Quantum Simulation of Second-Quantized Hamiltonians in Compact Encoding

• URL: http://arxiv.org/abs/2105.10941v3
• Date: Tue, 28 Jun 2022 15:16:11 GMT
• Title: Quantum Simulation of Second-Quantized Hamiltonians in Compact Encoding
• Authors: William M. Kirby, Sultana Hadi, Michael Kreshchuk, and Peter J. Love
• Abstract summary: We show how to use sparse Hamiltonian simulation methods for second-quantized Hamiltonians in compact encoding. We also describe several example applications including the free boson and fermion theories, the $phi4$-theory, and the massive Yukawa model.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We describe methods for simulating general second-quantized Hamiltonians using the compact encoding, in which qubit states encode only the occupied modes in physical occupation number basis states. These methods apply to second-quantized Hamiltonians composed of a constant number of interactions, i.e., linear combinations of ladder operator monomials of fixed form. Compact encoding leads to qubit requirements that are optimal up to logarithmic factors. We show how to use sparse Hamiltonian simulation methods for second-quantized Hamiltonians in compact encoding, give explicit implementations for the required oracles, and analyze the methods. We also describe several example applications including the free boson and fermion theories, the $\phi^4$-theory, and the massive Yukawa model, all in both equal-time and light-front quantization. Our methods provide a general-purpose tool for simulating second-quantized Hamiltonians, with optimal or near-optimal scaling with error and model parameters.

Related papers

• Gate Efficient Composition of Hamiltonian Simulation and Block-Encoding with its Application on HUBO, Fermion Second-Quantization Operators and Finite Difference Method [0.0]
  This article proposes a simple formalism which unifies Hamiltonian simulation techniques from different fields. It leads to a gate decomposition and a scaling different from the usual strategy. It can significantly reduce the quantum circuit number of rotational gates, multi-qubit gates, and the circuit depth.
  arXiv  Detail & Related papers  (2024-10-24T12:26:50Z)
• Systematic input scheme of many-boson Hamiltonians with applications to the two-dimensional $φ^4$ theory [0.0]
  We present our discussion of this input scheme based on the light-front Hamiltonian of the two-dimensional $phi 4$ theory. In our input scheme, we employ a set of quantum registers, where each register encodes the occupation of a distinct boson mode as binaries. We present the spectral calculations of the Hamiltonian utilizing the hybrid quantum-classical symmetry-adapted quantum Krylov subspace diagonalization algorithm.
  arXiv  Detail & Related papers  (2024-07-18T16:47:53Z)
• Digital-Analog Quantum Computation with Arbitrary Two-Body Hamiltonians [0.0]
  Digital-analog quantum computing is a computational paradigm which employs an analog Hamiltonian resource together with single-qubit gates to reach universality. We design a new scheme which employs an arbitrary two-body source Hamiltonian, extending the experimental applicability of this computational paradigm to most quantum platforms.
  arXiv  Detail & Related papers  (2023-07-03T12:36:32Z)
• Variational Adiabatic Gauge Transformation on real quantum hardware for effective low-energy Hamiltonians and accurate diagonalization [68.8204255655161]
  We introduce the Variational Adiabatic Gauge Transformation (VAGT) VAGT is a non-perturbative hybrid quantum algorithm that can use nowadays quantum computers to learn the variational parameters of the unitary circuit. The accuracy of VAGT is tested trough numerical simulations, as well as simulations on Rigetti and IonQ quantum computers.
  arXiv  Detail & Related papers  (2021-11-16T20:50:08Z)
• 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)
• Parallel Quantum Algorithm for Hamiltonian Simulation [9.680246554758343]
  A parallel quantum algorithm is proposed for simulating the dynamics of a large class of Hamiltonians. The running time of our parallel quantum simulation algorithm measured by the quantum circuit depth has a doubly (poly-)logarithmic dependence. We show that the total gate depth of our algorithm has a $operatornamepolyloglog (1/epsilon)$ dependence in the parallel setting.
  arXiv  Detail & Related papers  (2021-05-25T12:46:33Z)
• 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)
• Low-depth Hamiltonian Simulation by Adaptive Product Formula [3.050399782773013]
  Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. Here, we propose an adaptive approach to construct a low-depth time evolution circuit. Our work sheds light on practical Hamiltonian simulation with noisy-intermediate-scale-quantum devices.
  arXiv  Detail & Related papers  (2020-11-10T18:00:42Z)
• 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)
• 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)

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.