Exploring Ground States of Fermi-Hubbard Model on Honeycomb Lattices with Counterdiabaticity

• URL: http://arxiv.org/abs/2405.09225v1
• Date: Wed, 15 May 2024 10:05:01 GMT
• Title: Exploring Ground States of Fermi-Hubbard Model on Honeycomb Lattices with Counterdiabaticity
• Authors: Jialiang Tang, Ruoqian Xu, Yongcheng Ding, Xusheng Xu, Yue Ban, Manhong Yung, Axel Pérez-Obiol, Gloria Platero, Xi Chen,
• Abstract summary: Shortcuts to adiabaticity by counter-diabatic driving serve to accelerate these processes by suppressing energy excitations. We develop variational quantum algorithms incorporating the auxiliary counterdiabatic interactions, comparing them with digitized adiabatic algorithms. These algorithms are then implemented on gate-based quantum circuits to explore the ground states of the Fermi-Hubbard model on honeycomb lattices.
• Score: 2.756976915658684
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Exploring the ground state properties of many-body quantum systems conventionally involves adiabatic processes, alongside exact diagonalization, in the context of quantum annealing or adiabatic quantum computation. Shortcuts to adiabaticity by counter-diabatic driving serve to accelerate these processes by suppressing energy excitations. Motivated by this, we develop variational quantum algorithms incorporating the auxiliary counterdiabatic interactions, comparing them with digitized adiabatic algorithms. These algorithms are then implemented on gate-based quantum circuits to explore the ground states of the Fermi-Hubbard model on honeycomb lattices, utilizing systems with up to 26 qubits. The comparison reveals that the counter-diabatic inspired ansatz is superior to traditional Hamiltonian variational ansatz. Furthermore, the number and duration of Trotter steps are analyzed to understand and mitigate errors. Given the model's relevance to materials in condensed matter, our study paves the way for using variational quantum algorithms with counterdiabaticity to explore quantum materials in the noisy intermediate-scale quantum era.

Related papers

• Shortcuts for Adiabatic and Variational Algorithms in Molecular Simulation [3.5621685463862356]
  We introduce shortcuts-to-adiabaticity techniques into adiabatic and variational algorithms for calculating the molecular ground state. Our approach achieves comparable accuracy to other established ansatzes, while enhancing the potential for applications in material science, drug discovery, and molecular simulations.
  arXiv  Detail & Related papers  (2024-07-30T16:30:22Z)
• Quantum quench dynamics as a shortcut to adiabaticity [31.114245664719455]
  We develop and test a quantum algorithm in which the incorporation of a quench step serves as a remedy to the diverging adiabatic timescale. Our experiments show that this approach significantly outperforms the adiabatic algorithm.
  arXiv  Detail & Related papers  (2024-05-31T17:07:43Z)
• The quantum adiabatic algorithm suppresses the proliferation of errors [0.29998889086656577]
  We analyze the proliferation of a single error event in the adiabatic algorithm. Our findings indicate that low energy states could remain attainable even in the presence of a single error event.
  arXiv  Detail & Related papers  (2024-04-23T18:00:00Z)
• Quantum error mitigation for Fourier moment computation [49.1574468325115]
  This paper focuses on the computation of Fourier moments within the context of a nuclear effective field theory on superconducting quantum hardware. The study integrates echo verification and noise renormalization into Hadamard tests using control reversal gates. The analysis, conducted using noise models, reveals a significant reduction in noise strength by two orders of magnitude.
  arXiv  Detail & Related papers  (2024-01-23T19:10:24Z)
• Amplification of quantum transfer and quantum ratchet [56.47577824219207]
  We study a model of amplification of quantum transfer and making it directed which we call the quantum ratchet model. The ratchet effect is achieved in the quantum control model with dissipation and sink, where the Hamiltonian depends on vibrations in the energy difference synchronized with transitions between energy levels. Amplitude and frequency of the oscillating vibron together with the dephasing rate are the parameters of the quantum ratchet which determine its efficiency.
  arXiv  Detail & Related papers  (2023-12-31T14:04:43Z)
• Orders of magnitude reduction in the computational overhead for quantum many-body problems on quantum computers via an exact transcorrelated method [0.0]
  We show that the Hamiltonian becomes non-Hermitian, posing problems for quantum algorithms based on the variational principle. We overcome these limitations with the ansatz-based quantum imaginary time evolution algorithm. Our work paves the way for the use of exact transcorrelated methods for the simulations of ab initio systems on quantum computers.
  arXiv  Detail & Related papers  (2022-01-09T16:37:32Z)
• Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry [51.827942608832025]
  Near-term quantum computers can calculate the ground-state properties of small molecules. We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
  arXiv  Detail & Related papers  (2021-12-31T16:33:10Z)
• Circuit Symmetry Verification Mitigates Quantum-Domain Impairments [69.33243249411113]
  We propose circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state. In particular, we propose the Fourier-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain formalism to circuit-oriented stabilizers.
  arXiv  Detail & Related papers  (2021-12-27T21:15:35Z)
• 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)
• Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits [58.720142291102135]
  We simulate a noisy quantum Fourier transform processor with up to 21 qubits. We take into account microscopic dissipative processes rather than relying on digital error models. We show that depending on the dissipative mechanisms at play, the choice of input state has a strong impact on the performance of the quantum algorithm.
  arXiv  Detail & Related papers  (2021-02-08T14:55:44Z)
• Shortcuts to Adiabaticity in Digitized Adiabatic Quantum Computing [3.106630515217536]
  counter-diabatic (CD) driving provides a promising means to speed up quantum many-body systems. We show the applicability of CD driving to enhance the digitized adiabatic quantum computing paradigm in terms of fidelity and total simulation time. We implement this proposal in the IBM quantum computer, proving its usefulness for the speed up of adiabatic quantum computing in noisy intermediate-scale quantum devices.
  arXiv  Detail & Related papers  (2020-09-08T06:28:32Z)

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.