Easing the Monte Carlo sign problem

Hangleiter, Dominik; Roth, Ingo; Nagaj, Daniel; Eisert, Jens

doi:10.48550/arxiv.1906.02309

Cited by 10 publications

(13 citation statements)

References 47 publications

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“…Note added. During the completion of this manuscript we became aware of a similar work [28] on the complexity of easing the sign problem in quantum Monte Carlo.…”

Section: Discussionmentioning

confidence: 99%

Wavefunction positivization via automatic differentiation

Torlai,

Carrasquilla,

Fishman

et al. 2019

Preprint

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We introduce a procedure to systematically search for a local unitary transformation that maps a wavefunction with a non-trivial sign structure into a positive-real form. The transformation is parametrized as a quantum circuit compiled into a set of one and two qubit gates. We design a cost function that maximizes the average sign of the output state and removes its complex phases. The optimization of the gates is performed through automatic differentiation algorithms, widely used in the machine learning community. We provide numerical evidence for significant improvements in the average sign, for a two-leg triangular Heisenberg ladder with next-to-nearest neighbour and ring-exchange interactions. This model exhibits phases where the sign structure can be removed by simple local one-qubit unitaries, but also an exotic Bose-metal phase whose sign structure induces "Bose surfaces" with a fermionic character and a higher entanglement that requires two-qubit gates.

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“…Note added. During the completion of this manuscript we became aware of a similar work [28] on the complexity of easing the sign problem in quantum Monte Carlo.…”

Section: Discussionmentioning

confidence: 99%

Wavefunction positivization via automatic differentiation

Torlai,

Carrasquilla,

Fishman

et al. 2019

Preprint

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“…In the rotated basis in which Z i ↔ X i the same Hamiltonian will be written as H = i<j J ij X i X j and will possess a sign problem [2]. Thus, often times curing the sign problem boils down to finding a transformation U to the Hamiltonian such that the decomposition of the partition function of the rotated Hamiltonian H to positive-valued terms is known [2,3,20,21]. It should be noted nonetheless that since in QMC some physical observables are more easily accessible than others depending on whether or not they are diagonal, curing the sign problem via rotation is not always a practical resolution as observables in the rotated frame may be inaccessible as compared to those in the original frame.…”

Section: Curing the Sign Problemmentioning

confidence: 99%

Elucidating the Interplay between Non‐Stoquasticity and the Sign Problem

Gupta

Hen

2019

Adv Quantum Tech

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The sign problem is a key challenge in computational physics, encapsulating the inability to properly understand many important quantum many‐body phenomena in physics, chemistry, and the material sciences. Despite its centrality, the circumstances under which the problem arises or can be resolved as well as its interplay with the related notion of “non‐stoquasticity” are often not very well understood. In this study, an attempt is made to elucidate the circumstances under which the sign problem emerges and to clear up some of the confusion surrounding this intricate computational phenomenon. To that aim, the recently introduced off‐diagonal series expansion quantum Monte Carlo scheme is used to analyze in detail a number of examples that capture the essence of the results.

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“…Note: During the final stages of this work, a number of related works appeared on the arXiv [34], [35], and [36].…”

Section: Acknowledgementsmentioning

confidence: 99%

Mitigating the Sign Problem Through Basis Rotations

Levy,

Clark

2019

Preprint

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Easing the Monte Carlo sign problem

Cited by 10 publications

References 47 publications

Wavefunction positivization via automatic differentiation

Wavefunction positivization via automatic differentiation

Elucidating the Interplay between Non‐Stoquasticity and the Sign Problem

Mitigating the Sign Problem Through Basis Rotations

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