Validity of many-body approximation methods for a solvable model

Meshkov, N.; Glick, Arnold J.; Lipkin, Harry J.

doi:10.1016/0029-5582(65)90863-1

Cited by 300 publications

(201 citation statements)

References 7 publications

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“…The general LMG model was introduced as an exactly solvable Hamiltonian for a many-body system (the example of the many-body system considered is a finite system of nuclei) to compare to various techniques and formalisms. The LMG model has subsequently been studied numerically and analytically [16][17][18][19][20][21][22][23]. By considering these analytic and numerical studies of the LMG model, the infinite-range transverse-field Ising model breaks up into submatrices, where each submatrix block is an eigenstate of the S 2 tot , and the submatrix with S 2 tot = N part.…”

Section: Introductionmentioning

confidence: 99%

Diabatic-ramping spectroscopy of many-body excited states

2014

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Due to the experimental time constraints of state of the art quantum simulations, the direct preparation of the ground state by adiabatically ramping the field of a transverse-field Ising model becomes more and more difficult as the number of particles increase. We propose a spectroscopy protocol that intentionally creates excitations through diabatic ramping and measures a low-noise observable as a function of time for a constant Hamiltonian to reveal the structure of the coherent dynamics of the resulting many-body states. To simulate experimental data, noise from counting statistics and decoherence error are added. Compressive sensing is then applied to Fourier transform the simulated data into the frequency domain and extract the low-lying energy excitation spectrum. By using compressive sensing, the amount of data in time needed to extract this energy spectrum is sharply reduced, making such experiments feasible with current technology in, for example, ion trap quantum simulators.

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Section: Introductionmentioning

confidence: 99%

Diabatic-ramping spectroscopy of many-body excited states

2014

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“…The Lipkin-Meshkov-Glick (LMG) model was proposed in 1965 to describe shape phase transitions in nuclei 1,2,3 . This model is often used to describe the magnetic properties of molecules such as Mn 12 acetate 4 .…”

Section: Introductionmentioning

confidence: 99%

Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections

2008

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The spectrum of the Lipkin-Meshkov-Glick model is exactly derived in the thermodynamic limit by means of a spin-coherent-state formalism. In the first step, a classical analysis allows one to distinguish between four distinct regions in the parameter space according to the nature of the singularities arising in the classical energy surface; these correspond to spectral critical points. The eigenfunctions are then analyzed more precisely in terms of the associated roots of the Majorana polynomial, leading to exact expressions for the density of states in the thermodynamic limit. Finitesize effects are also analyzed, leading in particular to logarithmic corrections near the singularities occurring in the spectrum. Finally, we also compute expectation values of the spin operators in a semiclassical analysis in order to illustrate some subtle effects occurring in one region of the parameter space.

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“…In this respect, it would be interesting to use methods developed in this paper to explore QA in mean-field models with different types of driver Hamiltonians whose ground states are not simple product states where ferromagnetic order competes with the transverse (XY) ferromagnetism or superfluidity [46][47][48][49].…”

Section: Discussionmentioning

confidence: 99%

Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy

Kechedzhi

Smelyanskiy

2016

Phys. Rev. X

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Real-life quantum computers are inevitably affected by intrinsic noise resulting in dissipative nonunitary dynamics realized by these devices. We consider an open-system quantum annealing algorithm optimized for such a realistic analog quantum device which takes advantage of noise-induced thermalization and relies on incoherent quantum tunneling at finite temperature. We theoretically analyze the performance of this algorithm considering a p-spin model that allows for a mean-field quasiclassical solution and, at the same time, demonstrates the first-order phase transition and exponential degeneracy of states, typical characteristics of spin glasses. We demonstrate that finite-temperature effects introduced by the noise are particularly important for the dynamics in the presence of the exponential degeneracy of metastable states. We determine the optimal regime of the open-system quantum annealing algorithm for this model and find that it can outperform simulated annealing in a range of parameters. Large-scale multiqubit quantum tunneling is instrumental for the quantum speedup in this model, which is possible because of the unusual nonmonotonous temperature dependence of the quantum-tunneling action in this model, where the most efficient transition rate corresponds to zero temperature. This model calculation is the first analytically tractable example where open-system quantum annealing algorithm outperforms simulated annealing, which can, in principle, be realized using an analog quantum computer.

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Validity of many-body approximation methods for a solvable model

Cited by 300 publications

References 7 publications

Diabatic-ramping spectroscopy of many-body excited states

Diabatic-ramping spectroscopy of many-body excited states

Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections

Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy

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