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Decoherence and Entanglement Simulation in a Model of Quantum Neural Network Based on Quantum Dots

M. V. Altaĭsky, N. N. Zol’nikova, N. E. Kaputkina, В. А. Крылов, Yu. E. Lozovik, Nikesh S. Dattani

Published Jan 1, 2016• 4 citations
Publisher

Abstract

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.

DOI
10.1051/epjconf/201610802006

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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.
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.
Noise and decoherence are two major obstacles to the implementation of large-scale quantum computing. Because of the no-cloning theorem, which says we cannot make an exact copy of an arbitrary quantum state, simple redundancy will not work in a quantum context, and unwanted interactions with the environment can destroy coherence and thus the quantum nature of the computation. Because of the parallel and distributed nature of classical neural networks, they have long been successfully used to deal with incomplete or damaged data. In this work, we show that our model of a quantum neural network (QNN) is similarly robust to noise, and that, in addition, it is robust to decoherence. Moreover, robustness to noise and decoherence is not only maintained but improved as the size of the system is increased. Noise and decoherence may even be of advantage in training, as it helps correct for overfitting. We demonstrate the robustness using entanglement as a means for pattern storage in a qubit array. Our results provide evidence that machine learning approaches can obviate otherwise recalcitrant problems in quantum computing.
Noise and decoherence are two major obstacles to the implementation of large-scale quantum computing. Because of the no-cloning theorem, which says we cannot make an exact copy of an arbitrary quantum state, simple redundancy will not work in a quantum context, and unwanted interactions with the environment can destroy coherence and thus the quantum nature of the computation. Because of the parallel and distributed nature of classical neural networks, they have long been successfully used to deal with incomplete or damaged data. In this work, we show that our model of a quantum neural network (QNN) is similarly robust to noise, and that, in addition, it is robust to decoherence. Moreover, robustness to noise and decoherence is not only maintained but improved as the size of the system is increased. Noise and decoherence may even be of advantage in training, as it helps correct for overfitting. We demonstrate the robustness using entanglement as a means for pattern storage in a qubit array. Our results provide evidence that machine learning approaches can obviate otherwise recalcitrant problems in quantum computing.
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.
The time evolution of the quantum mechanical state of an electron is calculated in the framework of the effective-mass envelope function theory for an InAs/GaAs quantum dot. The results indicate that the superposition state electron density oscillates in the quantum dot, with a period on the order of femtoseconds. The interaction energy Eij between two electrons located in different quantum dots is calculated for one electron in the ith pure quantum state and another in the jth pure quantum state. We find that E11〉E12〉E22, and Eij decreases as the distance between the two quantum dots increases. We present a parameter-phase diagram which defines the parameter region for the use of an InAs/GaAs quantum dot as a two-level quantum system in quantum computation. A static electric field is found to efficiently prolong the decoherence time. Our results should be useful for designing the solid-state implementation of quantum computing.