Quantum Simulation of Boson-Related Hamiltonians: Techniques, Effective Hamiltonian Construction, and Error Analysis

• URL: http://arxiv.org/abs/2307.06580v2
• Date: Thu, 27 Feb 2025 04:46:03 GMT
• Title: Quantum Simulation of Boson-Related Hamiltonians: Techniques, Effective Hamiltonian Construction, and Error Analysis
• Authors: Bo Peng, Yuan Su, Daniel Claudino, Karol Kowalski, Guang Hao Low, Martin Roetteler,
• Abstract summary: This tutorial review focuses on encoding and simulating certain bosonic-related model Hamiltonians.<n>We discuss recently developed quantum algorithms for these interacting models and the construction of effective Hamiltonians.
• Score: 4.533969990771866
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A broad spectrum of physical systems in condensed-matter and high-energy physics, vibrational spectroscopy, and circuit and cavity QED necessitates the incorporation of bosonic degrees of freedom, such as phonons, photons, and gluons, into optimized fermion algorithms for near-future quantum simulations. In particular, when a quantum system is surrounded by an external environment, its basic physics can usually be simplified to a spin or fermionic system interacting with bosonic modes. Nevertheless, troublesome factors such as the magnitude of the bosonic degrees of freedom typically complicate the direct quantum simulation of these interacting models, necessitating the consideration of a comprehensive plan. This strategy should specifically include a suitable fermion/boson-to-qubit mapping scheme to encode sufficiently large yet manageable bosonic modes, and a method for truncating and/or downfolding the Hamiltonian to the defined subspace for performing an approximate but highly accurate simulation, guided by rigorous error analysis. In this pedagogical tutorial review, we aim to provide such an exhaustive strategy, focusing on encoding and simulating certain bosonic-related model Hamiltonians, inclusive of their static properties and time evolutions. Specifically, we emphasize two aspects: (1) the discussion of recently developed quantum algorithms for these interacting models and the construction of effective Hamiltonians, and (2) a detailed analysis regarding a tightened error bound for truncating the bosonic modes for a class of fermion-boson interacting Hamiltonians.

Related papers

• Quantum-computing within a bosonic context: Assessing finite basis effects on prototypical vibrational Hamiltonian spectra [0.0]
  We address a formal problem that arises when simulating a vibrational model under harmonic second quantization. This relates intimately to the normal ordering of products of ladder operators. In addition, we discuss the relevance of choosing an adequate primitive basis set within the present context.
  arXiv  Detail & Related papers  (2025-03-31T11:52:04Z)
• Learning interactions between Rydberg atoms [4.17037025217542]
  We introduce a scalable approach to Hamiltonian learning using graph neural networks (GNNs) We demonstrate that our GNN model has a remarkable capacity to extrapolate beyond its training domain.
  arXiv  Detail & Related papers  (2024-12-16T17:45:30Z)
• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
  We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment. We find sufficient conditions under which dynamical decoupling works for such systems. Our bounds reproduce the correct scaling in various relevant system parameters.
  arXiv  Detail & Related papers  (2024-09-24T04:58:28Z)
• Simulating continuous-space systems with quantum-classical wave functions [0.0]
  Non-relativistic interacting quantum many-body systems are naturally described in terms of continuous-space Hamiltonians. Current algorithms require discretization, which usually amounts to choosing a finite basis set, inevitably introducing errors. We propose an alternative, discretization-free approach that combines classical and quantum resources in a global variational ansatz.
  arXiv  Detail & Related papers  (2024-09-10T10:54:59Z)
• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Entanglement with neutral atoms in the simulation of nonequilibrium dynamics of one-dimensional spin models [0.0]
  We study the generation and role of entanglement in the dynamics of spin-1/2 models. We introduce the neutral atom Molmer-Sorensen gate, involving rapid adiabatic Rydberg dressing interleaved in a spin-echo sequence. In quantum simulation, we consider critical behavior in quench dynamics of transverse field Ising models.
  arXiv  Detail & Related papers  (2024-06-07T23:29:16Z)
• Hamiltonian Engineering of collective XYZ spin models in an optical cavity [0.0]
  Quantum simulation using synthetic quantum systems offers unique opportunities to explore open questions in many-body physics. Here, we are able to realize an all-to-all interaction with arbitrary quadratic Hamiltonian or effectively an infinite range tunable Heisenberg XYZ model. The versatility of our platform to include more than two relevant momentum states, combined with the flexibility of the simulated Hamiltonians by adding cavity tones opens rich opportunities for quantum simulation and quantum sensing in matter-wave interferometers and other quantum sensors such as optical clocks and magnetometers.
  arXiv  Detail & Related papers  (2024-02-29T18:26:13Z)
• Inverse Hamiltonian design of highly-entangled quantum systems [0.0]
  We apply an inverse design framework using automatic differentiation to quantum spin systems. We show that the method automatically finds the Kitaev model with bond-dependent anisotropic interactions. The comparative study reveals that bond-dependent anisotropic interactions, rather than isotropic Heisenberg interactions, amplify quantum entanglement.
  arXiv  Detail & Related papers  (2024-02-24T12:33:50Z)
• Hamiltonian truncation tensor networks for quantum field theories [42.2225785045544]
  We introduce a tensor network method for the classical simulation of continuous quantum field theories. The method is built on Hamiltonian truncation and tensor network techniques. One of the key developments is the exact construction of matrix product state representations of global projectors.
  arXiv  Detail & Related papers  (2023-12-19T19:00:02Z)
• Quantum Algorithms for Simulating Nuclear Effective Field Theories [40.83664249192338]
  We use state-of-the-art Hamiltonian-simulation methods to estimate the qubit and gate costs to simulate low-energy effective field theories (EFTs) of nuclear physics. We demonstrate how symmetries of the low-energy nuclear Hamiltonians can be utilized to obtain tighter error bounds on the simulation algorithm.
  arXiv  Detail & Related papers  (2023-12-08T20:09:28Z)
• Boundary scattering tomography of the Bose Hubbard model on general graphs [0.0]
  We present a scheme for tomography of quantum simulators that can be described by a Bose-Hubbard Hamiltonian. We show that with the additional ability to switch on and off the on-site repulsion in the simulator, we can sense the Hamiltonian parameters beyond the standard quantum limit.
  arXiv  Detail & Related papers  (2023-10-22T05:42:48Z)
• Quantum Simulations in Effective Model Spaces (I): Hamiltonian Learning-VQE using Digital Quantum Computers and Application to the Lipkin-Meshkov-Glick Model [0.0]
  We introduce an iterative hybrid-classical-quantum algorithm, Hamiltonian learning variational quantum eigensolver (HL-VQE) HL-VQE is found to provide an exponential improvement in Lipkin-Meshkov-Glick model calculations. This work constitutes a step in the development of entanglement-driven quantum algorithms for the description of nuclear systems.
  arXiv  Detail & Related papers  (2023-01-14T21:10:02Z)
• Quantum emulation of the transient dynamics in the multistate Landau-Zener model [50.591267188664666]
  We study the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity. Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.
  arXiv  Detail & Related papers  (2022-11-26T15:04:11Z)
• Hybridized Methods for Quantum Simulation in the Interaction Picture [69.02115180674885]
  We provide a framework that allows different simulation methods to be hybridized and thereby improve performance for interaction picture simulations. Physical applications of these hybridized methods yield a gate complexity scaling as $log2 Lambda$ in the electric cutoff. For the general problem of Hamiltonian simulation subject to dynamical constraints, these methods yield a query complexity independent of the penalty parameter $lambda$ used to impose an energy cost.
  arXiv  Detail & Related papers  (2021-09-07T20:01:22Z)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• Quantum Variational Learning of the Entanglement Hamiltonian [0.0]
  Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum many-body states in analog quantum simulation. We describe a protocol where spatial deformations of the many-body Hamiltonian, physically realized on the quantum device, serve as an efficient variational ansatz for a local EH. We simulate the protocol for the ground state of Fermi-Hubbard models in quasi-1D geometries, finding excellent agreement of the EH with Bisognano-Wichmann predictions.
  arXiv  Detail & Related papers  (2021-05-10T12:54:50Z)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Quantum Markov Chain Monte Carlo with Digital Dissipative Dynamics on Quantum Computers [52.77024349608834]
  We develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. We evaluate the algorithm by simulating thermal states of the transverse Ising model.
  arXiv  Detail & Related papers  (2021-03-04T18:21:00Z)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)
• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM) [0.0]
  An open quantum system refers to a system that is further coupled to a bath system. The hierarchical equations of motion (HEOM) can describe numerically "exact" dynamics of a reduced system.
  arXiv  Detail & Related papers  (2020-06-09T21:00:32Z)

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.