We introduce a model of quantum computation intermediate between the gate-based and measurement-based models. A quantum register is manipulated remotely with the help of a single ancilla that “drives” the evolution of the register. The fully controlled ancilla qubit is coupled to the computational register only via a fixed unitary two-qubit interaction and then measured in suitable bases, driving both single- and two-qubit operations on the register. Arbitrary single-qubit operations directly on register qubits are not needed. We characterize all interactions $E$ that induce a unitary, stepwise deterministic measurement back-action on the register sufficient to implement any quantum channel. Our scheme offers experimental advantages for computation, state preparation, and generalized measurements, since no tunable control of the register is required.

We report on the observation of six large Feshbach resonances in a Fermi-Bose mixture of ${}^6\mathrm{Li}$ and ${}^{85}\mathrm{Rb}$ atoms. Near the resonances, both the elastic and inelastic collision rates are enhanced, and this results primarily in the loss of ${}^6\mathrm{Li}$ from an optical dipole trap since it is less massive and less confined than its ${}^{85}\mathrm{Rb}$ collision partner. We interpret our experimental data using a coupled-channels calculation which fully characterizes the ground-state scattering properties in any combination of spin states.

In this paper, we extend strong-field double ionization from diatomic molecules to triatomic molecules. Strong-field double ionization of CO${}_2$ is studied here with both linear and circular polarizations. A clear nonsequential signature is seen in doubly ionized CO${}_2$. We also compare nonsequential double ionization behaviors of CO${}_2$ to those of the well-studied diatomic molecules, and the difference is attributed to the detailed electronic structures in molecules.

We investigate the quantum phase diagram of Bose-Fermi mixtures of ultracold dipolar particles trapped in one-dimensional optical lattices in the thermodynamic limit. With the presence of nearest-neighbor (NN) interactions, a long-ranged ordered crystalline phase (Bose-Fermi solid) is found stabilized in the limit of weak intersite tunneling ($J$). When $J$ is increased, such a Bose-Fermi solid can be quantum melted into a Bose-Fermi liquid through different procedures, depending on whether the crystalline order is dominated by the NN interaction between fermions or bosons. These properties are qualitatively different from the classical picture of solid-liquid phase transition.

By applying the recently proposed antisymmetric superfluid local density approximation (ASLDA) to strongly interacting polarized atomic gases at unitarity in very elongated traps, we find families of solutions of the Larkin-Ovchinnikov (LO) type with prominent transversal oscillation of the pairing potential. These LO states coexist with a superfluid state having a smooth pairing potential. We suggest that the LO phase could be accessible experimentally by increasing the trap aspect ratio adiabatically. We show that the local asymmetry effects contained in the ASLDA do not support a deformed superfluid core predicted by previous Bogoliubov–de Gennes treatments.

We propose and experimentally demonstrate a universal quantum averaging process implementing the harmonic mean of quadrature variances. The averaged variances are prepared probabilistically by means of linear optical interference and measurement-induced conditioning. We verify that the implemented harmonic mean yields a lower value than the corresponding value obtained for the standard arithmetic-mean strategy. The effect of quantum averaging is experimentally tested for squeezed and thermal states as well as for uncorrelated and partially correlated noise sources. The harmonic-mean protocol can be used to efficiently stabilize a set of squeezed-light sources with statistically fluctuating noise levels.

Recently, Kossakowski and Ohya (K-O) proposed a new teleportation scheme which enables perfect teleportation even for a nonmaximal entangled state [A. Kossakowski and M. Ohya, Infinite Dimensional Analysis Quantum Probability and Related Topics 10, 411 (2007)]. To discuss a physical realization of the K-O scheme, we propose a model based on quantum optics. In our model, we take a superposition of Schrödinger’s cat states as an input state being sent from Alice to Bob, and their entangled state is generated by a photon number state through a beam splitter. When the average photon number for our input states is equal to half the number of photons into the beam splitter, our model has high fidelity.

We show that when $N\gg 1$ the geometric entanglement measure of general $N$-qubit $W$ states, except maximally entangled $W$ states, is a one-variable function and depends only on the Bloch vector with the minimal $z$ component. Hence one can prepare a $W$ state with the required maximal product overlap by altering the Bloch vector of a single qubit. Next we compute analytically the geometric measure of large-scale $W$ states by describing these systems in terms of very few parameters. The final formula relates two quantities, namely the maximal product overlap and the Bloch vector, that can be easily estimated in experiments.

We present a theoretical study of molecular-trap loss induced by collisions with slow atomic beams based on an explicit analysis of collision kinematics in the laboratory frame and a rigorous quantum description of atom-molecule scattering in external fields. The theory is applied to elucidate the effects of nonuniform magnetic and optical trapping fields on low-temperature collisions of OH ($J=3/2,M_J=3/2,f$) molecules with ${}^4\mathrm{He}$ atoms. Our calculations quantify the extent to which both elastic and inelastic cross sections are suppressed by external trapping fields, clarify the role of small-angle scattering in trap loss, and may benefit future experiments on collisional cooling of molecules in electromagnetic traps. The calculated cross sections for trap loss in ${}^4\mathrm{He}$ $+$ OH collisions are consistent with recent experimental observations at low beam energies [B. C. Sawyer et al., Phys. Rev. Lett. 101, 203203 (2008)], demonstrating the importance of including the effects of nonuniform trapping fields in theoretical simulations of cold collision experiments with trapped molecules and slow atomic beams.

We demonstrate the ultrafast coherent control of a nonlinear two-photon absorption in a dynamically shifted energy level structure. We use a spectrotemporal laser-pulse shaping that is programed to preserve the resonant absorption condition during the intense laser-field interaction. Experiments carried out in the strong-field regime of two-photon absorption in the ground state of atomic cesium reveal that the analytically obtained offset and curvature of a laser spectrum compensate the effect of both static and dynamic energy shifts of the given light-atom interaction.

An analytic study is presented of the efficient multiphoton excitation and strong harmonic generation in three-level systems specified by a pair of nearly degenerate, strongly dipole-coupled excited states. Such systems are physically formed by the three lowest states in, e.g., the hydrogen atom or evenly charged homonuclear diatomic molecular ions under reasonably chosen laser intensities. As a detailed analytic result, we found that the laser pulse of photon energy $2.05\text{eV}$, duration $0.23\text{ps}$, and intensity $5\times {10}^{13}\frac{\mathrm{W}}{{\mathrm{cm}}^2}$ is able to produce complete inversion of the initial population in the hydrogen atom through the five-photon excitation. At the same photon energy, the pulse of duration $0.41\text{ps}$ and intensity $3.44\times {10}^{14}\frac{\mathrm{W}}{{\mathrm{cm}}^2}$ was found to produce the same effect in the molecular ion but through the nine-photon excitation. We show that the accompanying scattering of light has very rich spectrum differing substantially from that of the two-level system.

We find that feedback control may induce “pseudo”-nonlinear dynamics in a damped harmonic oscillator, whose centroid trajectory in the phase space behaves like a classical nonlinear system. Thus, similar to nonlinear amplifiers (e.g., rf-driven Josephson junctions), feedback control on the harmonic oscillator can induce nonlinear bifurcation, which can be used to amplify small signals and further to measure quantum states of qubits. Using the cavity QED and the circuit QED systems as examples, we show how to apply our method to measuring the states of two-level atoms and superconducting charge qubits.

In contrast with software-generated randomness (called pseudo-randomness), quantum randomness can be proven incomputable; that is, it is not exactly reproducible by any algorithm. We provide experimental evidence of incomputability—an asymptotic property—of quantum randomness by performing finite tests of randomness inspired by algorithmic information theory.

The ability to store information is of fundamental importance to any computer, be it classical or quantum. To identify systems for quantum memories, which rely, analogously to classical memories, on passive error protection (“self-correction”), is of greatest interest in quantum information science. While systems with topological ground states have been considered to be promising candidates, a large class of them was recently proven unstable against thermal fluctuations. Here, we propose two-dimensional (2D) spin models unaffected by this result. Specifically, we introduce repulsive long-range interactions in the toric code and establish a memory lifetime polynomially increasing with the system size. This remarkable stability is shown to originate directly from the repulsive long-range nature of the interactions. We study the time dynamics of the quantum memory in terms of diffusing anyons and support our analytical results with extensive numerical simulations. Our findings demonstrate that self-correcting quantum memories can exist in 2D at finite temperatures.

We consider a process of parameter estimation in a spin-$j$ system surrounded by a quantum-critical spin chain. Quantum Fisher information lies at the heart of the estimation task. We employ Ising spin chain in a transverse field as the environment which exhibits a quantum phase transition. Fisher information decays with time almost monotonously when the environment reaches the critical point. By choosing a fixed time or taking the time average, one can see the quantum Fisher information presents a sudden drop at the critical point. Different initial states of the environment are considered. The phenomenon that the quantum Fisher information, namely, the precision of estimation, changes dramatically can be used to detect the quantum criticality of the environment. We also introduce a general method to obtain the maximal Fisher information for a given state.

Rapid purification by feedback—specifically, reducing the mean impurity faster than by measurement alone—can be achieved by choosing the eigenbasis of the density matrix to be unbiased relative to the measurement basis. Here we further examine the protocol introduced by Combes and Jacobs [Phys. Rev. Lett. 96, 010504 (2006)] involving continuous measurement of the observable $J_z$ for a $D$-dimensional system. We rigorously rederive the lower bound $(2/3)(D+1)$ on the achievable speedup factor and also an upper bound, namely $D^2/2$, for all feedback protocols that use measurements in unbiased bases. Finally, we extend our results to $n$ independent measurements on a register of $n$ qubits and derive an upper bound on the achievable speedup factor that scales linearly with $n$.

We report a numerical study of strong-field ionization rates of the ${\mathrm{H}}_2$ molecule using time-dependent density-functional theory (TDDFT). In the dc field limit, TDDFT results for the rate of tunneling ionization agree with molecular Ammosov-Delone-Kralnov (MO-ADK) predictions, as well as results from a complex scaling method at the full configuration interaction level. Our study demonstrates the effect of photon energy, molecular vibration, and orientation on the ionization. Calculated rates for 800-nm lasers are about four times greater than the values predicted by the slowly varying field approximation for tunneling ionization. The rate for the ground vibrational state is higher than that of the fixed nuclei value at the equilibrium distance. This difference decreases with increasing field intensity. When the field intensity is sufficiently high, the two rates are very similar, and the fixed nuclear distance rate may be used to approximate the ground-vibrational-state rate. TDDFT methods predict an anisotropy slightly larger than the prediction obtained from the MO-ADK method. We also find that the field intensity plays a role in the anisotropy, which the MO-ADK results do not show.

We recall the framework of a consistent quantum description of polarization of light. Accordingly, the degree of polarization of a two-mode state $\mathrm{\rho ̂}$ of the quantum radiation field can be defined as a distance of a related state ${\mathrm{\rho ̂}}_b$ to the convex set of all SU(2)-invariant two-mode states. We explore a distance-type polarization measure in terms of the quantum Chernoff bound and derive its explicit expression. A comparison between the Chernoff and Bures degrees of polarization leads to interesting conclusions for some particular states chosen as illustrative examples.

Recently, Ji et al. disproved the local-unitary–local Clifford (LU-LC) conjecture and showed that the local unitary (LU) and local Clifford (LC) equivalence classes of the stabilizer states are not always the same. Despite the fact that this settles the LU-LC conjecture, a sufficient condition for stabilizer states that violate the LU-LC conjecture is not known. In this paper, we investigate further the properties of stabilizer states with respect to local equivalence. Our first result shows that there exist infinitely many stabilizer states that violate the LU-LC conjecture. In particular, we show that for all numbers of qubits $n⩾28$, there exist distance-two stabilizer states which are counterexamples to the LU-LC conjecture. We prove that, for all odd $n⩾195$, there exist stabilizer states with distance greater than two that are LU equivalent but not LC equivalent. Two important classes of stabilizer states that are of great interest in quantum computation are the cluster states and stabilizer states of the surface codes. We show that, under some minimal restrictions, both these classes of states preclude any counterexamples. In this context, we also show that the associated surface codes do not have any encoded non-Clifford transversal gates. We characterize the Calderbank-Shor-Steane (CSS) surface-code states in terms of a class of minor closed binary matroids. In addition to making a connection to an important open problem in binary matroid theory, this characterization does in some cases provide an efficient test for CSS states that are not counterexamples.