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Journal of Computational and Theoretical Nanoscience

Quantum Dynamics of Gate Operations on Charge Qubits

R. Green, Jingbo B. Wang

Published Oct 1, 2004• 1 citation
Publisher

Abstract

We present a detailed analysis of the time evolution of a charge qubit realized in the lowest bound states of a double well potential. A mechanism for quantum gate operations on this qubit is modeled by directly solving the corresponding time-dependent Schrodinger equation. We demonstrate that the mechanism induces complicated non-adiabatic time evolution of the qubit system. With ideal potentials and instantaneous switching, this mechanism is shown to be capable of carrying out a NOT gate operation, and rotations by pi/4 and 3 pi/4. Effects of non-ideal potentials and smooth switching are also examined.

DOI
10.1166/jctn.2004.026

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We present a detailed analysis of the time evolution of a charge qubit realized in the lowest bound states of a double well potential. A mechanism for quantum gate operations on this qubit is modeled by directly solving the corresponding time-dependent Schrodinger equation. We demonstrate that the mechanism induces complicated non-adiabatic time evolution of the qubit system. With ideal potentials and instantaneous switching, this mechanism is shown to be capable of carrying out a NOT gate operation, and rotations by pi/4 and 3 pi/4. Effects of non-ideal potentials and smooth switching are also examined.
In this paper, we develop a nonperturbation theory for describing decoherence dynamics of electron charges in a double quantum dot gated by electrodes. We extend the Feynman-Vernon influence functional theory to fermionic environments and derive an exact master equation for the reduced density matrix of electrons in the double dot for a general spectral density at arbitrary temperature and bias. We then investigate the decoherence dynamics of the double-dot charge qubit with backreaction of the reservoirs being fully taken into account. Time-dependent fluctuations and leakage effects induced from the dot-reservoir coupling are explicitly explored. The charge qubit dynamics from the Markovian to non-Markovian regime is systematically studied under various manipulating conditions. The decay behavior of charge qubit coherence and the corresponding relaxation time T1{T}_{1}T1​ and dephasing time T2{T}_{2}T2​ are analyzed in detail.
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Abstract. The coherent time evolution of electrons in double quantum dots induced by fast bias-voltage switches is studied theoretically. As it was shown experimentally, such driven double quantum dots are potential devices for controlled manipulation of charge qubits. By numerically solving a quantum master equation we obtain the energy- and time-resolved electron transfer through the device which resembles the measured data. The observed oscillations are found to depend on the level offset of the two dots during the manipulation and, most surprisingly, also the on initialization stage. By means of an analytical expression, obtained from a large-bias model, we can understand the prominent features of these oscillations seen in both the experimental data and the numerical results. These findings strengthen the common interpretation in terms of a coherent transfer of electrons between the dots. PACS numbers: 73.63.Kv,73.23.Hk,72.10.-d
Abstract This chapter begins the discussion of the time evolution of an active quantum system. From the earlier chapters, time dependent physics has been observed through the presence of the time evolution of the phase of each eigenstate. The Hamiltonian itself is time independent. This represents the same kind of evolution of a classical system like the vibration of a tuning fork when it has been struck or the oscillation of an LC circuit if the capacitor is charged to some voltage and then the switch is closed. In the quantum case, the Hamiltonian has also been time independent. The time evolution evolves according the full-time dependent Schrödinger equation, depending only on a single initial condition of the state vector or wave function and the corresponding time evolution of the phase factor for each eigenstate. However in this chapter, we consider the case of when there is a time dependent Hamiltonian such as a sinewave generator or laser. As in the case of resonant tunneling, we see the importance in dynamics of resonant coupling. With an oscillating potential energy term, we see the presence of Rabi oscillations in the probability amplitude of a two-state system on resonance, which can be viewed as a quantum flip-flop between two states of a quantum bit (qubit).
We examine the realization of a quantum CNOT gate by adiabatic operations.The principles of such systems and their analysis are briefly discussed and a model consisting of two weakly coupled double- potential well qubits is studied numerically. Regions of the parameter space with suitable well-defined sets of wavefunctions are found, in which then an adiabatic sweep of an external bias produces the switching behavior of CNOT. Results are presented on the adiabatic condition and the identification with the parameters of a flux-coupled two-SQUID system is given.For typical parameters adiabatic times in the nanosecond regime are obtained.
The coherent time evolution of electrons in double quantum dots (DQDs) induced by fast bias-voltage switches is studied theoretically. As it was shown experimentally, such driven DQDs are potential devices for controlled manipulation of charge qubits. By numerically solving a quantum master equation, we obtain the energy- and time-resolved electron transfer through the device that resembles the measured data. The observed oscillations are found to depend on the level offset of the two dots during the manipulation and, most surprisingly, also the initialization stage. By means of an analytical expression, obtained from a large-bias model, we can understand the prominent features of these oscillations seen in both the experimental data and the numerical results. These findings strengthen the common interpretation in terms of a coherent transfer of electrons between the dots.