Quantum information processing with macroscopic two-component Bose-Einstein condensates

Pyrkov, Alexey N.; Byrnes, Tim

doi:10.1117/12.2522432

Cited by 3 publications

(2 citation statements)

References 54 publications

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“…The Gross–Pitaevskii equation is one particular case of the NLSE and the most efficient way to describe the time evolution of Bose–Einstein condensates (BECs) . The use of BECs to solve classical optimization problems and perform quantum algorithms has been investigated in recent years.…”

Section: Introductionmentioning

confidence: 99%

Nontrivial Attractors of the Perturbed Nonlinear Schrödinger Equation: Applications to Associative Memory and Pattern Recognition

2019

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Computers are dynamical systems that carry out information processing through their change of state with time. For instance, neural networks such as Hopfield's associative memory are dissipative dynamical systems in a finite dimensional configuration space with attractors that represent stored patterns. In particular, dissipative dynamical systems with an infinite dimensional configuration space are of broad interest and have the possibility to store and restore complex and strongly distorted data structures. In this work, the nonlinear Schrödinger equation (NLSE) with a dissipative perturbation which creates a frictional force acting on soliton is considered. It is shown that the control of the perturbative term allows one to decrease the velocity of soliton to zero and conserve a positive value of its amplitude. The existence of such a frictional force would suggest that the perturbation makes the zero‐velocity solitonic solution of non‐zero amplitude into an attractor for all evolution trajectories whose initial conditions are moving solitons. This allows a way to store information in the infinite dimensional dynamical system governed by NLSE using principles which are completely analogous to that of Hopfield's associative memory. This approach can be realized with solitons in Bose–Einstein condensates and nonlinear optical systems.

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Section: Introductionmentioning

confidence: 99%

Nontrivial Attractors of the Perturbed Nonlinear Schrödinger Equation: Applications to Associative Memory and Pattern Recognition

2019

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“…Thus this approach allows one to estimate in advance the parameters of weak measurements needed for advantages in the context of quantum technologies where quantum discord is used as resource. It can provide perspectives in calculating quantum discord especially between macroscopic qubits [57][58][59][60][61][62][63][64] where weak measurements can also be used to effectively characterize the system [65].…”

Section: Introductionmentioning

confidence: 99%

Super-quantum discord in ferromagnetic and antiferromagnetic materials

Fedorova

Byrnes

Pyrkov

2019

Quantum Inf Process

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Super-quantum discord is an extension of the quantum discord concept where weak measurements are made instead of projective measurements. We study the temperature behavior of the superquantum discord for two real magnetic materials. We extract information about super-quantum discord from the magnetic susceptibility data for iron nitrosyl complexes Fe2(SC3H5N2)2(NO)4 and binuclear Cu(II) acetate complex [Cu2L(OAc)] · 6H2O, where L is a ligand that allows us to compare the super-quantum discord with the standard one. The dependence of the super-quantum discord on the parameter describing weak measurements is studied. Obtained difference between super-quantum and quantum discords confirms the detection of additional quantum correlations that are usually destroyed during projective measurements. The use of the approach allows to predict quantitatively in advance the advantages of use of weak measurements versus projective one for quantum technologies in real settings where quantum discord is used as resource. This can be relevant particularly in macroscopic quantum systems where weak measurements can be used to extract information about the system.

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Solitonic Fixed Point Attractors in the Complex Ginzburg–Landau Equation for Associative Memories

2019

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It was recently shown [V.V. Cherny, T. Byrnes, A.N. Pyrkov, Adv. Quantum Technol. 2019 2, 1800087] that the nonlinear Schrodinger equation with a simplified dissipative perturbation of special kind features a zero-velocity solitonic solution of non-zero amplitude which can be used in analogy to attractors of Hopfield's associative memory. In this work, we consider a more complex dissipative perturbation adding the effect of two-photon absorption and the quintic gain/loss effects that yields formally the complex Ginzburg-Landau equation (CGLE). We construct a perturbation theory for the CGLE with a small dissipative perturbation and define the behavior of the solitonic solutions with parameters of the system and compare the solution with numerical simulations of the CGLE. We show that similarly to the nonlinear Schrodinger equation with a simplified dissipation term, a zero-velocity solitonic solution of non-zero amplitude appears as an attractor for the CGLE. In this case the amplitude and velocity of the solitonic fixed point attractor does not depend on the quintic gain/loss effects. Furthermore, the effect of two-photon absorption leads to an increase in the strength of the solitonic fixed point attractor.

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Quantum information processing with macroscopic two-component Bose-Einstein condensates

Cited by 3 publications

References 54 publications

Nontrivial Attractors of the Perturbed Nonlinear Schrödinger Equation: Applications to Associative Memory and Pattern Recognition

Nontrivial Attractors of the Perturbed Nonlinear Schrödinger Equation: Applications to Associative Memory and Pattern Recognition

Super-quantum discord in ferromagnetic and antiferromagnetic materials

Solitonic Fixed Point Attractors in the Complex Ginzburg–Landau Equation for Associative Memories

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