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.
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.
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.
The charge and spin degrees of freedom of an electron constitute natural bases for constructing quantum two level systems, or qubits, in semiconductor quantum dots. The quantum dot charge qubit offers a simple architecture and high-speed operation, but generally suffers from fast dephasing due to strong coupling of the environment to the electron’s charge. On the other hand, quantum dot spin qubits have demonstrated long coherence times, but their manipulation is often slower than desired for important future applications. This talk will present experimental progress of a ‘hybrid’ qubit, formed by three electrons in a Si/SiGe double quantum dot, which combines desirable characteristics (speed and coherence) in the past found separately in qubits based on either charge or spin degrees of freedom. Using resonant microwaves, we first discuss qubit operations near the ‘sweet spot’ for charge qubit operation. Along with fast ( >GHz) manipulation rates for any rotation axis on the Bloch sphere, we implement two independent tomographic characterization schemes in the charge qubit regime: traditional quantum process tomography (QPT) and gate set tomography (GST). We also present resonant qubit operations of the hybrid qubit performed on the same device, DC pulsed gate operations of which were recently demonstrated. We demonstrate three-axis control and the implementation of dynamic decoupling pulse sequences. Performing QPT on the hybrid qubit, we show that AC gating yields π rotation process fidelities higher than 93% for X-axis and 96% for Z-axis rotations, which demonstrates efficient quantum control of semiconductor qubits using resonant microwaves. We discuss a path forward for achieving fidelities better than the threshold for quantum error correction using surface codes.
There are many successful proposals for using electron spins in quantum dots as qubits. However, a semiconductor quantum dot-based qubit that is scalable, reliable and robust enough for actual quantum information applications has not been realized yet. Common problems in semiconductor quantum dot-based spin qubits are (i) the manipulation and coupling of spin states in a scalable way and (ii) the decoherence of the qubit. While the first problem has been overcome with the so-called exchange-only qubit, the second problem is still hindering the progress towards large-scale quantum computation using quantum dot-based spin qubits.\n \n In this regard, we propose a feasible and scalable exchange-only spin qubit composed of four quantum dots that is, to leading order, intrinsically insensitive to randomly fluctuating magnetic noise, while still offering a full electric control. Motivated by our findings, we then analyze in full detail the main relaxation mechanisms in exchange-only spin qubits composed of three and four dots, and find the regimes where the coherence time of the qubit can be extended by several orders of magnitude. We then explore the possibility of implementing our proposal for an exchange-only qubit in a device composed of three quantum dots—which would offer an unprecedented degree of tunability—and in an already existing device with five quantum dots, proving that a straightforward implementation of our proposal is feasible.\n \n We conclude this project with a thorough analysis of a common electric dipole spin resonance (EDSR) experiment in a system composed of two quantum dots with intrinsic spin-mixing mechanisms. EDSR is a broadly used tool for spectroscopy of quantum dots, yet a detailed theoretical analysis of the physics of an electrically driven system of quantum dots at resonance is still lacking.
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.
Recent studies in self-assembled InAs quantum dots (QDs) for applications in quantum information processing have demonstrated initialization, readout and long decoherence time of an electron spin confined in a single QD. These arguably fulfill three out of the five DiVincenzo criteria for the physical implementation of quantum computation. Based on recent developments self-assembled InAs quantum dot molecules (QDMs), several advancements in the optical manipulation of two-electron spin states have been made. As a continuation of these studies towards a full two-qubit system, this thesis addresses one of the remaining criteria concerning a universal set of quantum gates. The physical platform for two-qubit gates is provided by two electrons confined in the QDM where the Coulomb exchange interaction gives rise to the singlet and triplet manifolds. In a transverse magnetic field, an eight-level system consisting of four singlet-triplet spin states, four optical excited states and twelve dipole allowed transitions arises. Spin initialization via multi-laser optical pumping is demonstrated with near unity fidelity for three of the spin states, while the remaining one can, in principle, be achieved by coherent optical pumping using four CW lasers. The effects of dynamic nuclear spin polarization, arising from the coupling between the electrons and the surrounding nuclei, is evident in the frequency pulling and pushing lineshapes in absorption profiles. This thesis shows that the optical nuclear spin locking that was demonstrated in a single QD earlier is effective in QDMs, yielding a long spin decoherence time of about 1 microsecond. Spectroscopic evidence suggests that this is accompanied by the first evidence of a narrowing in the Overhauser field distribution. The results reveal that stabilization of nuclear spin polarization in both QDs is achieved by optical manipulations in the top QD, demonstrating the effect of non-local nuclear spin locking. Finally, it is shown theoretically that pulsed excitation results in single spin rotations and in conjunction with the Coulomb exchange interaction, provides the ingredients for a universal two-qubit gate. A feasible experimental demonstration of the two-qubit gate is proposed, along with the methodology for the population readout of individual spin states.
Single spins in semiconductor quantum dots form a promising platform for solid-state quantum information processing. The spin-up and spin-down states of a single electron or hole, trapped inside a quantum dot, can represent a single qubit with a reasonably long decoherence time. The spin qubit can be optically coupled to excited (charged exciton) states that are also trapped in the quantum dot, which provides a mechanism to quickly initialize, manipulate and measure the spin state with optical pulses, and to interface between a stationary matter qubit and a 'flying' photonic qubit for quantum communication and distributed quantum information processing. The interaction of the spin qubit with light may be enhanced by placing the quantum dot inside a monolithic microcavity. An entire system, consisting of a two-dimensional array of quantum dots and a planar microcavity, may plausibly be constructed by modern semiconductor nano-fabrication technology and could offer a path toward chip-sized scalable quantum repeaters and quantum computers. This article reviews the recent experimental developments in optical control of single quantum dot spins for quantum information processing. We highlight demonstrations of a complete set of all-optical single-qubit operations on a single quantum dot spin: initialization, an arbitrary SU(2) gate, and measurement. We review the decoherence and dephasing mechanisms due to hyperfine interaction with the nuclear-spin bath, and show how the single-qubit operations can be combined to perform spin echo sequences that extend the qubit decoherence from a few nanoseconds to several microseconds, more than 5 orders of magnitude longer than the single-qubit gate time. Two-qubit coupling is discussed, both within a single chip by means of exchange coupling of nearby spins and optically induced geometric phases, as well as over longer-distances. Long-distance spin-spin entanglement can be generated if each spin can emit a photon that is entangled with the spin, and these photons are then interfered. We review recent work demonstrating entanglement between a stationary spin qubit and a flying photonic qubit. These experiments utilize the polarization- and frequency-dependent spontaneous emission from the lowest charged exciton state to single spin Zeeman sublevels.