “Ground-state-energy calculation for the water molecule on a superconducting quantum processor”, Physical Review Applied 21 6, 064017 (2024).

[4] Rihito Sakurai, Oliver J. Backhouse, George H. Booth, Wataru Mizukami, and Hiroshi Shinaoka, “Comparative study on compact quantum circuits of hybrid quantum-classical algorithms for quantum impurity models”, Physical Review Research 6 2, 023110 (2024).

[5] Rei Sakuma, Shu Kanno, Kenji Sugisaki, Takashi Abe, and Naoki Yamamoto, “Entanglement-assisted phase estimation algorithm for calculating dynamical response functions”, arXiv:2404.19554, (2024).

The above citations are from SAO/NASA ADS (last updated successfully 2024-06-21 01:55:25). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2024-06-21 01:55:23).

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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Source: https://quantum-journal.org/papers/q-2024-06-20-1383/

Time Stamp: June 20, 2024

Time Stamp: May 8, 2024

Republished By Plato

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