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arXiv:cond-mat/0507178 · Physical Review B

Intrinsic phonon decoherence and quantum gates in coupled lateral quantum-dot charge qubits

M. J. Storcz, Udo Hartmann, Sigmund Kohler, Frank K. Wilhelm

Published Dec 16, 2005• 39 citations
arXivHTMLPDF

Abstract

Recent experiments by [Hayashi et al., Phys. Rev. Lett. 91, 226804 (2003)] demonstrate coherent oscillations of a charge quantum bit in laterally defined quantum dots. We study the intrinsic electron-phonon decoherence and gate performance for the next step: a system of two coupled charge qubits. The effective decoherence model contains properties of local as well as collective decoherence. Decoherence channels can be classified by their multipole moments, which leads to different low-energy spectra. It is shown that due to the super-Ohmic spectrum, the gate quality is limited by the single-qubit Hadamard gates. It can be significantly improved, by using double dots with weak tunnel coupling.

DOI
10.1103/physrevb.72.235321

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Recent experiments by [Hayashi et al., Phys. Rev. Lett. 91, 226804 (2003)] demonstrate coherent oscillations of a charge quantum bit in laterally defined quantum dots. We study the intrinsic electron-phonon decoherence and gate performance for the next step: a system of two coupled charge qubits. The effective decoherence model contains properties of local as well as collective decoherence. Decoherence channels can be classified by their multipole moments, which leads to different low-energy spectra. It is shown that due to the super-Ohmic spectrum, the gate quality is limited by the single-qubit Hadamard gates. It can be significantly improved, by using double dots with weak tunnel coupling.
In this dissertation we discuss decoherence in charge qubits formed by multiple lateral quantum dots in the framework of the spin-boson model and the Born-Markov approximation. We consider the intrinsic decoherence caused by the coupling to bulk phonon modes and electromagnetic environmental fluctuations. In the case of decoherence caused by phonon coupling, two distinct quantum dot configurations are studied and proposed as setups that mitigate its nocive effects : (i) Three quantum dots in a ring geometry with one excess electron in total and (ii) arrays of quantum dots where the computational basis states form multipole charge configurations. For the three-dot qubit, we demonstrate the possibility of performing one- and two-qubit operations by solely tuning gate voltages. Compared to a previous proposal involving a linear three-dot spin qubit, the three-dot charge qubit allows for less overhead on two-qubit operations. For small interdot tunnel amplitudes, the three-dot qubits have Q factors much higher than those obtained for double-dot systems. The high-multipole dot configurations also show a substantial decrease in decoherence at low operation frequencies when compared to the double-dot qubit. We also discuss decoherence due to electromagnetic fluctuations in charge qubits formed by two lateral quantum dots. We use effective circuit models to evaluate correlations of voltage fluctuations in the qubit setup. These correlations allows us to estimate energy (T1) and phase (T2) relaxation times of the the qubit system. We also discuss the dependence the quality factor Q shows with respect to parameters of the setup, such as temperature and capacitive coupling between the electrodes.
We discuss decoherence in charge qubits formed by multiple lateral quantum dots in the framework of the spin-boson model and the Born-Markov approximation. We consider the intrinsic decoherence caused by the coupling to bulk phonon modes. Two distinct quantum dot configurations are studied: (i) Three quantum dots in a ring geometry with one excess electron in total and (ii) arrays of quantum dots where the computational basis states form multipole charge configurations. For the three-dot qubit, we demonstrate the possibility of performing one- and two-qubit operations by solely tuning gate voltages. Compared to a previous proposal involving a linear three-dot spin qubit, the three-dot charge qubit allows for less overhead on two-qubit operations. For small interdot tunnel amplitudes, the three-dot qubits have QQQ factors much higher than those obtained for double-dot systems. The high-multipole dot configurations also show a substantial decrease in decoherence at low operation frequencies when compared to the double-dot qubit.
The spin of an electron confined into a lateral semiconductor quantum dot has been proposed as a possible physical realization of a qubit. While the spin has the advantage of large decoherence times, operations with more than one qubit will necessarily involve orbital degrees of freedom, namely, charge, which is much more prone to decoherence. There are also alternative quantum dot qubit proposals that are entirely based on charge. We have used a realistic model to quantify the limitations imposed by acoustic phonons on the operation of quantum dot-based qubits. Our treatment includes essential aspects of the setup geometry, wave function profile and materials characteristics. The time dependence of the qubit density matrix is the presence of a phonon bath solved within the Born-Markov approximation. We find that the inclusion of geometric form factors makes the phonon-induced decoherence rates in double dot charge qubits nearly one order of magnitude lower than estimates previously in the literature. Moreover, our theoretical prediction for the quality factor of coherent charge oscillations based on phonon decoherence are higher than the values recently observed experimentally. This allows us to conclude that phonons are not the primary source of decoherence in double quantum dot qubits.
We investigate the decoherence of a charge qubit in a double quantum dot which is formed in a free-standing semiconductor slab. The dots are spatially arranged to align along a particular direction. Confined phonons in the slab have a remarkable influence on the dynamics of a qubit system. We show that the decoherence of such a qubit strongly depends on the positions of the dots. By varying the tunnel coupling, the decoherence differs significantly in laterally and vertically coupled quantum dots. A robust qubit is further achieved due to suppression of electron-phonon coupling. Moreover, the coherent evolution of the system is analyzed by modulating the interdot direction.
Lateral semiconductor quantum dot structures have been proposed as an effective quantum bit (qubit) for quantum computation. A single excess electron with the freedom to move between two capacitively coupled quantum dots creates a `pseudo'-spin system with the same qubit behavior as the more natural two level system of a single electron spin. The excess electron in the double dot system is restricted to one of the two dots, thereby creating two separate and distinct states (usually referred to as |L> and |R>). The benefit of these charge qubits lie in the relative ease with which they can be manipulated and created. Experiments have been performed in this area and have shown controllable coherent oscillations and thus efficient single-qubit operations. However, the decoherence rates observed in the experiments is still quite high, making double dot charge qubits not very appealing for large-scale implementations. The following work describes the effect of the electromagnetic (EM) environment of the double quantum dot system on the decoherence of the charge state. Sources of decoherence in similar systems have been extensively investigated before and this paper follows a close theoretical framework to previous work done in the area. The effect of the EM environment can been seen in the calculations discussed below, although it is clear that the decoherence seen in experiments cannot be fully explained by the voltage fluctuations as they are investigated here. The limitations of the calculations are discussed and improvements are suggested.
We investigate electron charge decoherence in a laterally coupled single-electron semiconductor double quantum dot through electron-phonon interaction. We analytically and numerically evaluate the relaxation and dephasing rates due to electron coupling to both acoustic and optical phonons, and explore the system parameter space in terms of interdot distance, strength of single-dot confinement, and interdot coupling strength. Our numerical results show that the electron scattering rates are strongly dependent on the strength of the electron confinement and the size of the system. In addition, although the most dominant factor that determines the charge decoherence rate is the energy splitting between the charge qubit states, the details of the double dot configuration are also very important.