Spin manipulation in semiconductor quantum dots qubit

Thirty years of effort in semiconductor quantum dots has resulted in significant developments in the control of spin quantum bits(qubits). The natural two-energy level of spin states provides a path toward quantum information processing. In particular, the experimental implementation of spin control with high fidelity provides the possibility of realizing quantum computing. In this review, we will discuss the basic elements of spin qubits in semiconductor quantum dots and summarize some important experiments that have demonstrated the direct manipulation of spin states with an applied electric field and/or magnetic field. The results of recent experiments on spin qubits reveal a bright future for quantum information processing.     

Quantum speed limit for qubit systems: Exact results

Given an initial state, a target state, and a driving Hamiltonian, how fast can the initial state evolve into the target state according to the Schröchinger dynamics? This problem arises in a variety of contexts such as quantum computation, quantum control, and in particular, the problem of maximum information processing rate of quantum systems, and has been studied extensively due to its fundamental importance. In this paper, we purse further the study in the qubit case in which the particular structure admits stronger results. We use the quantum fidelity as well as relative entropy as a figure of merit to characterize the closeness between a fixed initial qubit state and another one undergoing unitary evolution. We work out explicitly maximal and minimal fidelity and relative entropy by determining the closest and the farthest states to the target state and show that these results are unique for qubit systems. We also determine the minimal time for a state to evolve to the extremal states (that is, the farthest one evolved from the initial state in the sense of minimal fidelity or maximal relative entropy), which generalizes the celebrated Mandelstam–Tamm bound and the Margolus–Levitin bound for qubit systems. We further reveal an interesting fact that this minimal time is independent of the initial states.     

Detecting Quantum Dissonance and Discord in Exact Dynamics of qubit Systems

In this paper, we evaluate the quantum and classical correlations in exact dynamics of qubit systems interacting with a common dephasing environment. We show the existence of a sharp transition between the classical and quantum loss of correlations during the time evolution. We show that it is possible to exploit a large class of initial states in different tasks of quantum information and processing without any perturbation of the correlations from the environment noisy for large time intervals. On the other hand, we include the dynamics of a new kind of correlation so-called quantum dissonance, which contains the rest of the nonclassical correlations. We show that the quantum dissonance can be considered as an indicator to expect the behavior of the dynamics of classical and quantum correlations in composite open quantum systems.     

Exact solutions of a spin-orbit coupling model in two-dimensional central-potentials and quantum-classical correspondence

In this paper we present both the classical and quantum periodic-orbits of a neutral spinning particle constrained in two-dimensional central-potentials with a cylindrically symmetric electric-field in addition, which leads to an effective non-Abelian gauge field generated by the spin-orbit coupling. Coherent superposition of orbital angular-eigenfunctions obtained explicitly under the condition of zero-energy exhibits the quantum-classical correspondence in the meaning of exact coincidence between classical orbits and spatial patterns of quantum wave-functions, which as a consequence results in the fractional quantization of orbital angular-momentum by the requirement of the same rotational symmetry of quantum and classical orbits. A non-Abelian anyon-model emerges in a natural way.     

Preparation of optimal entropy squeezing state of atomic qubit inside the cavity via two-photon process and manipulation of atomic qubit outside the cavity

Considering two atomic qubits initially in Bell states, we send one qubit into a vacuum cavity with two-photon resonance and leave the other one outside. Using quantum information entropy squeezing theory, the time evolutions of the entropy squeezing factor of the atomic qubit inside the cavity are discussed for two cases, i.e., before and after rotation and measurement of the atomic qubit outside the cavity. It is shown that the atomic qubit inside the cavity has no entropy squeezing phenomenon and is always in a decoherent state before the operating atomic qubit outside the cavity. However,the periodical entropy squeezing phenomenon emerges and the optimal entropy squeezing state can be prepared for the atomic qubit inside the cavity by adjusting the rotation angle, choosing the interaction time between the atomic qubit and the cavity, controlling the probability amplitudes of subsystem states. Its physical essence is cutting the entanglement between the atomic qubit and its environment, causing the atomic qubit inside the cavity to change from the initial decoherent state into maximum coherent superposition state, which is a possible way of recovering the coherence of a single atomic qubit in the noise environment.     

Exact solutions for a type of electron pairing model with spin-orbit interactions and Zeeman coupling

A type of electron pairing model with spin-orbit interactions or Zeeman coupling is solved exactly in the framework of the Richardson ansatz. Based on the exact solutions for the case with spin-orbit interactions, it is shown rigorously that the pairing symmetry is of the p + ip wave and the ground state possesses time-reversal symmetry, regardless of the strength of the pairing interaction. Intriguingly, how Majorana fermions can emerge in the system is also elaborated. Exact results are illustrated for two systems, respectively, with spin-orbit interactions and Zeeman coupling.     

Exact SU(2) symmetry and persistent spin helix in a spin-orbit coupled system

Spin-orbit coupled systems generally break the spin rotation symmetry. However, for a model with equal Rashba and Dresselhauss coupling constants, and for the [110] Dresselhauss model, a new type of SU(2) spin rotation symmetry is discovered. This symmetry is robust against spin-independent disorder and interactions and is generated by operators whose wave vector depends on the coupling strength. It renders the spin lifetime infinite at this wave vector, giving rise to a persistent spin helix. We obtain the spin fluctuation dynamics at, and away from, the symmetry point and suggest experiments to observe the persistent spin helix.     

Soft qubit

A model of a soft qubit is offered. It is a system reproducing the information properties of a quantum object that carries a qubit of information. At the same time, a soft qubit can be implemented as a computer program.     

Andreev level qubit

We investigate the dynamics of a two-level Andreev bound state system in a transmissive quantum point contact embedded in an rf SQUID. Coherent coupling of the Andreev levels to the circulating supercurrent allows manipulation and readout of the level states. The two-level Hamiltonian for the Andreev levels is derived, and the effect of interaction with the quantum fluctuations of the induced flux is studied. We also consider an inductive coupling of qubits and discuss the relevant SQUID parameters for qubit operation and readout.     

Baryon-nucleon spin-orbit forces from symmetric quark-quark spin-orbit interactions

Baryon-nucleon spin-orbit forces generated from symmetric quark-quark spin-orbit interactions are studied. Under certain conditions, the results for both hyperon-nucleon and nucleon-nucleon channels are found to be roughly the same whether the quark-quark interactions arise from one-gluon exchange or one-boson exchanges. Both are in rough agreement with the Nijmegen one-boson-exchange potential models. The reasons for these similarities are discussed.     

Exchangeable qubit states

We present a characterisation of the two-site marginals of exchangeable and Bose-exchangeable states and provide an elementary proof for the qubit case. A link between the ground state problem for ferromagnetic mean-field models and the additivity of the maximal two-norm for quantum channels is established. We then analyse the corrections on N-particle symmetric states with respect to the exchangeable ones. The finite-size effects on the average ground state energy of the BCS model are explicitly computed.     

Faithful qubit distribution assisted by one additional qubit against collective noise

We propose a distribution scheme of polarization states of a single photon over a collective-noise channel. By adding one extra photon with a fixed polarization, we can protect the state against collective noise via a parity-check measurement and postselection. While the scheme succeeds only probabilistically, it is simpler and more flexible than the schemes utilizing decoherence-free subspace. An application to the Bennett-Brassard 1984 protocol through a collective-noise channel, which is robust to the Trojan horse attack, is also given.     

Controlling qubit arrays with anisotropic XXZ Heisenberg interaction by acting on a single qubit

We investigate anisotropic XXZ Heisenberg spin-1 / 2 chains with control fields acting on one of the end spins, with the aim of exploring local quantum control in arrays of interacting qubits. In this work, which uses a recent Lie-algebraic result on the local controllability of spin chains with “always-on” interactions, we determine piecewise-constant control pulses corresponding to optimal fidelities for quantum gates such as spin-flip (NOT), controlled-NOT (CNOT), and square-root-of-SWAP (). We find the minimal times for realizing different gates depending on the anisotropy parameter Δ of the model, showing that the shortest among these gate times are achieved for particular values of Δ larger than unity. To study the influence of possible imperfections in anticipated experimental realizations of qubit arrays, we analyze the robustness of the obtained results for the gate fidelities to random variations in the control-field amplitudes and finite rise time of the pulses. Finally, we discuss the implications of our study for superconducting charge-qubit arrays.     

Teleportation of a vacuum--one-photon qubit

We report the experimental realization of teleporting a one-particle entangled qubit. The qubit is physically implemented by a two-dimensional subspace of states of a mode of the electromagnetic field, specifically, the space spanned by the vacuum and the one-photon state. Our experiment follows the line suggested by Lee and Kim [Phys. Rev. A 63, 012305 (2000)] and Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)]. An unprecedented large value of the teleportation "fidelity" has been attained: F = (95.3 +/- 0.6)%.     

Non-Markovian random unitary qubit dynamics

We compare two approaches to non-Markovian quantum evolution: one based on the concept of divisible maps and the other one based on distinguishability of quantum states. The former concept is fully characterized in terms of local generator whereas it is in general not true for the latter one. A simple example of random unitary dynamics of a qubit shows the intricate difference between those approaches. Moreover, in this case both approaches are fully characterized in terms of local decoherence rates.     

Controllability of multiple qubit systems

This paper explores the problem of manipulating multiple-qubit systems when only single-qubit operations or two-qubit-interactive operations are permitted. It is demonstrated that if there exist 2 directional control Hamiltonian for each individual qubit, and one interactive Hamiltonian for each pair of qubits, then multiple qubit systems are open-loop controllable. An important observation of physical interest is emphasized: when only single-qubit operations or two-qubit-interactive operations are permitted, only n(n+3)/2 control Hamilton may guarantee open-loop controllability of n qubit systems, and n(n+3) is, in the restricted sense, also the lower limit on the number of operators needed for controllability. At last, we demonstrate that an n-quantum-dot system is open-loop controllable even when only single-qubit operations or two-qubit-interactive operations are permitted.     

The heavy-ion spin-orbit interaction

An expression for the induced spin-orbit potential in a heavy-ion collision is derived by making and adiabatic approximation to the effective interaction in second-order perturbation theory. An explicit form for the induced spin-orbit interaction for the case of a projectile of arbitrary ground state spin S is given and is shown to be equivalent to the result obtained using the methods of geometrical magnetism.