A study of entangled systems in the many‐body signed particle formulation of quantum mechanics

Sellier, Jean Michel; Kapanova, Kristina G.

doi:10.1002/qua.25447

Cited by 3 publications

(2 citation statements)

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“…This relatively new formalism is based on the concept of an ensemble of field-less Newtonian particles completely describing the system, provided with a sign, and which create couples of new signed particles according to some pre-computed probability. Because of its simplicity, and in spite of its recent appearance, it has already been applied with success to the simulation of a relatively big number of different situations, both in the context of single-and many-body systems, showing unprecedent advantages in terms of computational resources [4] (the interested reader can find practical examples involving time-dependent simulations of quantum manybody systems in [5]- [9]). Even if this innovative approach has important unique features, one of its bottleneck is represented by the computation of the so-called Wigner kernel, a multi-dimensional integral which is necessary in order to evolve signed particles.…”

Section: Introductionmentioning

confidence: 99%

“…As a practical instance, a three-dimensional wave packet moving in a semiconductor substrate in the presence of a Coulombic potential and various phonon scattering events has been successfully simulated (at different temperatures) and in the presence of both reflective and absorbing boundary conditions, a quite daunting task in other more standard approaches. More recently, the same approach has also been applied to the study of resilience of entanglement in quantum systems in the presence of environmental noise, showing to be a very promising candidate to the development of technology computer aided design (TCAD) software for the development of quantum computing devices [12]. To the best of the author knowledge, this is the only formulation of quantum mechanics which can tackle such problems by means of relatively affordable computational resources.…”

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Combining neural networks and signed particles to simulate quantum systems more efficiently

Sellier¹

2018

Physica A: Statistical Mechanics and its Applications

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Recently a new formulation of quantum mechanics has been suggested which describes systems by means of ensembles of classical particles provided with a sign. This novel approach mainly consists of two steps: the computation of the Wigner kernel, a multi-dimensional function describing the effects of the potential over the system, and the field-less evolution of the particles which eventually create new signed particles in the process. Although this method has proved to be extremely advantageous in terms of computational resources -as a matter of fact it is able to simulate in a time-dependent fashion manybody systems on relatively small machines -the Wigner kernel can represent the bottleneck of simulations of certain systems. Moreover, storing the kernel can be another issue as the amount of memory needed is cursed by the dimensionality of the system. In this work, we introduce a new technique which drastically reduces the computation time and memory requirement to simulate time-dependent quantum systems which is based on the use of an appropriately tailored neural network combined with the signed particle formalism. In particular, the suggested neural network is able to compute efficiently and reliably the Wigner kernel without any training as its entire set of weights and biases is specified by analytical formulas. As a consequence, the amount of memory for quantum simulations radically drops since the kernel does not need to be stored anymore as it is now computed by the neural network itself, only on the cells of the (discretized) phase-space which are occupied by particles. As its is clearly shown in the final part of this paper, not only this novel approach drastically reduces the computational time, it also remains accurate. The author believes this work opens the way towards effective design of quantum devices, with incredible practical implications.Keywords: Quantum mechanics, Neural networks, Signed particle formulation, Wigner kernel, Quantum technology, Computer aided design Preprint submitted to ElsevierOctober 31, 2017 The need for efficient quantum TCADAbout a century ago, in order to understand a series of experiments involving small physical objects such as electrons, atoms and molecules, a peculiar theory was conceived, known today as quantum mechanics. This remarkable theoretical framework consists of a distinct set of rules which can (in a broad sense) explain and predict the observed features of what we call a quantum system. The implications of such theory are not only of philosophical importance, they also have a huge relevance in applied fields such as electronics and nanoelectronics. In fact, as today semiconductor devices have active lengths in the range of a few tens of nanometers, quantum effects are dominant and classically designed complementary metal-oxide-semiconductor (CMOS) transistors do not operate reliably any longer.Presently, we are entering in the post-CMOS era. Although this might sound like the end of a very successful period for the semiconductor industry, one ...

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Combining neural networks and signed particles to simulate quantum systems more efficiently

Sellier¹

2018

Physica A: Statistical Mechanics and its Applications

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Machine learning and signed particles, an alternative and efficient way to simulate quantum systems

Sellier¹,

Kapanova

Leygonie³

et al. 2019

Int J of Quantum Chemistry

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Recently neural networks have been applied in the context of the signed particle formulation of quantum mechanics to rapidly and reliably compute the Wigner kernel of any provided potential. Important advantages were introduced, such as the reduction of the amount of memory required for the simulation of a quantum system by avoiding the storage of the kernel in a multi-dimensional array, as well as attainment of consistent speedup by the ability to realize the computation only on the cells occupied by signed particles. An inherent limitation was the number of hidden neurons to be equal to the number of cells of the discretized real space. In this work, anew network architecture is presented, decreasing the number of neurons in its hidden layer, thereby reducing the complexity of the network and achieving an additional speedup. The approach is validated on a onedimensional quantum system consisting of a Gaussian wave packet interacting with a potential barrier. K E Y W O R D S machine learning, neural networks, quantum mechanics, signed particle formulation, simulation of quantum systems 1 | INTRODUCTION The aim of quantum chemistry is to understand the properties of matter by modeling its behavior on the scale of assembly of nuclei and electrons.At this scale, the most widely used equation for the interactions between those elements is the Schrödinger's equation. Yet, the exact solution of the Schrödinger equation necessitates exponential need for resources due to increase of the dimensionality of the Hilbert space making such methods intractable for more than a few atoms. [1] The ability to describe systems consisting of thousands of interacting particles requires new highly parallel algorithms running on modern high-performance computers. [2,3] Recently a new formulation of quantum mechanics has been introduced, which does not rely on the standard concept of a wave function but, instead, is based on the new notion of an ensemble of particles provided with a sign. This novel approach is usually referred to as the signed particle formulation of quantum mechanics, [4] while its numerical discretization is known as the Wigner Monte Carlo method. In spite of its relatively recent appearance, it has already been applied to the simulation of a plethora of different quantum systems, in both the single-and many-body cases, showing unprecedented advantages, for example, in the simulation of the hydrogen atom as a full quantum two-body system and thus moving beyond the Born-Oppenheimer approximation, a very promising tool for first-principle-only quantum chemistry. [5] The same approach has also been applied to the study of the resilience of entangled quantum systems in the presence of environmental noise. [6] To the best of the authors knowledge, this is the only formulation of quantum mechanics, which can concretely tackle such problems by means of relatively affordable computational resources and without having to recur to arbitrary unphysical approximations. Despite the unique features of the signed

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Signed particles and neural networks, towards efficient simulations of quantum systems

Sellier¹,

Caron²,

Leygonie³

2019

Journal of Computational Physics

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A study of entangled systems in the many‐body signed particle formulation of quantum mechanics

Cited by 3 publications

References 27 publications

Combining neural networks and signed particles to simulate quantum systems more efficiently

Combining neural networks and signed particles to simulate quantum systems more efficiently

Machine learning and signed particles, an alternative and efficient way to simulate quantum systems

Signed particles and neural networks, towards efficient simulations of quantum systems

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