Elucidating the Interplay between Non‐Stoquasticity and the Sign Problem

Gupta, Lalit; Hen, Itay

doi:10.1002/qute.201900108

Cited by 17 publications

(18 citation statements)

References 35 publications

(98 reference statements)

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“…The ground state of the system is a stationary state; there are no time dynamics and the LHS is equal to zero. Attempting to simulate the imaginary time Schrödinger equation via the application of the approximated imaginary time operator naïvely one would encounter the sign problem [8,29], resulting from the antisymmetry constraint of exchange of electrons. The most successful approach to avoiding the sign problem in DMC simulations is the fixed node approximation [30].…”

Section: Diffusion Monte Carlomentioning

confidence: 99%

Simulations of state-of-the-art fermionic neural network wave functions with diffusion Monte Carlo

Wilson,

Gao,

Wudarski

et al. 2021

Preprint

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Recently developed neural network-based ab-initio solutions (Pfau et. al arxiv:1909.02487v2) for finding ground states of fermionic systems can generate state-of-the-art results on a broad class of systems. In this work, we improve the results for this Ansatz with Diffusion Monte Carlo. Additionally, we introduce several modifications to the network (Fermi Net) and optimization method (Kronecker Factored Approximate Curvature) that reduce the number of required resources while maintaining or improving the modelling performance. In terms of the model, we remove redundant computations and alter the way data is handled in the permutation equivariant function. The Diffusion Monte Carlo results exceed or match state-of-the-art performance for all systems investigated: atomic systems Be-Ne, and the carbon cation C + .

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Section: Diffusion Monte Carlomentioning

confidence: 99%

Simulations of state-of-the-art fermionic neural network wave functions with diffusion Monte Carlo

Wilson,

Gao,

Wudarski

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Suitable anticrossings are required in DQA, and thus for the protocol to be universally applicable a method of guaranteeing they exist for arbitrary problems is required, among other requirements such as a large spectral separation between the first and second excited states. Furthermore, considering that QMC algorithms generally fail due to so-called sign problems, which are intricately related to the notion of nonstoquasticity of the Hamiltonian being sampled [25][26][27], it is believed that using DQA on problems of a nonstoquastic nature could lead to demonstrable quantum-enabled speedups [20]. Furthermore, it has recently been argued that nonstoquasticity is an essential requirement of an annealing Hamiltonian for demonstrating such speedups [24].…”

Section: Introductionmentioning

confidence: 99%

Locally suppressed transverse-field protocol for diabatic quantum annealing

et al. 2021

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Diabatic quantum annealing (DQA) is an alternative algorithm to adiabatic quantum annealing that can be used to circumvent the exponential slowdown caused by small minima in the annealing energy spectrum. We present the locally suppressed transverse-field (LSTF) protocol, a heuristic method for making stoquastic optimization problems compatible with DQA. We show that, provided an optimization problem intrinsically has magnetic frustration due to inhomogeneous local fields, a target qubit in the problem can always be manipulated to create a double minimum in the energy gap between the ground and first excited states during the evolution of the algorithm. Such a double energy minimum can be exploited to induce diabatic transitions to the first excited state and back to the ground state. In addition to its relevance to classical and quantum algorithmic speedups, the LSTF protocol enables DQA proof-of-principle and physics experiments to be performed on existing hardware, provided independent controls exist for the transverse qubit magnetization fields. We discuss the implications on the coherence requirements of the quantum annealing hardware when using the LSTF protocol, considering specifically the cases of relaxation and dephasing. We show that the relaxation rate of a large system can be made to depend only on the target qubit, presenting opportunities for the characterization of the decohering environment in a quantum annealing processor.

show abstract

“…Suitable anti-crossings are required in DQA, and thus for the protocol to be universally applicable, a method of guaranteeing they exist for arbitrary problems is required, among other requirements such as a large spectral separation between the first and second excited states. Furthermore, considering that QMC algorithms generally fail due to socalled sign problems, which are intricately related to the notion of non-stoquasticity of the Hamiltonian being sampled [25][26][27], it is believed that using DQA on problems of a non-stoquastic nature could lead to demonstrable quantum-enabled speedups [20]. Furthermore, it has recently been argued that non-stoquasticity is an essential requirement of an annealing Hamiltonian for demonstrating such speedups [24].…”

Section: Introductionmentioning

confidence: 99%

Locally Suppressed Transverse-Field Protocol for Diabatic Quantum Annealing

Fry-Bouriaux,

O'Connor,

Feinstein

et al. 2021

Preprint

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Diabatic quantum annealing (DQA) is an alternative algorithm to adiabatic quantum annealing (AQA) that can be used to circumvent the exponential slowdown caused by small minima in the annealing energy spectrum. We present the locally suppressed transverse-field (LSTF) protocol, a heuristic method for making stoquastic optimization problems compatible with DQA. We show that, provided an optimization problem intrinsically has magnetic frustration due to inhomogeneous local fields, a target qubit in the problem can always be manipulated to create a double minimum in the energy gap between the ground and first excited states during the evolution of the algorithm. Such a double energy minimum can be exploited to induce diabatic transitions to the first excited state and back to the ground state. In addition to its relevance to classical and quantum algorithmic speedups, the LSTF protocol enables DQA proof-of-principle and physics experiments to be performed on existing hardware, provided independent controls exist for the transverse qubit magnetization fields. We discuss the implications on the coherence requirements of the quantum annealing hardware when using the LSTF protocol, considering specifically the cases of relaxation and dephasing. We show that the relaxation rate of a large system can be made to depend only on the target qubit presenting new opportunities for the characterization of the decohering environment in a quantum annealing processor.

show abstract

Elucidating the Interplay between Non‐Stoquasticity and the Sign Problem

Cited by 17 publications

References 35 publications

Simulations of state-of-the-art fermionic neural network wave functions with diffusion Monte Carlo

Simulations of state-of-the-art fermionic neural network wave functions with diffusion Monte Carlo

Locally suppressed transverse-field protocol for diabatic quantum annealing

Locally Suppressed Transverse-Field Protocol for Diabatic Quantum Annealing

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