We give a $\text{Clifford}+T$ representation of the Toffoli gate of $T$-depth one, using four ancillas. More generally, we describe a class of circuits whose $T$-depth can be reduced to one by using sufficiently many ancillas. We show that the cost of adding an additional control to any controlled gate is at most eight additional $T$ gates and $T$-depth two. We also show that the circuit $THT$ does not possess a $T$-depth one representation with an arbitrary number of ancillas initialized to $|0\rangle$.

The energy loss of an ion passing along a major crystal axis before and/or after undergoing a large-angle collision is strongly enhanced, because its path is close to a lattice-site atom located at the crystal axis; this is the so-called skimming effect. One may find this effect in high-resolution medium-energy ion scattering (MEIS) spectra from submonolayers of single crystals. In the present study, the MEIS spectra were observed for medium-energy He${}^{+}$ ions backscattered from KI(001) and RbI(001) crystals at various scattering geometries. The observed surface peaks were decomposed into scattering components from top-, second-, and third-layer atoms considering the hitting probabilities, which were derived from Monte Carlo simulations of ion trajectories, taking account of the enhanced and correlated thermal vibrations. The results obtained here demonstrate that the energy loss of the ions which move skimming trajectories is expressed reasonably well by the impact-parameter-dependent energy loss calculated using the nonperturbative coupled-channel method.

We investigate by numerical simulations the pattern formation after an oscillating attractive-repulsive obstacle inserted into the flow of a Bose-Einstein condensate. For slow oscillations we observe a complex emission of vortex dipoles. For moderate oscillations organized lined up vortex dipoles are emitted. For high frequencies no dipoles are observed but only lined up dark fragments. The results shows that the drag force turns negative for sufficiently high frequency. We also successfully model the ship waves in front of the obstacle. In the limit of very fast oscillations all the excitations of the system tend to vanish.

We present a real-time observation of electron motion in the ground state of the carbon atom. A wave packet is created in the ground triplet state of the atom via photodetachment of its negative ion in a strong laser field. Its dynamics is probed using the selectivity of strong-field ionization to orbital alignment in combination with an electron-imaging technique. A strong temporal modulation in the photoelectron yield at high kinetic energies is observed, which reveals a periodic motion of the electron cloud in the atom.

We introduce a quantum cellular automaton that achieves approximate phase-covariant cloning of qubits. The automaton is optimized for $1\to 2N$ economical cloning. The use of the automaton for cloning allows us to exploit different foliations for improving the performance with given resources.

We describe the decoherence process induced on a two-level quantum system in direct interaction with a nonequilibrium environment. The nonequilibrium feature is represented by a nonstationary random function corresponding to the fluctuating transition frequency between two quantum states coupled to the surroundings. In this framework, we compute the decoherence factors which have a characteristic “dip” related to the initial phases of the bath modes. We therefore study different types of environments, namely, ohmic and supraohmic. These environments present different decoherence time scales than the thermal environment we used to study. As a consequence, we compute analytically and numerically the nonunitary geometric phase for the qubit in a quasicyclic evolution under the presence of these particular nonequilibrium environments. We show in which cases decoherence effects could, in principle, be controlled in order to perform a measurement of the geometric phase using standard procedures.

We describe a scheme that enables a strong coherent coupling between a topological qubit and the quantized motion of a magnetized nanomechanical resonator. This coupling is achieved by attaching an array of magnetic tips to a namomechanical resonator under a quantum phase controller which coherently controls the energy gap of a topological qubit. Combined with single-qubit rotations the strong coupling enables arbitrary unitary transformations on the hybrid system of topological and mechanical qubits and may pave the way for the quantum information transfer between topological and optical qubits. Numerical simulations show that quantum-state transfer and entanglement distributing between the topological and mechanical qubits may be accomplished with high fidelity.

We define quantum-correlating power (QCP) of a local quantum channel acting on the left part of a bipartite quantum system as the maximum amount of left quantum correlation that can be created by this channel. We prove that for any local channel, the optimal input state, which corresponds to the maximum quantum correlation in the output state, must be a classical-classical state. Further, the single-qubit channels with maximum QCP can be found in the class of channels which take their optimal input states to rank-two quantum-classical states. A superactivation property of QCP, that is, two zero-QCP channels can constitute a positive-QCP channel, is observed and discussed for single-qubit phase damping channels. The analytic expression for QCP of single-qubit amplitude damping channel is obtained.

We estimate the resource requirements for the quantum simulation of the ground-state energy of the one-dimensional quantum transverse Ising model based on the surface code implementation of a fault-tolerant quantum computer. The surface code approach has one of the highest known tolerable error rates (∼1$\%$) which makes it currently one of the most practical quantum computing schemes. Compared to results of the same model using the concatenated Steane code, the current results indicate that the simulation time is comparable but the number of physical qubits for the surface code is one to two orders of magnitude larger than that of the concatenation code. Considering that the error threshold requirement of the surface code is four orders of magnitude higher than the concatenation code, building a quantum computer with a surface code implementation appears more promising given current physical hardware capabilities.

We provide a way of generating and observing molecular quantum gyroscopic motion that resembles gyroscopic motion of classical rotors. After producing a nonspreading rotational wave packet called a cogwheel state, one can generate a gyroscopic precession motion by applying an external magnetic field interacting through a rotational magnetic dipole moment. The quantum rotors, realized with linear nonparamagnetic ionic molecules trapped in an ion trap, can keep their gyroscopic motion for a long time in a collectively synchronized fashion. A Coulomb-explosion technique is suggested to observe the gyroscopic motion. Despite limited molecular species, the observation of the gyroscopic motion can be adopted as a method to measure rotational $g$ factors of molecules.

We demonstrate that the formation of negative hydrogen ions (H${}^{-}$) occurs in a wide class of atomic and molecular collisions. In our experiments, H${}^{-}$ emission from hydroxyl cations and acetone molecules was observed in keV-energy collisions. We show that hydride (H${}^{-}$) anions are formed via direct collisional fragmentation of molecules, followed by electron grabbing by fast hydrogen fragments. Such general mechanism in hydrogen-containing molecules may significantly influence reaction networks in planetary atmospheres and astrophysical media and new reaction pathways may have to be added in radiolysis studies.

We study the thermal activation of spin fluctuations in dynamically stable spinor Bose-Einstein condensates. We analyze the specific cases of a nondipolar spin-1 condensate in the state $m=0$, where thermal activation results from spin-changing collisions, and of a chromium condensate in the maximally stretched state $m=-3$, where thermal spin fluctuations are due to dipole-induced spin relaxation. In both cases, we show that the low energy associated to the spinor physics may be employed for thermometry purposes down to extremely low temperatures, typically impossible to measure in Bose-Einstein condensates with the usual thermometric techniques. Moreover, the peculiar dependence of the system's entropy with the applied Zeeman energy opens a possible route for adiabatic cooling.

We provide a complete experimental and numerical investigation of nonlinear beam propagation in a carbon disulfide liquid-filled Kerr slab waveguide using picosecond pulsed light. A first spatial analysis shows the generation of a multicolor solitary wave through the combined effects of cascaded Raman scattering and cross-phase modulation. The impact of temporal effects on this self-trapped optical beam is further studied through a spatiotemporal analysis. It is shown in particular how cascaded Raman slow light induces optical delays between the solitonic components which prevents higher-order spatial soliton and provides a remarkable beam stability. Experimental observations are in very good agreement with numerical simulations of the spatiotemporal (1+1D) nonlinear Schrödinger equation including the Raman scattering.

Two Kerr-squeezed optical beams can be combined in a beam splitter to produce non-Gaussian continuous-variable entangled states. We characterize the non-Gaussian nature of the output by calculating the third-order cumulant of quadrature variables and predict the level of entanglement that could be generated by evaluating the Duan-Simon and Reid Einstein-Podolsky-Rosen criteria. These states have the advantage over Gaussian states and non-Gaussian measurement schemes in that the well known, efficient, and proven technology of homodyne detection may be used for their characterization. A physical demonstration maintaining the important features of the model could be realized using optical fibers, beam splitters, and homodyne detection.

We present a calculation of the cross section for the process of double-electron capture by a bare nucleus with emission of a single photon. The calculation is performed within the framework of quantum electrodynamics. The cross section is presented as a function of the incident-electron energy for ions with the nuclear charge within the interval $8\le Z\le 92$. The available experiments on the double-electron capture by a bare nucleus are discussed.

In their recent paper, Yan-Xiong Du et al. [Phys. Rev. A 84, 034103 (2011)] claim to have found a non-Abelian adiabatic geometric phase associated with the energy eigenstates of a large-detuned three-level $\Lambda$ system. They further propose a test to detect the noncommutative feature of this geometric phase. On the contrary, we show that the non-Abelian geometric phase picked up by the energy eigenstates of a $\Lambda$ system is trivial in the adiabatic approximation, while, in the exact treatment of the time evolution, this phase is very small and cannot be separated from the non-Abelian dynamical phase acquired along the path in parameter space.

Frequency standards based on atomic states, such as Rb or Cs vapors, or single-trapped ions, are the most precise measures of time. Here we propose and analyze a precision oscillator approach based upon spins in a solid-state system, in particular, the nitrogen-vacancy defect in single-crystal diamond. We show that this system can have stability approaching portable atomic standards and is readily incorporable as a chip-scale device. Using a pulsed spin-echo technique, we anticipate an Allan deviation of ${\sigma }_y={10}^{-7}{\tau }^{-1/2}$ limited by thermally-induced strain variations; in the absence of such thermal fluctuations, the system is limited by spin dephasing and harbors an Allan deviation nearing $\sim {10}^{-12}{\tau }^{-1/2}$. Potential improvements based upon advanced diamond material processing, temperature stabilization, and nanophotonic engineering are discussed.

We study how to prepare two important types of entangled states (i.e., GHZ and $W$ states) via global controls in closed linear Ising spin chains with nearest-neighbor couplings. To achieve the goal, we use a numerical optimization algorithm to search an optimal set of control parameters, and then analytically obtain the time-optimal solutions for a three-spin chain by a geometrical explanation on the Bloch sphere. For experimental demonstration, we also consider the most robust sequence under the realistic imperfections such as the errors of global controls and the time evolutions as well as in the numerical optimization algorithm, and experimentally implement the numerically derived robust pulse sequences in a three-spin system where the closed linear Ising spin chain is simulated by nuclear-magnetic-resonance technique. This experiment demonstrates that our scheme is feasible in realistic settings under the experimental imperfections.

A complementarity relation is established between the capacity of multiport classical information transmission via quantum states and multiparty quantum correlation measures for three-qubit pure states. The multiparty quantum correlation measures considered are the generalized geometric measure, the tangle, and the discord monogamy score. The complementarity relation is revealed by the identification of a one-parameter family of pure three-qubit states, which we call the maximally-dense-coding-capable quantum states. These states have the maximal multiport dense coding capacity among all three-qubit pure states with an arbitrary fixed amount of the multiparty quantum correlations.