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.     

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.     

Nodal free geometric phases: Concept and application to geometric quantum computation

Nodal free geometric phases are the eigenvalues of the final member of a parallel transporting family of unitary operators. These phases are gauge invariant, always well defined, and can be measured interferometrically. Nodal free geometric phases can be used to construct various types of quantum phase gates.     

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.     

Parameter differentiation and quantum state decomposition for time varying Schrödinger equations

For the unitary operator, solution of the Schrödinger equation corresponding to a time-varying Hamiltonian, the relation between the Magnus and the product of exponentials expansions can be expressed in terms of a system of first-order differential equations in the parameters of the two expansions. A method is proposed to compute such differential equations explicitly and in a closed form.     

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.     

Quantum dynamical phase transition in a system with many-body interactions

Recent experiments, [G.A. Álvarez, E.P. Danieli, P.R. Levstein, H.M. Pastawski, J. Chem. Phys. 124 (2006) 194507], have reported the observation of a quantum dynamical phase transition in the dynamics of a spin swapping gate. In order to explain this result from a microscopic perspective, we introduce a Hamiltonian model of a two level system with many-body interactions with an environment whose excitation dynamics is fully solved within the Keldysh formalism. If a particle starts in one of the states of the isolated system, the return probability oscillates with the Rabi frequency ω₀. For weak interactions with the environment , we find a slower oscillation whose amplitude decays with a rate . However, beyond a finite critical interaction with the environment, , the decay rate becomes . The oscillation period diverges showing a quantum dynamical phase transition to a Quantum Zeno phase consistent with the experimental observations.     

Exotic quantum holonomy in Hamiltonian systems

We consider evolution of quantum eigenstates in the presence of level crossing under slow cyclic change of environmental parameters. We find that exotic holonomies, indicated by exchange of the eigenstates after a single cyclic evolution, can arise from non-Abelian gauge potentials among non-degenerate levels. We illustrate our arguments with solvable two and three level models.     

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.     

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.     

Exactly complete solutions of the Schrödinger equation with a spherically harmonic oscillatory ring-shaped potential

A spherically harmonic oscillatory ring-shaped potential is proposed and its exactly complete solutions are presented by the Nikiforov-Uvarov method. The effect of the angle-dependent part on the radial solutions is discussed.     

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.     

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.     

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.     

Stationary phase method and delay times for relativistic and non-relativistic tunneling particles

The stationary phase method is frequently adopted for calculating tunneling phase times of analytically-continuous Gaussian or infinite-bandwidth step pulses which collide with a potential barrier. This report deals with the basic concepts on deducing transit times for quantum scattering: the stationary phase method and its relation with delay times for relativistic and non-relativistic tunneling particles. After reexamining the above-barrier diffusion problem, we notice that the applicability of this method is constrained by several subtleties in deriving the phase time that describes the localization of scattered wave packets. Using a recently developed procedure - multiple wave packet decomposition - for some specifical colliding configurations, we demonstrate that the analytical difficulties arising when the stationary phase method is applied for obtaining phase (traversal) times are all overcome. In this case, we also investigate the general relation between phase times and dwell times for quantum tunneling/scattering. Considering a symmetrical collision of two identical wave packets with an one-dimensional barrier, we demonstrate that these two distinct transit time definitions are explicitly connected. The traversal times are obtained for a symmetrized (two identical bosons) and an antisymmetrized (two identical fermions) quantum colliding configuration. Multiple wave packet decomposition shows us that the phase time (group delay) describes the exact position of the scattered particles and, in addition to the exact relation with the dwell time, leads to correct conceptual understanding of both transit time definitions. At last, we extend the non-relativistic formalism to the solutions for the tunneling zone of a one-dimensional electrostatic potential in the relativistic (Dirac to Klein-Gordon) wave equation where the incoming wave packet exhibits the possibility of being almost totally transmitted through the potential barrier. The conditions for the occurrence of accelerated and, eventually, superluminal tunneling transmission probabilities are all quantified and the problematic superluminal interpretation based on the non-relativistic tunneling dynamics is revisited. Lessons concerning the dynamics of relativistic tunneling and the mathematical structure of its solutions suggest revealing insights into mathematically analogous condensed-matter experiments using electrostatic barriers in single- and bi-layer graphene, for which the accelerated tunneling effect deserves a more careful investigation.     

Scheme for reliable realization of quantum logic gates for two atoms separately trapped in two distant cavities via optical fibers

An approach for realizing conditional phase gate for two atoms separately trapped in two distant cavities mediated by an optical fiber is proposed. Utilizing the adiabatic passage, the atomic spontaneous emission, and the decays of the fiber and cavities are avoided under certain condition. The effects of the losses in the fiber and cavities on the fidelity are analyzed. Moreover, our scheme is not restricted to Lamb-Dicke limit. We also generalize the approach to generate one-dimensional cluster state and entangled state for two collections of atoms.     

Macroscopic entanglement on a hybrid quantum circuit

A scheme is proposed to deterministically create maximal entanglement between hybrid artificial atoms: superconducting charge and flux qubits. By tuning the circuit, the two qubits are dynamically decoupled and entanglement can be long-lived. This provides a new version of the Einstein-Podolsdy-Rosen (EPR) situation where the components of a macroscopic EPR pair are in opposite regimes.     

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.