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Physical Review A

Time-evolution simulation of a controlled-NOT gate with two coupled asymmetric quantum dots

S. Moskal, S. Bednarek, Janusz Adamowski

Published Jun 21, 2005• 9 citations
Publisher

Abstract

We study a possible physical realization of a quantum controlled-NOT gate with the use of two weakly coupled asymmetric quantum dots. Solving the time-dependent Schr\"odinger equation for the model two-electron system, we simulate the infrared-radiation-induced quantum transitions that correspond to basic gate operations. We require the transition probabilities to be close to 1 and optimize the parameters of the nanostructure in order to make the gate operation time as short as possible. In the simulations, we have taken into account the entire energy spectrum, which can be populated by the absorption or emission of the infrared radiation. We discuss the consequences of the existence of many bound two-electron states on the probability of radiative transitions.

DOI
10.1103/physreva.71.062327

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We study a possible physical realization of a quantum controlled-NOT gate with the use of two weakly coupled asymmetric quantum dots. Solving the time-dependent Schr"odinger equation for the model two-electron system, we simulate the infrared-radiation-induced quantum transitions that correspond to basic gate operations. We require the transition probabilities to be close to 1 and optimize the parameters of the nanostructure in order to make the gate operation time as short as possible. In the simulations, we have taken into account the entire energy spectrum, which can be populated by the absorption or emission of the infrared radiation. We discuss the consequences of the existence of many bound two-electron states on the probability of radiative transitions.
Abstract: We discuss a possible realization of a quantum controlled-NOT gate with the use of two coupled quantum dots. Transitions between quantum states of a computational basis are driven by the microwave pi-pulse. The parameters of the proposed nanodevice have been optimized in order to make the operation cycle of the gate as short as possible. Numerical solutions of the time-dependent Schrödinger equation allow us to simulate transitions between the quantum states which correspond to the subsequent stages of the gate’s operation. The performed time-dependent simulations are a test of realizability of the quantum controlled-NOT gate in the nanodevice.
A quantum computer based on an asymmetric coupled-dot system has been proposed and shown to operate as a controlled-NOT gate. The basic ideas are the following. (1) The electron is localized in one of the asymmetric coupled dots. (2) The electron transfer takes place from one dot to the other when the energy levels of the coupled dots are set to be close. (3) The Coulomb interaction between the coupled dots mutually affects the energy levels of the other coupled dots. The decoherence time of the quantum computation and the measurement time are estimated. The proposed system can be realized by developing the technology of the single-electron memory using Si nanocrystals, and a direct combination of the quantum circuit and the conventional circuit is possible.
Recent works indicate that coupled quantum dots (QD) are promising nanostructures for realizing quantum gates that are the basic elements of a quantum computer. In QDs, fundamental quantum logic operations can be achieved in a quantum gate by controlling the entanglement between two electron spins by means of external electric and magnetic fields. This chapter describes the computational approach used to solve the many-body Schrodinger equation. It provides results of the simulations for both the strongly coupled and weakly coupled QDs and analyzes the important differences between the two cases. The utilization of simple trial wavefunctions in VMC have lead to good agreement with the ED method, when electrons are decoupled, which validates two-level approaches such as the Heitler-London approximation in weakly coupled QDs.
We study the possibility of implementing a two-qubit controlled-NOT gate operation in a structure consisting of two semiconductor double quantum dots placed in a high- Q optical microcavity and governed by a resonant laser field. The effect of relaxation processes on the dynamics of the two-electron system is discussed. The dissipation rates allowing quantum error correction algorithms to be used are determined. The existing additional excitation channel (laser pulse) is shown to weaken the effect of the nonideality of the cavity on the evolution of the states. Optimal electron coupling coefficients in the quantum dots with control fields are fitted, in which the controlled qubit is switched with the highest probability and the gate implementation takes several hundreds of picoseconds.
We investigate optimal control strategies for state to state transitions in a model of a quantum dot molecule containing two active strongly interacting electrons. The resulting optimized electric pulses are in the THz regime and can populate combinations of states with very short transition times. The speedup compared to intuitively constructed pulses is an order of magnitude. We furthermore make use of optimized pulse control in the simulation of an experimental preparation of the molecular quantum dot system. It is shown that exclusive population of certain excited states leads to a complete suppression of spin dephasing, as predicted in Nepstad et al. [1].
A crucial requirement for scalable quantum-information processing is the realization of multiple-qubit quantum gates. Universal multiple-qubit gates can be implemented by a set of universal single qubit gates and any one kind of two-qubit gate, such as a controlled-NOT (CNOT) gate. Semiconductor quantum dot qubits are a leading approach for the physical implementation of quantum computation, due to their potential for large-scale integration. Two-qubit gate operations have been so far only demonstrated in individual electron spin-based quantum dot systems. Due to the relatively short de-coherence time, charge qubits in quantum dots are generally considered to be inferior for going beyond single qubit level. Here, we demonstrate the benchmarking CNOT gate in two capacitively coupled charge qubits, each consisting of an electron confined in a GaAs/AlGaAs double quantum dot. Owing to the strong inter-qubit coupling strength, gate operations with a clock speed up to 5GHz has been realized. A processing tomography shows encouragingly that the universal two-qubit gate operations have comparable fidelities to that of spin-based two-qubit gates. Our results suggest that semiconductor charge qubits have a considerable potential for scalable quantum computing and may stimulate the use of long-range Coulomb interaction for coherent quantum control in other devices.