Quantum Algorithm for Green's Functions Measurements in the Fermi-Hubbard Model

• URL: http://arxiv.org/abs/2310.10412v2
• Date: Wed, 6 Dec 2023 15:44:09 GMT
• Title: Quantum Algorithm for Green's Functions Measurements in the Fermi-Hubbard Model
• Authors: Gino Bishop, Dmitry Bagrets, Frank K. Wilhelm
• Abstract summary: We propose a new quantum algorithm, which uses an analog of the Kubo formula within linear response theory adapted to a quantum circuit the Hubbard model. We find a drastic reduction in gate count of two-qubits gates and limitations on hardware design as compared to previous approaches.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the framework of the hybrid quantum-classical variational cluster approach (VCA) to strongly correlated fermion systems one of the goals of a quantum subroutine is to find single-particle correlation functions of lattice fermions in polynomial time. Previous works suggested to use variants of the Hadamard test for this purpose. However, it requires an implementation of controlled unitaries specifying the full dynamics of the simulated model. In this work, we propose a new quantum algorithm, which uses an analog of the Kubo formula within linear response theory adapted to a quantum circuit simulating the Hubbard model. It allows to access the Green's function of a cluster directly and thereby circumvents the usage of the Hadamard test. We find a drastic reduction in gate count of two-qubits gates and limitations on hardware design as compared to previous approaches.

Related papers

• Utilizing Quantum Processor for the Analysis of Strongly Correlated Materials [34.63047229430798]
  This study introduces a systematic approach for analyzing strongly correlated systems by adapting the conventional quantum cluster method to a quantum circuit model. We have developed a more concise formula for calculating the cluster's Green's function, requiring only real-number computations on the quantum circuit instead of complex ones.
  arXiv  Detail & Related papers  (2024-04-03T06:53:48Z)
• Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries [0.0]
  We develop a quantum circuit ansatz inspired by the Density Matrix Renormalization Group (DMRG) algorithm. We find that, with realistic error rates, our DMRG-VQE hybrid algorithm delivers good results for strongly correlated systems.
  arXiv  Detail & Related papers  (2024-01-04T16:53:47Z)
• An occupation number quantum subspace expansion approach to compute the single-particle Green function: an opportunity for noise filtering [0.0]
  We introduce a hybrid quantum-classical algorithm to compute the Green function for strongly correlated electrons on noisy quantum devices. The technique allows for noise filtering, a useful feature for NISQ devices.
  arXiv  Detail & Related papers  (2023-12-21T00:21:17Z)
• Variational-quantum-eigensolver-inspired optimization for spin-chain work extraction [39.58317527488534]
  Energy extraction from quantum sources is a key task to develop new quantum devices such as quantum batteries. One of the main issues to fully extract energy from the quantum source is the assumption that any unitary operation can be done on the system. We propose an approach to optimize the extractable energy inspired by the variational quantum eigensolver (VQE) algorithm.
  arXiv  Detail & Related papers  (2023-10-11T15:59:54Z)
• Quantum Computed Green's Functions using a Cumulant Expansion of the Lanczos Method [0.0]
  We present a quantum computational method to calculate the many-body Green's function matrix in a spin orbital basis. We demonstrate the calculation of Green's functions on Quantinuum's H1-1 trapped-ion quantum computer.
  arXiv  Detail & Related papers  (2023-09-18T11:45:04Z)
• Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search [77.34726150561087]
  We consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control. We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates.
  arXiv  Detail & Related papers  (2023-02-28T07:36:02Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• Gutzwiller wave function on a quantum computer using a discrete Hubbard-Stratonovich transformation [0.7734726150561086]
  We propose a quantum-classical hybrid scheme for implementing the nonunitary Gutzwiller factor. The proposed scheme is demonstrated with numerical simulations for the half-filled Fermi-Hubbard model.
  arXiv  Detail & Related papers  (2022-01-27T08:57:04Z)
• Simulating the Mott transition on a noisy digital quantum computer via Cartan-based fast-forwarding circuits [62.73367618671969]
  Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models. This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
  arXiv  Detail & Related papers  (2021-12-10T17:32:15Z)
• Simulating nonnative cubic interactions on noisy quantum machines [65.38483184536494]
  We show that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. On noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates.
  arXiv  Detail & Related papers  (2020-04-15T05:16:24Z)
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond [46.39654665163597]
  We report on experimental tests of topological defect formation via the one-dimensional transverse-field Ising model. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system.
  arXiv  Detail & Related papers  (2020-01-31T02:55:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.