We define the qubit as a pair of singlet and triplet states of two electrons in a He-type quantum dot (QD) placed in a diluted magnetic semiconductor (DMS) medium. The molecular field is here essential as it removes the degeneracy of the triplet state and strongly enhances the Zeeman splitting. Methods of qubit rotation as well as two-qubit operations are suggested. The system of a QD in a DMS is described in a way which allows an analysis of the decoherence due to spin waves in the DMS subsystem.
The recent huge increase of the interest in the implementation of quantum information processing (QIP) focused an attention on the semiconductor quantum dots (QDs) as nano-systems with controllable quantum states both in charge and spin degrees of freedom.This creates an opportunity for discussing and modeling of QD-based qubits and quantum-logic gates for prospective quantum computer.Despite of many efforts in this respect the progress is, however, disappointing and the barrier of so-called diVincenzo criteria required to be fulfilled for the QIP technology is not broken and even not approached in any realistic proposal of using QDs for qubits and quantum gates.The reason of this situation is linked with unavoidable restrictions imposed on the coherence and the coherent control of quantum states in QDs, which precludes scalable implementation of qubits and quantum gates based on QDs.The decoherence of charge and of spin degrees of freedom in QDs and QD-systems locates inconveniently straight in the middle of the required six-orders of magnitude diVincenzo window for time scale of the control in comparison to the decoherence rate.This leads to the so-called 'three-orders time-limit' for QIP implementations in QDs.Some advantages of spin degrees of freedom in QDs can be noticed, however.Even though the time scale of the decoherence of spin in of particular practical importance magnetic QDs still is located in the center of six-orders diVincenzo window, the amplitude of the phase decoherence of spin might be frozen on a small level in proximity of the zero temperature.Short critical overview of the dephasing restrictions imposed on the QD technology is the aim of this chapter.
Abstract In this review we discuss a recent proposal to perform partial Bell‐state (parity) measurements on two‐electron spin states for electrons confined to quantum dots. The realization of this proposal would allow for a physical implementation of measurement‐based quantum computing. In addition, we consider the primary sources of energy relaxation and decoherence which provide the ultimate limit to all proposals for quantum information processing using electron spins in quantum dots. We give an account of the Hamiltonians used for the most important interactions (spin–orbit and hyperfine) and survey some of the recent work done to understand dynamics, control, and decoherence under the action of these Hamiltonians. We conclude the review with a table of important decay times found in experiment, and relate these time scales to the potential viability of measurement‐based quantum computing. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We investigate theoretically the hyperfine-induced dephasing of two-electron-spin states in a double quantum dot with a finite singlet-triplet splitting
J. In particular, we derive an effective pure dephasing Hamiltonian, which is valid when the hyperfine-induced mixing is suppressed due to the relatively large
J and the external magnetic field. Using both a quantum theory based on resummation of ring diagrams and semiclassical methods, we identify the dominant dephasing processes in regimes defined by values of the external magnetic field, the singlet-triplet splitting, and inhomogeneity in the total effective magnetic field. We address both free induction and Hahn echo decay of superposition of singlet and unpolarized triplet states (both cases are relevant for singlet-triplet qubits realized in double quantum dots). We also study hyperfine-induced exchange gate errors for two single-spin qubits. Results for III-V semiconductors as well as silicon-based quantum dots are presented.
Since the development of microsized devices is moving forward at enormous speed, there is huge amount of new industrial opportunities. However such devices also require high precision and understanding of the operating of their constituent parts up to the quantum level. The device of the purely quantum nature being developed so far is quantum computer. However the physical realization of it is still not performed, as the requirements for it are very rigorous. \n \nIn the pioneering work by Loss and DiVincenzo it was suggested to use a spin of electron placed in a quantum dot as an information qubit. Following this work the study of electron or hole spin qubits developed. Both experimental and theoretical tools for studying them greatly advanced. \n \nIn the first part of the thesis we study the phonon-induced decoherence and relaxation of singlet-triplet qubits in the double quantum dots. First of all we consider AlGaAs/GaAs double quantum dots. The important result we present here is the strong dephasing that occurs at large detuning. This dephasing is due to two-phonon process that affects mainly singlet state of the qubit and consequently changes the splitting between singlet and triplet leading to dephasing. Remarkably at small detuning this dephasing process is suppressed and the decoherence time is by orders of magnitude longer than in case of large detuning and is mainly defined by one-phonon process. We also present the dependence of relaxation time and decoherence time on the strength of spin-orbit interaction and different directions of the system. Our results provide a deeper insight into the recently obtained experimental data. \n \nWe also studied Si/SiGe quantum dots as a potential candidate for a qubit. Apart from the absence of hyperfine interaction and bulk spin-orbit interaction in the isotopically purified
28Si, its electron-phonon interaction is different from GaAs that also leads to longer qubit lifetimes. We study
S-
T− qubit near the anticrossing of the basis states. This particular region is interesting due to possibilities in operating the qubit. We show that the type of singlet plays a crucial role, i.e. whether it is a singlet with each dot singly occupied or a singlet with only one dot doubly occupied. Depending on the type of singlet the qubit lifetimes change by several orders of magnitude. We also study the influence of a micromagnet, usually used in experiments to operate the qubit, on the relaxation time and decoherence time and present the regime where its effect is negligible. We suggest how to test experimentally our theory of one-phonon and two-phonon processes separately. We also show how the relaxation and decoherence time depend on different system parameters for
S-
T0 qubits. \n \nThe second part of the thesis is devoted to the other important constituent part of microsized devices, namely nanowires. We are interested in the dynamic of polarization of localized spins in the nanowires, as it can affect such important device characteristics as e.g. conductance. \n \nWe studied Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction-induced polarization in the nanowire in case when the voltage is applied to it. It was already proposed theoretically that in the ground state the localized spins in 1D systems align in a helix due to RKKY interaction. This polarization is still present until some critical temperature. The presence of such polarization acts as a spin filter for electrons, that most likely affects the conductance of the nanowire. Therefore we studied how this helical polarization changes when the voltage is applied. The key result is the appearance of the uniform polarization perpendicular to the helix plane, that occurs due to backscattering of electrons that is accompanied by flip-flop process with localized spins. When this uniform polarization is formed, the helix starts to rotate as a whole around the direction of the uniform polarization. We present the dependence of polarization of the localized spins on temperature and voltage. Remarkably the uniform polarization grows both with voltage and temperature in the given range of parameters. \n \nWe also considered the electron-induced relaxation of the nuclear spins. As the electron spins and nuclear spins interact via hyperfine interaction, the nuclear relaxation time reflects some properties of electron bath. Namely, we see a strong dependence of nuclear relaxation time on spin-orbit interaction strength. We present here the dependence of the nuclear relaxation time on the external magnetic field and chemical potential of the wire, that can be experimentally varied via gate. The dependences for the strong spin-orbit interaction and for the weak one are substantially different. Moreover, they have distinct peaks, that allow to get the value of spin-orbit interaction amplitude with the high precision.
Abstract We shall present a review of semiconductor spin‐based implementation schemes for the realization of quantum information/computation solid‐state devices. After briefly describing the fundamentals of quantum computation theory, we shall introduce and discuss potential implementation schemes based on the spin degrees of freedom in semiconductor nanostructures. More specifically, we shall describe an implementation scheme for quantum information processing in which the spin degrees of freedom of electrons confined to a quantum dot are the computational degrees of freedom, and spins are manipulated/controlled through interaction between trionic states created by interband optical transitions by ultrafast sequences of multicolor laser pulses. We will also review briefly an adiabatic method for operating the two‐qubit gate that avoids the main imperfections present in real quantum dots: exciton decay, hole mixing, and phonon decoherence.