Monte Carlo Simulation of Quantum Spin Systems. I

Suzuki, Masuo; Miyashita, Seiji; Kuroda, Aki

doi:10.1143/ptp.58.1377

Cited by 274 publications

(168 citation statements)

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“…The factor N −2 corrects for the trivial free walk behavior that is present even in the absence of barriers. We now quantize the problem by introducing a standard Trotter-Suzuki time discretization [16]. We choose a regular temporal lattice with N τ = 128 or 256 time slices, a finite step size τ = 1 in the τ direction, and periodic boundary conditions in Trotter time.…”

Section: Results Of Simulationmentioning

confidence: 99%

Classical and quantum annealing in the median of three-satisfiability

et al. 2011

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We determine the classical and quantum complexities of a specific ensemble of three-satisfiability problems with a unique satisfying assignment for up to N = 100 and 80 variables, respectively. In the classical limit, we employ generalized ensemble techniques and measure the time that a Markovian Monte Carlo process spends in searching classical ground states. In the quantum limit, we determine the maximum finite correlation length along a quantum adiabatic trajectory determined by the linear sweep of the adiabatic control parameter in the Hamiltonian composed of the problem Hamiltonian and the constant transverse field Hamiltonian. In the median of our ensemble, both complexities diverge exponentially with the number of variables. Hence, standard, conventional adiabatic quantum computation fails to reduce the computational complexity to polynomial. Moreover, the growth-rate constant in the quantum limit is 3.8 times as large as the one in the classical limit, making classical fluctuations more beneficial than quantum fluctuations in ground-state searches.

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Section: Results Of Simulationmentioning

confidence: 99%

Classical and quantum annealing in the median of three-satisfiability

et al. 2011

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“…Note that τ needs to be chosen small enough with respect to the energy scales and the other relevant time scales of H (t) such that the exact mathematical solution of the TDSE is obtained up to some fixed numerical precision. Subsequently, the exponential of H (t + τ/2) is decomposed using the Lie-Trotter-Suzuki product formula [54]. This is done by partitioning the tridiagonal matrices into even and odd sums of 2 × 2 block-diagonal matrices such that each matrix exponential can be evaluated analytically (cf.…”

Section: Appendix A: Description Of the Algorithmmentioning

confidence: 99%

Gate-error analysis in simulations of quantum computers with transmon qubits

et al. 2017

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In the model of gate-based quantum computation, the qubits are controlled by a sequence of quantum gates. In superconducting qubit systems, these gates can be implemented by voltage pulses. The success of implementing a particular gate can be expressed by various metrics such as the average gate fidelity, the diamond distance, and the unitarity. We analyze these metrics of gate pulses for a system of two superconducting transmon qubits coupled by a resonator, a system inspired by the architecture of the IBM Quantum Experience. The metrics are obtained by numerical solution of the time-dependent Schrödinger equation of the transmon system. We find that the metrics reflect systematic errors that are most pronounced for echoed cross-resonance gates, but that none of the studied metrics can reliably predict the performance of a gate when used repeatedly in a quantum algorithm.

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“…In early world-line Monte Carlo algorithms, updates of a configuration were done in many steps, 1,22,23) each being a local update that modifies only a small part of the system. Before the loop algorithm, the unit of the local update was a square whose spatial dimension equals the lattice spacing and the temporal dimension the discretization unit of time.…”

Section: Path Integral and Quantum Monte Carlomentioning

confidence: 99%

Recent Developments of World-Line Monte Carlo Methods

2004

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World-line quantum Monte Carlo methods are reviewed with an emphasis on breakthroughs made in recent years. In particular, three algorithms -the loop algorithm, the worm algorithm, and the directedloop algorithm -for updating world-line configurations are presented in a unified perspective. Detailed descriptions of the algorithms in specific cases are also given.KEYWORDS: quantum spin system, Heisenberg model, quantum Monte Carlo, XY model, XXZ model, cluster algorithm, loop algorithm, worm algorithm, directed-loop algorithm, world-line method

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Monte Carlo Simulation of Quantum Spin Systems. I

Cited by 274 publications

References 1 publication

Classical and quantum annealing in the median of three-satisfiability

Classical and quantum annealing in the median of three-satisfiability

Gate-error analysis in simulations of quantum computers with transmon qubits

Recent Developments of World-Line Monte Carlo Methods

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