Determining QMC simulability with geometric phases

• URL: http://arxiv.org/abs/2012.02022v1
• Date: Thu, 3 Dec 2020 16:07:07 GMT
• Title: Determining QMC simulability with geometric phases
• Authors: Itay Hen
• Abstract summary: We provide a construction for non-stoquastic, yet sign-problem-free and hence QMC-simulable, quantum many-body models. We also demonstrate why the simulation of truly sign-problematic models using the QMC weights of the stoquasticized Hamiltonian is generally sub-optimal.
• Score: 0.4061135251278187
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Although stoquastic Hamiltonians are known to be simulable via sign-problem-free quantum Monte Carlo (QMC) techniques, the non-stoquasticity of a Hamiltonian does not necessarily imply the existence of a QMC sign problem. We give a sufficient and necessary condition for the QMC-simulability of Hamiltonians in a fixed basis in terms of geometric phases associated with the chordless cycles of the weighted graphs whose adjacency matrices are the Hamiltonians. We use our findings to provide a construction for non-stoquastic, yet sign-problem-free and hence QMC-simulable, quantum many-body models. We also demonstrate why the simulation of truly sign-problematic models using the QMC weights of the stoquasticized Hamiltonian is generally sub-optimal. We offer a superior alternative.

Related papers

• Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement [42.896772730859645]
  We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations. We apply this approach to the classic logistic and Lorenz systems in both integrable and chaotic regimes.
  arXiv  Detail & Related papers  (2024-10-04T18:06:12Z)
• Infusing Self-Consistency into Density Functional Theory Hamiltonian Prediction via Deep Equilibrium Models [30.746062388701187]
  We introduce a unified neural network architecture, the Deep Equilibrium Density Functional Theory Hamiltonian (DEQH) model. DEQH model inherently captures the self-consistency nature of Hamiltonian. We propose a versatile framework that combines DEQ with off-the-shelf machine learning models for predicting Hamiltonians.
  arXiv  Detail & Related papers  (2024-06-06T07:05:58Z)
• Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators [0.7799708033005247]
  Magnus operator is a popular method for time-dependent Hamiltonian simulation in computational mathematics. The development of commutator-free quasi-Magnus operators (CFQMs) circumvents this obstacle. We show that CFQMs are often the most efficient product-formula technique available by more than an order of magnitude.
  arXiv  Detail & Related papers  (2024-03-20T18:01:27Z)
• Work statistics, quantum signatures and enhanced work extraction in quadratic fermionic models [62.997667081978825]
  In quadratic fermionic models we determine a quantum correction to the work statistics after a sudden and a time-dependent driving. Such a correction lies in the non-commutativity of the initial quantum state and the time-dependent Hamiltonian. Thanks to the latter, one can assess the onset of non-classical signatures in the KDQ distribution of work.
  arXiv  Detail & Related papers  (2023-02-27T13:42:40Z)
• Catastrophic failure of quantum annealing owing to non-stoquastic Hamiltonian and its avoidance by decoherence [0.0]
  We present examples showing that non-stoquastic Hamiltonians can lead to catastrophic failure of Quantum annealing (QA) In our example, owing to a symmetry, the Hamiltonian is block-diagonalized, and a crossing occurs during the QA, which leads to a complete failure of the ground-state search. Our results provide a deep insight into the fundamental mechanism of QA.
  arXiv  Detail & Related papers  (2022-09-22T13:10:58Z)
• Quantum annealing with symmetric subspaces [0.0]
  We propose a drive Hamiltonian that preserves the symmetry of the problem Hamiltonian for more efficient Quantum annealing (QA) As non-adiabatic transitions occur only inside the specific subspace, our approach can potentially suppress unwanted non-adiabatic transitions. We find that our scheme outperforms the conventional scheme in terms of the fidelity between the target ground state and the states after QA.
  arXiv  Detail & Related papers  (2022-09-20T09:44:23Z)
• Simultaneous Stoquasticity [0.0]
  Stoquastic Hamiltonians play a role in the computational complexity of the local Hamiltonian problem. We address the question of whether two or more Hamiltonians may be made simultaneously stoquastic via a unitary transformation.
  arXiv  Detail & Related papers  (2022-02-17T19:08:30Z)
• 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)
• 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)
• Stoquasticity in circuit QED [78.980148137396]
  We show that scalable sign-problem free path integral Monte Carlo simulations can typically be performed for such systems. We corroborate the recent finding that an effective, non-stoquastic qubit Hamiltonian can emerge in a system of capacitively coupled flux qubits.
  arXiv  Detail & Related papers  (2020-11-02T16:41:28Z)

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.