In the present chapter, the possibility of spin states control in quantum dots as bases of creation of logic elements on the basis of quantum semi-conductor systems is discussed. In particular, the multi-particle approach to the description of spin system and control of coherent spin conditions is developed. It is shown that at action by an impulse of a magnetic field two types of spin conditions are possible, depending on initial data: conditionally steady and absolutely steady. The second type of conditions is important for information storage.
In the present chapter, the possibility of spin states control in quantum dots as bases of creation of logic elements on the basis of quantum semi-conductor systems is discussed. In particular, the multi-particle approach to the description of spin system and control of coherent spin conditions is developed. It is shown that at action by an impulse of a magnetic field two types of spin conditions are possible, depending on initial data: conditionally steady and absolutely steady. The second type of conditions is important for information storage.
Recently, an implementation of a universal set of one- and two-quantum-bit gates for quantum computation using spin states of coupled single-electron quantum dots was proposed. It was demonstrated that it is possible to execute a coherent control of a quantum system based on two-electron spin states in a double quantum dot, allowing state preparation, coherent manipulation, and projective readout. This possibility is based on rapid electrical control of the spin exchange interaction. These results motivated us to develop a formal theoretical study of the corresponding model of two coupled spins placed in a magnetic field and subjected to a time-dependent mutual Heisenberg interaction. Using possible exact solutions of the corresponding quantum problem, we study entangling of different separable initial states in this model. It is demonstrated that the entanglement due to a time-dependent Heisenberg interaction is dominating in comparison with the entanglement due to the action of an external magnetic field.
The physical basis of the method of implementing quantum logical operations in a continuous microwave field in a system of two electrons with different g-factors and a constant exchange interaction is developed. A small variable additive Δ B ( t ) to the magnetic field is proposed as a control action. It is obtained that a simple functional dependence Δ B ( t ), based on harmonic functions, allows us to perform elementary quantum logical operations and their sequences. This method is adapted to the experimental conditions.
This thesis discusses various schemes and protocols for quantum information processing in mesoscopic systems with particular focus on using the spin of a particle as the bearer of information. The first chapter introduce various aspects of the field of quantum information used in this thesis such as qubits, entanglement, its quantification, quantum logic gates and entanglement swapping. In this chapter concepts such as AKLT states, decoherence and adiabatic elimination are introduced as they will be relevant in the thesis. In chapter 2 we introduce the Quantum Dots as the solid state system that will primarily be used as the hardware for the development of Quantum Information Processing (QIP). The different properties of quantum dots depending on their size are discussed. The exchange interaction between tunnel coupled quantum dots and the background of quantum computation in quantum dots is described. The principal sources of decoherence and the measurement techniques for spin qubits are presented. In chapter 3, carbon nanowires filled with N@C60 dimers are studied to analyse the entanglement between nuclear spins. The dimer is modelled as a two coupled nuclear spin- electron spin pair with a Heisenberg interaction. The entanglement have been studied depending on the temperature and the intensity of an external magnetic field. Witnessing the entanglement, and particularly bound entanglement are discussed. In chapter 4, the way to extract a singlet from a quantum dot is explored. The system that we model will be consisting of a triple dot and analyse the best way to get the singlet out, with each electron in a separate dot. The chief motivation is to create a singlet between separate dots in a time-scale much faster than that given by spinspin exchange interactions. In chapter 5, quantum logic gates in a triple dot system has been studied. Such gates have been widely studied in double and single quantum dots. Motivated by the advent of experimental set ups of triple dots, we have studied the natural quantum gates that came out of a triple dot system. There are still two spin quantum bits in the three dots and there is an empty intervening dot, which imparts the scheme some advantages, as well as a substantial difference from the class of schemes studied so far. In chapter 6, we model a large square dot. As we describe in chapter 2, the properties of the large dots make them behave with some interesting properties such as hosting Wigner molecules of electrons inside. We explore the application of these structures for quantum information processing. We show here how to get singlet/triplet measurement, entanglement swapping, and how to prepare a 1D AKLT state, using the square dot as a construction block of the system. Finally in chapter 7 conclusions and further work. Here we indicate the further work that could be done with the knowledge present in this thesis and motivated by future advances in the technology.
Quantum sensors play an important role in many branches of modern science, and they occupy a huge segment of the growing market for quantum devices. Quantum sensors use qubits and their analogs as detecting and analyzing quantum elements. Some sensors can be based on a single qubit, which is often presented as a system making its evolution on the so-called Bloch sphere. Different criteria are used to evaluate the efficiency of the sensing process. One of the most popular is the Quantum Fisher Information Matrix (QFIM) based on Fisher information. The magnitudes of the QFIM elements are strongly related to the precision of the sensing. As an analog of the classical Cramér theorem, one can define the quantum Cramér-Rao bound for the variance V, which is equal to V = 1/NF where F is the corresponding quantum Fisher information element, and N stands for the number of repeated sensory measurements. In this work, we develop our quantum Fisher information-based approach for a single feedback-driven qubit-type element for sensing external magnetic fields. We demonstrate the efficiency of our algorithm and discuss its further possible improvement. The approach developed here can be easily extended to other sensing schemes: collective spin systems and multi-qubit-based sensors. Alternative control algorithms can be applied to drive the probe state vector for maximization of the QFIM components. The particular choice of the control algorithm is defined by the specific experimental set-up.
The realization of a quantum computer, after being considered only a wishful thinking for many years, \nlooks now more solid, with the major issues about its realization looking like “engineering problems”, whose \nsolution is not far to be found. \nThe most considerable open problems concerning the realization of a quantum computer concern: the \nsensitivity to external disturbances, the addressability of any single qubit, and the scalability of the proposed \narchitectures. These problems may have opposite solutions, since a good scalability would require high \ndensity of qubits embedded in solid state matrices, making it more difficult to address and protect each of \nthem. Conversely, well separated qubits realized by atoms or ions are easily addressed and protected, but \nmake it more difficult to achieve scalability. \nAnother aspect related to the realization of generic quantum devices (i.e. devices which exploit the \nquantum features of their constituents to realize some operations) is connected to the way one interfaces \nwith them: we live in a “classical world”, and any quantum device will have to interface with it at some \nstage, e.g. to be controlled or measured. The problem, in this case, is keeping our classical disturbances as \nfar as possible from the action taking place at the heart of the quantum device. \nHowever, the problem of being able to find the proper “interface” can be turned into an advantage, \nsince macroscopic systems may posses robustness features which can be exploited for the realization of novel \nquantum devices where the sensitivity problem is much alleviated. A good interface can be thus provided by \nsemi-classical systems, i.e. objects whose nature is intimately quantum, but whose features and behaviour is \nwell framed within a classical description. Any scheme, application or device, where a semi-classical system \ninteracts with some pure quantum object (e.g. a qubit) for realizing a quantum operation, will be referred \nto as hybrid. \nIn this thesis, we have developed the idea of exploiting the robustness features of some non-linear classical \nsystems in order to realize quantum devices where the sensitivity problem is alleviated. Hence, we have \nproposed a hybrid scheme for accomplishing the most basic actions related with the realization of a magnetic- \nbased quantum device, i.e. the control of a qubit state and entanglement generation. In particular, we have \ndeveloped it focusing on magnetic one-dimensional systems, i.e. spin chains, as channels connecting one or \nmore qubits to some external control apparatus. \nThis choice follows from the observation that classical spin chains are non-linear systems which enumerate \nsolitons among their dynamical configurations which are solutions of their equations of motion. In fact, \nsolitons are those particular solutions of non-linear systems which show space-time localization and shape- \ninvariant evolution and are celebrated for their impressive properties of robustness against scattering and \nexternal disturbances. These properties make them suitable candidates for practical purposes. \nWe have considered systems made by one-dimensional discrete lattices hosting, at each lattice site, one \nclassical spin (classical spin chain) or a large-S spin, i.e. a quantum spin characterized by a S-value large \nenough for the spin to be well described by a semi-classical behaviour (large-S spin chain). \nA classical, or a large-S, spin chain (with its solitons) can play the role of the robust partner while \nthe role of the fragile quantum system is played by the qubit, which is the agent of the relevant quantum \noperations in our hybrid quantum device.We have first introduced a method for generating solitons on discrete, classical Heisenberg chains by \napplying a time-dependent magnetic field to one of the chain extremities. The method has been numerically \nchecked, revealing the actual possibility of producing soliton-like dynamical configurations running on the \nspin chain, which resemble the known analytical solitons of the continuous chain if their typical width is \nlarge with respect to the chain spacing. The robustness of the generated solitons has been also tested with \nrespect to thermal noise present in the system. \nWe have then proposed a set-up where the generated soliton acts as a magnetic signal that travels along \nthe chain and eventually reaches a qubit and changes its quantum state. Since any unitary action on a single \nqubit can be represented in terms of a Zeeman interaction lasting for a precise time interval, qubit state \ncontrol is usually assumed to be obtained by applying suitable sequences of external magnetic fields. Indeed, \nfor this particular application, the spin chain needs not to be quantum and the suitable magnetic field is \nprovided by the moving deformation of the uniform chain represented by the magnetic soliton travelling \nalong the chain. Numerical results confirm that solitons are suitable for this task, giving the possibility to \nremotely control the qubit state by an appropriate choice of soliton shape and qubit-chain coupling. \nWe have finally addressed the problem of generating entanglement between distant qubits by introducing \na model where two qubits, distant and non-interacting, are locally coupled with a large-S Heisenberg chain, \nwhose dynamics is assumed to be characterized by the presence of solitons. The aim of this study was to \nverify if, by properly choosing the state of the spin chain, the evolution of such a robust semi-classical system \ncan bring the two qubits from a separable initial state to a non-separable state after a certain amount of \ntime, i.e., if a semi-classical channel could generate entanglement between the two qubits. \nAt variance with the previous application, the spin chain must here be considered, and consequently \ntreated, as a quantum system in order to allow for entanglement generation/transfer, but a suitable approximation \nis needed to solve the chain dynamics, as accounting for the exact evolution of large-S spin chain \nis out of reach, even numerically. This leads us to introduce a particular set of chain states built as product \nof single-spin coherent states which are in one-to-one correspondence with the configurations of the classical \nspin chain and are thus referred to as the semi-classical states of the chain. Being able to solve the evolution \nof the coherent state products, allow us to complete the hybrid scheme for entanglement generation: in \nfact, it is shown that, choosing the chain initial state as a semi-classical state corresponding to a soliton \nconfiguration, the correlations, generated between one qubit and the corresponding spin-S, are efficiently \ntransferred along the chain up to the other qubit, finally leaving the two qubits in an entangled state. \nThe results about the proposed hybrid schemes, showing their effectiveness for remotely controlling qubit \nstates and generating entanglement between distant qubits, encourage further studies opening also new \nperspectives for the realization of novel quantum devices based on the exploitation of the robustness features \nof semi-classical systems.
Spins localized in semiconductor nanostructures have been intensively investigated for quantum spintronics. These include the spin of single electron localized by quantum dots or impurities, and spins of the lattice nuclei. These localized spins can be exploited as carriers of quantum information, while in some circumstances they also play the role of deleterious noise sources for other quantum objects through their couplings. Quantum control of the spins in semiconductor nanostructures is therefore of central interest for quantum applications. In this thesis, we address several problems related to the quantum control of electron or hole spin and nuclear spins in semiconductor quantum dots and impurity centers. The first problem studied is the control of nuclear spin bath for a hole spin qubit in III-V semiconductor quantum dot. In quantum dots formed on III-V compounds, the direct band gap of the host material allows ultrafast optical addressability of a single electron or hole spin qubit. However, nonzero nuclear spins of group III and group V elements result in a large statistical fluctuation in the Zeeman splitting of the spin qubit which then dephases in nanosecond time scale. We present a novel feedback scheme to suppress the statistical fluctuation of the nuclear spin field for enhancing the coherence time of the hole spin qubit. We also find positive feedback control which can amplify the magnitude of the nuclear field, so that a bimodal distribution can develop, realizing a quantum environment that can not be described by a single temperature. The second problem addressed here is the control of donor spin qubits in silicon architecture which have ultra-long quantum coherence time. We developed the quantum control scheme to realize the quantum metrology of magnetic field gradient, based on the celebrated Kane’s architecture for quantum computation. The scheme can also be generalized to calibrate the locations of the donors. In the third part of the thesis, we investigate a novel type of quantum dot formed in a new class of two-dimensional semiconductors, monolayer transition metal dichalcogenides (TMDs), which exhibit interesting spin and pseudospin physics. This novel quantum dot system may offer new opportunity for quantum spintronics in the ultimate 2D limit, and we investigate here the valley pseudospin as a possible quantum bit carrier. A main finding is that, contrary to the intuition, the lateral confinement by the quantum dot potential does not lead to noticeable valley hybridization, and therefore the valley pseudospin in monolayer TMDs QD can well inherit the valley physics such as the valley optical selection rules from the 2D bulk which implies a variety of quantum control possibilities.