We study a system made up of one or two two-level quantum emitters, coupled to a single transverse mode of a closed waveguide, in which photon wavenumbers and frequencies are discretized, and characterize the states in which one excitation is steadily shared between the field and the emitters. We unearth finite-size effects in the field-emitter interactions and identify a family of dressed bound states that represent the forerunners of bound states in the continuum in the limit of an infinite waveguide. We finally consider the potential interest of such states for applications in the field of quantum information.

An exciting frontier in quantum information science is the realization and control of complex quantum many-body systems. The hybrid nanophotonic system with cold atoms has emerged as a paradigmatic platform for realizing long-range spin models from the bottom up, exploiting their modal geometry and group dispersion for tailored interactions. An important challenge is the physical limitation imposed by the photonic bath, constraining the types of local Hamiltonians that decompose the available physical models and restricting the spatial dimensions to that of the dielectric media. However, at the nanoscopic scale, atom-field interaction inherently accompanies significant driven-dissipative quantum forces that may be tamed as a new form of a mediator for controlling the atomic internal states. Here we formulate a quantum optics toolbox for constructing universal quantum matter with individual atoms in the vicinity of one-dimensional photonic crystal waveguides. The enabling platform synthesizes analog quantum materials of universal 2-local Hamiltonian graphs mediated by phononic superfluids of the trapped atoms. We generalize our microscopic theory of an analog universal quantum simulator to the development of dynamical gauge fields. In the spirit of gauge theories, we investigate emergent lattice models of arbitrary graphs, for which strongly coupled $\mathrm{SU}\left(n\right)$ excitations are driven by an underlying multibody interaction. As a minimal model in the infrared, we explore the realization of an archetypical strong-coupling quantum field theory, the $\mathrm{SU}\left(n\right)$ Wess-Zumino-Witten model, and discuss a diagnostic tool to map the conformal data of the field theory to the static and dynamical correlators of the fluctuating photons in the guided mode.

Quantum nonlocality has different manifestations that, in general, are revealed by local measurements of the parts of a composite system. In this paper, we study nonlocality arising from a set of orthogonal states that cannot be perfectly distinguished by local operations and classical communication (LOCC). Such a set is deemed nonlocal, for a joint measurement on the whole system is necessary for perfect discrimination of the states with certainty. On the other hand, a set of orthogonal states that can be perfectly distinguished by LOCC is believed to be devoid of nonlocal properties. Here, we show that there exist orthogonal sets that are locally distinguishable but without local redundancy (i.e., they become nonorthogonal on discarding one or more subsystems) whose nonlocality can be activated by local measurements. In particular, a state chosen from such a set can be locally converted, with certainty, into another state, the identity of which can now only be ascertained by global measurement and no longer by LOCC. In other words, a locally distinguishable set without local redundancy may be locally converted into a locally indistinguishable set with certainty. We also suggest an application, namely, local hiding of information, that allows us to locally hide locally available information without losing any part. Once hidden, the information in its entirety can only be retrieved using entanglement.

The task of estimating the ground state of Hamiltonians is an important problem in physics with numerous applications ranging from solid-state physics to combinatorial optimization. We provide a hybrid quantum-classical algorithm for approximating the ground state of a Hamiltonian that builds on the powerful Krylov subspace method in a way that is suitable for current quantum computers. Our algorithm systematically constructs the ansatz by using any given choice of the initial state and the unitaries describing the Hamiltonian. The only task of the quantum computer is to measure overlaps and no feedback loops are required. The measurements can be performed efficiently on current quantum hardware without requiring any complicated measurements such as the Hadamard test. Finally, a classical computer solves a well-characterized quadratically constrained optimization program. Our algorithm can reuse previous measurements to calculate the ground state of a wide range of Hamiltonians without requiring additional quantum resources. Further, we demonstrate our algorithm for solving a class of problems with thousands of qubits. The algorithm works for almost every random choice of the initial state and circumvents the barren plateau problem.

Distributed quantum computing can provide substantial noise reduction due to shallower circuits. An experiment illustrates the advantages in the case of a Grover search. This motivates study of the quantum advantage of the distributed version of the Simon and Deutsch-Jozsa algorithms. We show that the distributed Simon algorithm retains the exponential advantage, but the complexity deteriorates from $O\left(n\right)$ to $O\left(n^2\right)$, where $n={log}_2\left(N\right)$. The distributed Deutsch-Jozsa algorithm deteriorates to being probabilistic but retains a quantum advantage over classical random sampling.

We consider few-photon ionization of atomic lithium by linearly polarized femtosecond laser pulses and demonstrate that asymmetries of the electron angular distribution can occur for initially polarized $(2p,$ $m$=$+1)$ target atoms. The dependence of the photoelectron emission angle relative to the electric field direction is investigated at different laser intensities and wavelengths. The experimental spectra show excellent agreement with numerical solutions of the time-dependent Schrödinger equation. In the perturbative picture, the angular shift is traced back to interferences between partial waves with mean magnetic quantum number $\langle m\rangle \ne 0$. This observation allows us to obtain quantum mechanical information on the final electronic state.

We present a model for ${\chi }^{\left(2\right)}$ waveguides accounting for three modes, two of which make an avoided crossing at the second harmonic wavelength. We introduce two linearly coupled pure modes and adjust the coupling to replicate the waveguide dispersion near the avoided crossing. Analysis of the nonlinear system reveals continuous wave (CW) solutions across much of the parameter space and prevalence of its modulational instability. We also predict the existence of the avoided-crossing solitons, and study peculiarities of their dynamics and spectral properties, which include formation of a pedestal in the pulse tails and associated pronounced spectral peaks. Mapping these solitons onto the linear dispersion diagrams, we make connections between their existence and CW existence and stability. We also simulate the two-color soliton generation from a single-frequency pump pulse to back up its formation and stability properties.

Nanoscale devices, either biological or artificial, operate in a regime where the usual assumptions of a structureless Markovian bath do not hold. Being able to predict and study the dynamics of such systems is crucial and is usually done by tracing out the bath degrees of freedom, which implies losing information about the environment. To go beyond these approaches we use a numerically exact method relying on a matrix product state representation of the quantum state of a system and its environment to keep track of the bath explicitly. This method is applied to a specific example of interaction that depends on the spatial structure of a system made of two sites. The result is that we predict a non-Markovian dynamics where long-range couplings induce correlations into the environment. The environment dynamics can be naturally extracted from our method and shine a light on long-time feedback effects that are responsible for the observed non-Markovian recurrences in the eigenpopulations of the system.

It is well known that, due to the uncertainty principle, the Planck constant sets a resolution boundary in phase space and the resulting trade-off in resolution between incompatible measurements has been thoroughly investigated. It is also known that, in the classical regime, sufficiently coarse measurements of position and momentum can simultaneously be determined. However, the picture of how the uncertainty principle gradually disappears as we transition from the quantum to the classical regime is not so vivid. In the present work we clarify this picture by studying the associated probabilities that quantify the effects of the uncertainty principle in the framework of finite-dimensional quantum mechanics on a lattice. We also study how these probabilities are perturbed by the granularity of the lattice and show that they can signal the discontinuity of the underlying space.

Kernel methods are ubiquitous in classical machine learning, and recently their formal similarity with quantum mechanics has been established. To grasp the potential advantage of quantum machine learning, it is necessary to understand the distinction between nonclassical kernel functions and classical kernels. This paper builds on a recently proposed phase-space nonclassicality witness [Bohmann and Agudelo, Phys. Rev. Lett. 124, 133601 (2020)] to derive a witness for the kernel's quantumness in continuous-variable systems. We discuss the role of the kernel's nonclassicality in data distribution in the feature space and the effect of imperfect state preparation. Furthermore, we show that the nonclassical kernels lead to the quantum advantage in parameter estimation. Our work highlights the role of the phase-space correlation functions in understanding the distinction of classical machine learning from quantum machine learning.

The reversible implementation of classical functions accounts for the bulk of most known quantum algorithms. As a result, a number of reversible circuit constructions over the $\mathrm{Clifford}+T$ gate set have been developed in recent years which use both the state and phase spaces, or $X$ and $Z$ bases, to reduce circuit costs beyond what is possible at the strictly classical level. We study and generalize two particular classes of these constructions: relative-phase circuits, including Giles and Selinger's multiply controlled $iX$ gates and Maslov's four-qubit Toffoli gate, and measurement-assisted circuits, including Jones' Toffoli gate and Gidney's temporary logical-and gate. In doing so, we introduce general methods for implementing classical functions up to phase and for measurement-assisted termination of temporary values. We then apply these techniques to find $T$-count efficient constructions of some classical functions in space-constrained regimes, notably multiply controlled Toffoli gates and temporary products.

We report precision measurements of the nuclear magnetic moment of ${}^{43}\mathrm{Ca}^{+}$, made by microwave spectroscopy of the $4s{}^{2}S_{1/2}|F=4,M=0\rangle \to |F=3,M=1\rangle$ ground level hyperfine clock transition at a magnetic field of $\approx 146\mathrm{G}$, using a single laser-cooled ion in a Paul trap. We measure a clock-transition frequency of $f=3199941076.920\left(46\right)\mathrm{Hz}$ from which we determine ${\mu }_I/{\mu }_N=-1.315350\left(9\right)\left(1\right)$ where the uncertainty (9) arises from uncertainty in the hyperfine $A$ constant, and the (1) arises from the uncertainty in our measurement. This measurement is not corrected for diamagnetic shielding due to the bound electrons. We make a second measurement which is less precise but agrees with the first. We use our ${\mu }_I$ value in combination with previous NMR results to extract the change in shielding constant of calcium ions due to solvation in ${\mathrm{D}}_2\mathrm{O}\text{:}\mathrm{\Delta }\sigma =-0.00022\left(1\right)$.

The effects of postcollision interaction (PCI) in the time evolution of photoinduced Auger decay, assisted by a terahertz (THz) field, is theoretically investigated. We propose a time-dependent model which is based on the quantum-mechanical description of the photoinduced Auger process and quasiclassical description of the PCI. The suggested model is used for calculating the PCI distortion of the Auger spectrum at different temporal overlaps of the exciting extreme ultraviolet pulse and the streaking THz pulse.

We show how quantized transport can be realized in Floquet chains through encapsulation of a chiral or helical shift. The resulting transport is immutable rather than topological in the sense that it neither requires a band gap nor is affected by arbitrarily strong perturbations. Transport is still characterized by topological quantities but encapsulation of the shift prevents topological phase transitions. To explore immutable transport we introduce the concept of a shiftbox, explain the relevant topological quantities both for momentum-space dispersions and real-space transport, and study model systems of Floquet chains with strictly quantized chiral and helical transport. Natural platforms for the experimental investigation of these scenarios are photonic Floquet chains constructed in waveguide arrays, as well as topolectrical or mechanical systems.

We put forward a measure based on Gaussian steering to quantify the non-Markovianity of continuous-variable (CV) Gaussian quantum channels. We employ the proposed measure to assess and compare the non-Markovianity of a quantum Brownian motion (QBM) channel, originating from the interaction with Ohmic and sub-Ohmic environments with spectral densities described by a Lorentz-Drude cutoff, both at high and low temperatures, showing that sub-Ohmic, high-temperature environments lead to highly non-Markovian evolution, with cyclic backflows of Gaussian steerability from the environment to the system. Our results add to the understanding of the interplay between quantum correlations and non-Markovianity for CV systems, and could be implemented at the experimental level to quantify non-Markovianity in some physical scenarios.

A device capable of converting single quanta of the microwave field to the optical domain is an outstanding endeavor in the context of quantum interconnects between distant superconducting qubits, but likewise can have applications in other fields, such as radio astronomy or, in the classical realm, microwave photonics. A variety of transduction approaches, based on optomechanical or electro-optical interactions, have been proposed and realized, yet the required vanishing added noises and an efficiency approaching unity, have not yet been attained. Here we present a transduction scheme that could in theory satisfy the requirements for quantum coherent bidirectional transduction. Our scheme relies on an intermediary mechanical mode, a high-overtone bulk acoustic resonance (HBAR), to coherently couple microwave and optical photons through the piezoelectric and strain-optical effects. Its efficiency results from the combination of integrated ${\mathrm{Si}}_3{\mathrm{N}}_4$ photonic circuits with ultra-low loss sustaining high intracavity photon numbers with the highly efficient microwave to mechanical transduction offered by piezoelectrically coupled HBAR. We develop a quantum theory for this multipartite system by first introducing a quantization method for the piezoelectric interaction between the microwave mode and the mechanical mode from first principles (which to our knowledge has not been presented in this form) and link the latter to the conventional Butterworth-Van Dyke model. The HBAR is subsequently coupled to a pair of hybridized optical modes from coupled optical ring cavities via the strain-optical effect. We analyze the conversion capabilities of the proposed device using signal flow graphs, and demonstrate that near quantum coherent transduction is possible, with realistic experimental parameters. Combined with the high thermal conduction via the device bulk, heating effects are mitigated, and the approach does not require superconducting resonators that are susceptible to absorption of optical photons.

Decay rates of the positronium molecule ${\text{Ps}}_2$ into two photons and into an electron-positron pair are determined. Previous studies find that these rates are very different, $\mathrm{\Gamma }({\text{Ps}}_2\to e^{+}{e}^{-})/\mathrm{\Gamma }({\text{Ps}}_2\to \gamma \gamma )\simeq 250$. This is puzzling since both processes have two-body final states and are of the same order in the fine-structure constant. We propose a simple calculational method and test it with the well-established decay of the positronium ion into an electron and a photon. We then employ it to correct predictions for both these ${\text{Ps}}_2$ decays. We find that previous studies overestimated the $e^{+}{e}^{-}$ channel and underestimated the $\gamma \gamma$ channel by factors of about 5.44 and 3.93, respectively. Our results give $\mathrm{\Gamma }({\text{Ps}}_2\to e^{+}{e}^{-})/\mathrm{\Gamma }({\text{Ps}}_2\to \gamma \gamma )\simeq 11.7$.