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Physics of Particles and Nuclei Letters

Dynamics of Quantum States in a System of 3 Quantum Dots with Dipole-Dipole Interaction

M. V. Altaĭsky, N. E. Kaputkina, В. А. Крылов

Published Nov 1, 2019• 0 citations
Publisher

Abstract

Abstract We present the results of simulation of the dynamics of a 3 quantum dot array by means of numerical solution of the von Neumann equation $$\imath \dot {\rho } = [H,\rho ].$$ The trace over the states of phonon bath was taken by Feynman path integral numerical calculation. It is shown that simplistic system of 3 quantum dots with common phonon bath can implement $$\neg $$XOR logic operation. The results of our model can be applied to the development of different quantum simulators, quantum gates, and quantum neural networks implemented in arrays of quantum dots.

DOI
10.1134/s1547477119060013

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Abstract We present the results of simulation of the dynamics of a 3 quantum dot array by means of numerical solution of the von Neumann equation ıρ˙=[H,ρ].\imath \dot {\rho } = [H,\rho ].ρ˙​=[H,ρ]. The trace over the states of phonon bath was taken by Feynman path integral numerical calculation. It is shown that simplistic system of 3 quantum dots with common phonon bath can implement ¬\neg ¬XOR logic operation. The results of our model can be applied to the development of different quantum simulators, quantum gates, and quantum neural networks implemented in arrays of quantum dots.
Evolution of quantum states of array of quantum dots is analyzed by means of numerical solution of the von Neumann equation. For two qubit system with dipole–dipole interaction and common phonon bath the evolution of the symmetric state ↑↓+↓↑2\frac{{ \uparrow \downarrow + \downarrow \uparrow }}{{\sqrt 2 }}2​↑↓+↓↑​ leads to the mixture of the triplet states, leaving the singlet decoupled. For three qubit system (D1/2⊗3=D3/2+2D1/2)\left( {D_{1/2}^{ \otimes 3} = D_{3/2} + 2D_{1/2} } \right)(D1/2⊗3​=D3/2​+2D1/2​) with common phonon bath we observed similar effects within the quartet state D3/2 if all qubits were symmetrically connected.
We present the results of the simulation of a quantum neural network based on quantum dots using numerical method of path integral calculation.In the proposed implementation of the quantum neural network using an array of single-electron quantum dots with dipole-dipole interaction, the coherence is shown to survive up to 0.1 nanosecond in time and up to the liquid nitrogen temperature of 77K.We study the quantum correlations between the quantum dots by means of calculation of the entanglement of formation in a pair of quantum dots on the GaAs based substrate with dot size of 10 0 ÷ 10 1 nanometer and interdot distance of 10 1 ÷ 10 2 nanometers order.
We propose an implementation of quantum neural networks using an array of quantum dots with dipole-dipole interactions. We demonstrate that this implementation is both feasible and versatile by studying it within the framework of GaAs based quantum dot qubits coupled to a reservoir of acoustic phonons. Using numerically exact Feynman integral calculations, we have found that the quantum coherence in our neural networks survive for over a hundred ps even at liquid nitrogen temperatures (77 K), which is three orders of magnitude higher than current implementations, which are based on SQUID-based systems operating at temperatures in the mK range.
We demonstrate theoretical stationary and dynamical generation of Bell states in a system of two parallel double quantum dots with one mobile electron each (proposed as two charge qubits) driven by an external potential difference applied to the second of the double dots. For coherent dynamics, it is shown that each one of the four Bell states is obtained through a suitable nonentangled initial condition as well as through the control of the time-dependent external electric field. We analyze dissipative effects on such state formation, due to the coupling with a thermal bath of phonons. Via a Markovian master equation approach, which includes the electron-phonon interaction, we found that Bell-state probabilities are preserved for very low temperature but are adversely affected as the temperature increases. In addition, we include concurrence and charge distribution calculations in order to characterize the double-dot array. This electrostatic mechanism could be of interest in quantum-computation, -information, and -communication schemes.
Abstract Quantum mechanics often results in extremely complex phenomena, especially when the quantum system under consideration is composed of many interacting particles. The states of these many‐body systems live in a space so large that classical numerical calculations cannot compute them. Quantum simulations can be used to overcome this problem: complex quantum problems can be solved by studying experimentally an artificial quantum system operated to simulate the desired hamiltonian. Quantum dot systems have shown to be widely tunable quantum systems, that can be efficiently controlled electrically. This tunability and the versatility of their design makes them very promising quantum simulators. This paper reviews the progress towards digital quantum simulations with individually controlled quantum dots, as well as the analog quantum simulations that have been performed with these systems. The possibility to use large arrays of quantum dots to simulate the low‐temperature Hubbard model is also discussed. The main issues along that path are presented and new ideas to overcome them are proposed.
We develope a method of mapping quantum nonequilibrium steady-state to an effective equilibrium system and present an algorithm to calculate electron-transport using an equilibrium technique. A systematic implementation of boundary conditions in steady-state nonequilibrium is made in the statistical operator $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{Y}$ constructed from scattering state operators. We explicitly demonstrate the equivalence of this method to nonequilibrium Green function techniques for a noninteracting quantum dot model. In electron-phonon coupled quantum dot systems, we formulate an algorithm to construct the statistical bias operator $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{Y}$ and perform a full many-body calculation with the quantum Monte Carlo technique. The results coherently demonstrate various transport behaviors such as phonon dephasing, $I\ensuremath{-}V$ staircase, and phonon-assisted tunneling phenomena. This formulation makes the existing computational quantum many-body techniques applicable to quantum steady-state nonequilibrium problems, which will complement the theories based on the diagrammatic approach.