Measurement-only topological quantum computation via anyonic interferometry

We describe measurement-only topological quantum computation using both projective and interferometrical measurement of topological charge. We demonstrate how anyonic teleportation can be achieved using “forced measurement” protocols for both types of measurement. Using this, it is shown how topological charge measurements can be used to generate the braiding transformations used in topological quantum computation, and hence that the physical transportation of computational anyons is unnecessary. We give a detailed discussion of the anyonics for implementation of topological quantum computation (particularly, using the measurement-only approach) in fractional quantum Hall systems.     

Implementation of single-qubit quantum gates by adiabatic passage and static laser phases

We propose and analyse experimentally feasible implementations of single-qubit quantum gates based on stimulated Raman adiabatic passage (STIRAP) between magnetic sublevels in atoms coupled by elliptically polarized pulsed laser fields, in part based on a proposal by Kis and Renzoni [Z. Kis, F. Renzoni, Phys. Rev. A 65 (2002) 032318]. These techniques require only the control of the relative phase of the driving fields but do not involve any dynamical or geometric phases, which makes it independent of the other interaction details: detuning, pulse shapes, pulse areas and pulse durations. The suggested techniques are immune to spontaneous emission since the qubit manipulation proceeds through non-absorbing dark states. We also propose an alternative technique using compensation of dynamical Stark shifts by two consecutive non-resonant fractional-STIRAP processes.     

Spin bath interaction effects on the geometric phase

We calculate the geometric phase of a spin-1/2 particle coupled to an external environment comprising N spin-1/2 particle in the framework of open quantum systems. We analyze the decoherence factor and the deviation of the geometric phase under a nonunitary evolution from the one gained under an unitary one. We show the dependence upon the system's and bath's parameter and analyze the range of validity of the perturbative approximation. Finally, we discuss the implications of our results.     

An optimum Hamiltonian for non-Hermitian quantum evolution and the complex Bloch sphere

For a quantum system governed by a non-Hermitian Hamiltonian, we studied the problem of obtaining an optimum Hamiltonian that generates nonunitary transformations of a given initial state into a certain final state in the smallest time τ. The analysis is based on the relationship between the states of the two-dimensional subspace of the Hilbert space spanned by the initial and final states and the points of the two-dimensional complex Bloch sphere.     

Examination of the adiabatic approximation in open systems

We examine the notion of the adiabatic approximation in open systems by applying it to closed systems. Our results shows that the notion is equivalent to the standard adiabatic approximation if the systems are initially in eigenstates, and it leads to a more general expression if the systems are in mixed states.     

Unconventional geometric quantum phase gates with two SQUIDs in a cavity

We present a potential scheme to implement two-qubit quantum phase gates through an unconventional geometric phase shift with two four-level SQUIDs in a cavity. The SQUID qubits undergo no transitions during the gate operation, while the cavity mode is displaced along a circle in the phase space, acquiring a geometric phase depending conditionally upon the SQUIDs’ states. Under certain conditions, the SQUID qubits are disentangled with the cavity mode and the SQUIDs’ states remain in their ground states during the gate operation, thus the gate is insensitive to both the SQUIDs’ “spontaneous emission” and the cavity decay.     

Interacting spin pairs in rotational magnetic fields and geometric phase

In virtue of the quantum invariant theory, we obtain the rigorous solution of the isotropic bipartite system in rotational magnetic fields, based on which the general expression of the noncyclic geometric phase is worked out and the entanglement dependence of the noncyclic geometric phase in this model is investigated. We show that the influence of the coupling on noncyclic geometric phase depends on the initial condition of the system. We also show that when the magnetic fields are stationary, there is a more general class of states existed of which the noncyclic geometric phase could be interpreted solely in terms of the solid angle enclosed by the geodesically closed curve on a two-sphere parameterized by the evolving Schmidt coefficients.     

A fault-tolerant one-way quantum computer

We describe a fault-tolerant one-way quantum computer on cluster states in three dimensions. The presented scheme uses methods of topological error correction resulting from a link between cluster states and surface codes. The error threshold is 1.4% for local depolarizing error and 0.11% for each source in an error model with preparation-, gate-, storage-, and measurement errors.     

Unconventional Geometric Quantum Gate in Circuit QED

We propose a scheme to implement an unconventional geometric phase gate in circuit QED, i.e. two superconducting charge qubits inside a superconducting transmission line resonator. The quantum operation depends only on global geometric features, and thus is insensitive to the state of the cavity mode.     

One-step implementation of the Toffoli gate via quantum Zeno dynamics

Based on the quantum Zeno dynamics, we present a scheme for one-step implementation of a Toffoli gate via manipulating three rf superconducting quantum interference device (SQUID) qubits to resonantly interact with a superconducting cavity. The effects of decoherence such as spontaneous emission and the loss of cavity are also considered.     

Intrinsic quantum computation

We introduce ways to measure information storage in quantum systems, using a recently introduced computation-theoretic model that accounts for measurement effects. The first, the quantum excess entropy, quantifies the shared information between a quantum process's past and its future. The second, the quantum transient information, determines the difficulty with which an observer comes to know the internal state of a quantum process through measurements. We contrast these with von Neumann entropy and quantum entropy rate and provide a closed-form expression for the latter for the class of deterministic quantum processes.     

Spin quantum computation in silicon nanostructures

Proposed silicon-based quantum-computer architectures have attracted attention because of their promise for scalability and their potential for synergetically utilizing the available resources associated with the existing Si technology infrastructure. Electronic and nuclear spins of shallow donors (e.g. phosphorus) in Si are ideal candidates for qubits in such proposals because of their long spin coherence times due to their limited interactions with their environments. For these spin qubits, shallow donor exchange gates are frequently invoked to perform two-qubit operations. We discuss in this review a particularly important spin decoherence channel, and bandstructure effects on the exchange gate control. Specifically, we review our work on donor electron spin spectral diffusion due to background nuclear spin flip-flops, and how isotopic purification of silicon can significantly enhance the electron spin dephasing time. We then review our calculation of donor electron exchange coupling in the presence of degenerate silicon conduction band valleys. We show that valley interference leads to orders of magnitude variations in electron exchange coupling when donor configurations are changed on an atomic scale. These studies illustrate the substantial potential that donor electron/nuclear spins in silicon have as candidates for qubits and simultaneously the considerable challenges they pose. In particular, our work on spin decoherence through spectral diffusion points to the possible importance of isotopic purification in the fabrication of scalable solid state quantum computer architectures. We also provide a critical comparison between the two main proposed spin-based solid state quantum computer architectures, namely, shallow donor bound states in Si and localized quantum dot states in GaAs.     

Berry phase and quantum criticality in Yang-Baxter systems

Spin interaction Hamiltonians are obtained from the unitary Yang-Baxter -matrix. Based on which, we study Berry phase and quantum criticality in the Yang-Baxter systems.     

Relativistic effects in quantum walks: Klein's paradox and zitterbewegung

Quantum walks are not only algorithmic tools for quantum computation but also non-trivial models describing various physical processes. The Letter compares one-dimensional version of the free particle Dirac equation with the discrete time quantum walk (DTQW). It is shown that two relativistic effects associated with the Dirac equation, namely zitterbewegung (quivering motion) and Klein's paradox, are manifested in DTQW. A special case of DTQW for Lorentz invariance not satisfied in the corresponding continuous limit is considered. The effects are examined.     

Measurement-induced nonlocality and geometric quantum discord in two SC-charge qubits

By using geometric quantum discord and measurement-induced nonlocality, quantum correlations are investigated for two superconducting (SC) charge qubits that share a large Josephson junction where the field is assumed to be prepared initially in a coherent state. It is found that the difference between measure measurement-induced nonlocality and geometric quantum discord, of the final state of the two SC-charge qubits system which is especial case of X-states, is equal to a constant value. It is found that the quantum correlations and entanglement of the qubits are very sensitive to the mean number of the coherent photons. The entanglement exists in small intervals of death quantum discord and measurement-induced nonlocality. This is further evidence in support of the fact that quantum correlation and entanglement are not synonymous.     

Teleportation of a general two-mode coherent-state superposition via attenuated quantum channels with ideal and/or threshold detectors

Three novel probabilistic yet conclusive schemes are proposed to teleport a general two-mode coherent-state superposition via attenuated quantum channels with ideal and/or threshold detectors. The calculated total success probability is highest (lowest) when only ideal (threshold) detectors are used.     

Holonomic quantum computation with superconducting charge-phase qubits in a cavity

We theoretically propose a feasible scheme to realize holonomic quantum computation with charge-phase qubits placed in a microwave cavity. By appropriately adjusting the controllable parameters, each charge-phase qubit is set as an effective four-level subsystem, based on which a universal set of holonomic quantum gates can be realized. Further analysis shows that our system is robust to the first-order fluctuation of the gate charges, and the intrinsic leakages between energy levels can be ignored.     

On spin evolution in a time-dependent magnetic field: Post-adiabatic corrections and geometric phases

We examine both quantum and classical versions of the problem of spin evolution in a slowly varying magnetic field. Main attention is given to the first- and second-order adiabatic corrections in the case of in-plane variations of the magnetic field. While the first-order correction relates to the usual adiabatic Berry phase and Coriolis-type lateral deflection of the spin, the second-order correction is shown to be responsible for the next-order geometric phase and in-plain deflection. A comparison between different approaches, including the exact (non-adiabatic) geometric phase, is presented.     

Resonance phenomena in macroscopic quantum tunneling: The small viscosity limit

We present a theoretical study of the resonant quantum behavior for a macroscopic superconducting system interacting with an external microwave at proper frequency. Here we consider a system described by a double well potential, an rf-SQUID, in the extremely underdamped regime. Numerical simulations for resonant phenomena have been performed for this system, whose parameters belong to the range typically used in the experiments. The dependence of the transition probability W on the external drive of the system, φx, can show three resonance peaks, in a small microwave frequency range. One peak is connected with the anticrossing and the other two with the external microwave frequency ν. The relative position and the height of the two lateral peaks depend on the microwave frequency. This behavior is studied here for the first time.