We investigate coined quantum-walk search and state-transfer algorithms, focusing on the complete $M$-partite graph with $N$ vertices in each partition. First, it is shown that by adding a loop to each vertex, the search algorithm finds the marked vertex with unit probability in the limit of a large graph. Next, we employ the evolution operator of the search with two marked vertices to perform a state transfer between the sender and the receiver. We show that when the sender and the receiver are in different partitions, the algorithm succeeds with fidelity approaching unity for a large graph. However, when the sender and the receiver are in the same partition, the fidelity does not reach exactly 1. To solve this problem, we propose a state-transfer algorithm with an active switch, whose fidelity can be estimated based on the single vertex search alone.

We consider a continuous-variable Clauser-Horne Bell-type inequality to study nonlocality in four-mode continuous-variable systems, which goes beyond two-photon states and can be applied to mixed as well as to states with fluctuating photon number. We apply the inequality to a wide variety of states such as pure and mixed Gaussian states (including squeezed thermal states) and non-Gaussian states. We consider beam splitters as a model for leakage and show that the inequality is able to detect nonlocality of noisy Gaussian states as well. Finally, we investigate nonlocality in pair-coherent states and entangled coherent states, which are prominent examples of nonclassical, non-Gaussian states.

We describe an efficient protocol to perform quantum state transfer using Hamiltonian dynamics with long-range interactions. The time to transfer $n$ qubits a sufficiently large distance is proportional to $\sqrt{n}$. Even without error correction, the fidelity of this multiqubit state transfer process remains finite for arbitrarily-well-separated qubits in the presence of uncorrelated random errors in coupling constants.

State-of-the-art classical neural networks are observed to be vulnerable to small crafted adversarial perturbations. A more severe vulnerability has been noted for quantum machine learning (QML) models classifying Haar-random pure states. This stems from the concentration of measure phenomenon, a property of the metric space when sampled probabilistically, and is independent of the classification protocol. To provide insights into the adversarial robustness of a quantum classifier on real-world classification tasks, we focus on the adversarial robustness in classifying a subset of encoded states that are smoothly generated from a Gaussian latent space. We show that the vulnerability of this task is considerably weaker than that of classifying Haar-random pure states. In particular, we find only mildly polynomially decreasing robustness in the number of qubits, in contrast to the exponentially decreasing robustness when classifying Haar-random pure states and suggesting that QML models can be useful for real-world classification tasks.

We study the statistical behavior of multimoded optical systems under equilibrium conditions. We investigate the role of variations of the system parameters in the thermodynamic description and derive an optical analog of the first law of thermodynamics, a generic expression for the work done to the system, and an optical Gibbs-Duhem equation. To demonstrate these effects, we focus on the case of two-dimensional photonic lattices. We study the conditions under which the entropy in such waveguide arrays can be considered as extensive. In this respect, small deviations from the extensive character of the entropy give rise to stress and strain terms. We examine how the conservation laws in such array configurations are affected by variations in the system parameters, and furthermore, we analyze the respective thermodynamic processes (isentropic and Joule-type expansions).

A few years ago Avetissian et al. [Phys. Rev. Lett. 113, 023904 (2014); Phys. Rev. A 92, 023820 (2015)] discovered that the exponential growth rate of the stimulated annihilation photons from a singlet positronium Bose-Einstein condensate should be proportional to the square root of the positronium number density, not to the number density itself. In order to elucidate this surprising result obtained via a field-theoretical analysis, we point out that the basic physics involved is the same as that of resonant subharmonic transitions between two quantum oscillators. Using this model, we show that nonlinearities of the type discovered by Avetissian et al. are not unique to positronium and in fact will be encountered in a wide range of systems that can be modeled as nonlinearly coupled quantum oscillators.

We develop a theoretical framework to optimize and understand uncertainty from in situ strong-field measurements of laser field parameters. We present a derivation of quantum and classical Fisher information in attoscience for an electron undergoing strong-field ionization. This is used for parameter estimation and to characterize the uncertainty of the ponderomotive energy, directly proportional to laser intensity. In particular, the quantum and classical Fisher information for the momentum basis displays quadratic scaling over time. This can be linked to above-threshold ionization interference rings for measurements in the momentum basis and to a “ponderomotive phase” for the optimal quantum measurements. Preferential scaling in uncertainty is found for increasing laser pulse length and intensity. We use this to demonstrate for in situ measurements of laser intensity that high-resolution momentum spectroscopy has the capacity to reduce the uncertainty by more than 25 times compared to measurements employing the ionization rate, while using the optimal quantum measurement would reduce it by a further factor of 2.6. A minimum uncertainty of the order $2.8\times {10}^{-3}\%$ is theorized for this framework. Finally, we examine previous in situ measurements, formulating a measurement that matches the experimental procedure, and suggest alterations to the measurement scheme that could reduce the laser intensity uncertainty.

We report on the observation of the spin-exchange dynamics of ${}^{171}\mathrm{Yb}$ atoms in the ground state ${}^1{S}_0$ and in the metastable state ${}^3{P}_0$. We implement the mixed-dimensional two-orbital system using near-resonant and magic-wavelength optical lattices, where the ${}^1{S}_0$ and ${}^3{P}_0$ atoms are itinerant in a one-dimensional tube and localized in three dimensions, respectively. By exploiting an optical Stern-Gerlach method, we observe the spin depolarization of the ${}^1{S}_0$ atoms induced by the spin-exchange interaction with the ${}^3{P}_0$ atom. Our work could pave the way to the quantum simulation of the Kondo effect.

We show that probability is locally conserved in discrete-time quantum walks, corresponding to a particle evolving in discrete space and time. In particular, for a spatial structure represented by an arbitrary directed graph, and any unitary evolution of a particle which respects that locality structure, we can define probability currents which also respect the locality structure and which yield the correct final probability distribution.

The generalization of the geometric phase to the realm of mixed states is known as the Uhlmann phase. Recently, applications of this concept to the field of topological insulators have been made and an experimental observation of a characteristic critical temperature at which the topological Uhlmann phase disappears has also been reported. Here we study the case of the Uhlmann phase of a paradigmatic system such as the spin-$j$ particle in the presence of a slowly rotating magnetic field at finite temperature in an exact analytical form. We find that the Uhlmann phase is given by the argument of a complex-valued second-kind Chebyshev polynomial of order $2j$. Correspondingly, the Uhlmann phase displays $2j$ singularities, occurring at the roots of such polynomials which define the critical temperatures at which the system undergoes topological order transitions. Appealing to the argument principle of complex analysis, each topological order is characterized by a winding number, which happens to be $2j$ for the ground state and decreases by unity each time the increasing temperature passes through a critical value. We hope this study encourages experimental verification of this phenomenon of thermal control of topological properties, as has already been done for the spin-$1/2$ particle.

We obtain worst-case performance guarantees for $p=2$ and 3 QAOA for MaxCut on uniform 3-regular graphs. Previous work by Farhi et al. obtained a lower bound on the approximation ratio of 0.692 for $p=1$. We find a lower bound of 0.7559 for $p=2$, where worst-case graphs are those with no cycles $\le 5$. This bound holds for any 3-regular graph evaluated at particular fixed parameters. We conjecture a hierarchy for all $p$, where worst-case graphs have with no cycles $\le 2p+1$. Under this conjecture, the approximation ratio is at least 0.7924 for all 3-regular graphs and $p=3$. In addition, using an indistinguishable argument we find an upper bound on the worst-case approximation ratio for all $p$, which indicates classes of graphs for which there can be no quantum advantage for at least $p<6$.

Super Coster-Kronig (SCK) decay following Kr $3p$ photoionization has been investigated using a multielectron coincidence method. It is found that the SCK pathway occupies 23% of the $3p_{1/2}$ decay and only 2.5% of the $3p_{3/2}$ decay. The significant difference between the two $3p$ spin-orbit levels mainly results from the difference in energetics: almost all SCK transitions are energetically allowed in the $3p_{1/2}$ decay but only SCK transitions to the ${}^{3}F$ levels of $3d^{-2}$ are possible in the $3p_{3/2}$ decay. Subsequent decay processes from the SCK-final $3d^{-2}$ states are investigated, where a maximum of fivefold electron coincidences are analyzed.

The disordered Bose-Hubbard model in two dimensions at noninteger filling admits a superfluid to Bose-glass transition at weak disorder. Less understood are the properties of this system at strong disorder and energy densities corresponding to excited states. In this work, we study the Bose-glass transition of the ground state and the related finite energy localization transition, the mobility edge of the quasiparticle spectrum, a critical energy separating extended from localized quasiparticle excitations. To study these the fluctuation operator expansion is used. The level spacing statistics of the quasiparticle excitations, the fractal dimension and decay of the corresponding wave functions are consistent with a many-body mobility edge. The finite-size scaling of the lowest gaps yields a correction to the mean-field prediction of the superfluid to Bose-glass transition. In its vicinity, we discuss spectral properties of the ground state in terms of the dynamic structure factor and the spectral function which also shows distinct behavior above and below the mobility edge.

The approach to equilibrium of quantum mechanical systems is a topic as old as quantum mechanics itself, but has recently seen a surge of interest due to applications in quantum technologies, including, but not limited to, quantum computation and sensing. The mechanisms by which a quantum system approaches its long-time, limiting stationary state are fascinating and, sometimes, quite different from their classical counterparts. In this respect, quantum networks represent mesoscopic quantum systems of interest. In such a case, the graph encodes the elementary quantum systems (say qubits) at its vertices, while the links define the interactions between them. We study here the relaxation to equilibrium for a fully connected quantum network with controlled-not (cnot) gates representing the interaction between the constituting qubits. We give a number of results for the equilibration in these systems, including analytic estimates. The results are checked using numerical methods for systems with up to 15–16 qubits. It is emphasized in which way the size of the network controls the convergency.

The formalism of continuous-time quantum walks on graphs has been widely used in the study of quantum transport of energy and information, as well as in the development of quantum algorithms. In experimental settings, however, there is limited control over the coupling coefficients between the different nodes of the graph (which are usually considered to be real valued), thereby restricting the types of quantum walks that can be implemented. In this paper, we apply the idea of Floquet engineering in the context of continuous-time quantum walks, i.e., we define periodically driven Hamiltonians which can be used to simulate the dynamics of certain target continuous-time quantum walks. We focus on two main applications: (i) simulating quantum walks that break time-reversal symmetry due to complex coupling coefficients and (ii) increasing the connectivity of the graph by simulating the presence of next-nearest-neighbor couplings. Our paper provides explicit simulation protocols that may be used for directing quantum transport, engineering the dispersion relation of one-dimensional quantum walks, or investigating quantum dynamics in highly connected structures.

Quantum computational approaches to some classic target identification and localization algorithms, especially for radar images, are investigated, and are found to raise a number of quantum statistics and quantum measurement issues with much broader applicability. Such algorithms are computationally intensive, involving coherent processing of large sensor data sets in order to extract a small number of low profile targets from a cluttered background. Target enhancement is accomplished through accurate statistical characterization of the environment, followed by optimal identification of statistical outliers. The algorithm is inspired by recent approaches to quantum machine learning, but requires significant extensions, including previously overlooked “quantum analog-digital” conversion steps (which are found to substantially increase the required number of qubits), “quantum statistical” generalization of the classic phase estimation and Grover search algorithms, and careful consideration of projected measurement operations. The key result of the paper is that the environmental covariance matrix estimation and manipulation at the heart of the statistical analysis, together with the target identification step, actually enable a highly efficient quantum implementation. However, several potential bottlenecks, especially those associated with data loading and conversion, are exhibited as well. Although no fundamental barrier to quantum speed-up is identified, optimal algorithm implementation, accounting for additional numbers of qubits and possible new error correction protocols associated with the quantum analog representation, remains an interesting question for future research.