The optimally designed control of quantum systems is playing an increasingly important role to engineer novel and more efficient quantum technologies. Here, in the scenario represented by controlling an arbitrary quantum system via the interaction with an another optimally initialized auxiliary quantum system, we show that the quantum channel capacity sets the scaling behavior of the optimal control error. Specifically, by fitting the model to numerical data, we verify that the minimum control error is ensured by maximizing the quantum capacity of the channel mapping the initial control state into the target state of the controlled system, i.e., optimizing the quantum information flow from the controller to the system to be controlled. Analytical results, supported by numerical evidences, are provided when the systems and the controller are either qubits or single Bosonic modes.

Solitons are known to occur in the context of atom-light interaction via the well-known semiclassical phenomenon of self-induced transparency (SIT). Separately, in the regime where both light and atoms are fully treated quantum mechanically, quantum few-photon bound states are known to be a ubiquitous phenomenon that arises in different systems such as atoms coupled to chiral or bidirectional waveguides, and in Rydberg atomic media. In the specific case of two-level atoms coupled to a chiral waveguide, a recent analysis based on Bethe ansatz has established that SIT emerges from the quantum realm as a superposition of quantum many-photon bound states. Beyond this case, however, the nature of any connection between the full quantum many-body regime and semiclassical behavior has not been established. Here, we employ a general spin-model formulation of quantum atom-light interfaces to numerically investigate this problem, taking advantage of the fact that this approach readily allows for powerful many-body simulations based on matrix product states (MPS). We first analytically derive the two-photon bound state dispersion relation for a variety of atom-light interfaces and then proceed to numerically investigate the multiexcitation bound states dynamics. Interestingly, for all the specific systems studied, we find that the large-photon number limit always coincides with the soliton phenomenon of self-induced transparency or immediate generalizations thereof.

We consider a dissipative quantum Ising model periodically driven by a train of $\pi$ pulses and investigate dissipative discrete time crystals (DTCs) in solids. In this model, the interaction between the spins spontaneously breaks the discrete time translation symmetry, giving rise to a dissipative DTC, where two ferromagnetic states are switched alternately by each pulse. We microscopically describe the generic dissipation due to thermal contact to an equilibrium heat bath using the Bloch-Redfield equation. In contrast to other DTC studies, this dissipation stabilizes, rather than destroys, the DTC order without fine-tuning as long as the temperature is low enough. Invoking the time-dependent mean-field theory and solving self-consistently the periodic drive, dissipation, and DTC order parameter, we investigate the nonequilibrium DTC phase transition and determine the critical exponents, including a dynamical one. We also find phase transitions without an equilibrium counterpart: a nontrivial interplay of the periodic drive and dissipation gives rise to reentrant DTC transition when changing the pulse interval at a fixed temperature. Also, to demonstrate the rigidity of the DTC, we consider imperfect $\pi$ pulses, showing that the DTC is robust against the small imperfections and finding that discrete time quasicrystals can appear for the larger imperfections. Together with experimental proposals in magnetic materials, our results pave the way for realizing the DTC and for uncovering nonequilibrium critical phenomena in real solid-state materials.

We experimentally observed an accumulative type of nonlinear attenuation and distortion of slow light, i.e., Rydberg polaritons, with the Rydberg state $|32D_{5/2}\rangle$ in the weak-interaction regime. The present effect of attenuation and distortion cannot be explained by considering only the dipole-dipole interaction (DDI) between Rydberg atoms in $|32D_{5/2}\rangle$. Our observation can be attributed to the atoms in the dark Rydberg states rather than those in the bright Rydberg state, i.e., $|32D_{5/2}\rangle$, driven by the coupling field. The dark Rydberg states are all the possible states in which the population decaying from $|32D_{5/2}\rangle$ accumulated over time, and they were not driven by the coupling field. Consequently, the DDI between the dark and bright Rydberg atoms increased the decoherence rate of the Rydberg polaritons. We performed three different experiments to verify the above hypothesis, to confirm the existence of the dark Rydberg states, and to measure the decay rate from the bright to the dark Rydberg states. In the theoretical model, we included the decay process from the bright to the dark Rydberg states and the DDI effect induced by both the bright and dark Rydberg atoms. All the experimental data of slow light taken at various probe Rabi frequencies were in good agreement with the theoretical predictions based on the model. This study points out an additional decoherence rate in the Rydberg-state electromagnetically induced transparency effect and provides a better understanding of the Rydberg-polariton system.

The binary perceptron is a fundamental model of supervised learning for nonconvex optimization, which is a root of the popular deep learning. The binary perceptron is able to achieve a classification of random high-dimensional data based on the marginal probabilities of binary synapses. The relationship between the belief propagation instability and the equilibrium analysis of the model remains elusive. Here, we establish the relationship by showing that the instability condition around the belief propagation fixed point is identical to the instability for breaking the replica symmetric saddle-point solution of the free-energy function. Therefore our analysis will hopefully provide insight towards other learning systems in bridging the gap between nonconvex learning dynamics and statistical mechanics properties of more complex neural networks.

Silicon vacancy centers in silicon carbide are promising candidates for storing and manipulating quantum information. Implementation of fast quantum gates is an essential requirement for quantum information processing. In a low magnetic field, the resonance frequencies of silicon vacancy spins are in the range of a few MHz, the same order of magnitude as the Rabi frequencies of typical control fields. As a consequence, the rotating wave approximation becomes invalid and nonlinear processes like the absorption and emission of multiple photons become relevant. This paper focuses on multi-photon transitions of negatively charged silicon vacancies driven by a strong RF field. We present continuous-wave optically detected magnetic resonance (ODMR) spectra measured at different RF powers to identify the 1-, 2-, and 3 RF photon transitions of different types of the silicon vacancy in the $6H$-SIC polytype. Time-resolved experiments of Rabi oscillations and free induction decays of these multiple RF photon transitions were observed. Apart from zero-field data, we also present spectra in magnetic fields with different strength and orientation with respect to the system's symmetry axis.

The photogalvanic effect—a rectified current induced by light irradiation—requires the intrinsic symmetry of the medium to be sufficiently low, which strongly limits candidate materials for this effect. In this paper we explore how in Weyl semimetals the photogalvanic effect can be enabled and controlled by design of the material surface. Specifically, we provide a theory of ballistic linear and circular photogalvanic current in a Weyl semimetal spatially confined to a slab under general and variable surface boundary conditions. The results are applicable to Weyl semimetals with an arbitrary number of Weyl nodes at radiation frequencies small compared to the energy of nonlinear terms in the dispersion at the Fermi level. The confinement-induced response is tightly linked to the configuration of Fermi-arc surface states, specifically the Fermi-arc connectivity and direction of emanation from the Weyl nodes, thus inheriting the same directionality and sensitivity to boundary conditions. As a result, the photogalvanic response of the system becomes much richer than that of an infinite system, and may be tuned via surface manipulations.

A parametrically driven quantum oscillator, stabilized by a nonlinear dissipation, exhibits a spontaneous breaking of the parity symmetry. It results in the quantum bistability, corresponding to a Bloch sphere of dark states. This makes such a driven-dissipative system an attractive candidate for a qubit. The parity symmetry breaking is exact both on the classical level and within the quantum mechanical perturbation theory. Here, we show that nonperturbative quantum effects lead to the symmetry restoration and result in an exponentially small but finite qubit decoherence rate. Technically, the symmetry restoration is due to real-time instanton trajectories of the Keldysh path integral, which represents the Lindbladian evolution of the driven-dissipative oscillator.

We estimate the resources required in the fusion-based quantum computing scheme to simulate electrolyte molecules in Li-ion batteries on a fault-tolerant, photonic quantum computer. We focus on the molecules that can provide practical solutions to industrially relevant problems. Certain fault-tolerant operations require the use of single-qubit “magic states” prepared by dedicated “magic state factories” (MSFs). Producing and consuming magic states in parallel is typically a prohibitively expensive task, resulting in the serial application of fault-tolerant gates. However, for the systems considered, the MSF constitutes a negligible fraction of the total footprint of the quantum computer, allowing for the use of multiple MSFs to produce magic states in parallel. We suggest architectural and algorithmic techniques that can accommodate such a capability. We propose a method to consume multiple magic states simultaneously, which can potentially lead to an order of magnitude reduction in the computational runtime without additional expense in the footprint.

We show the emergence of Floquet time crystal (FTC) phases in the Floquet dynamics of periodically driven $p$-spin models, which describe a collection of spin-1/2 particles with all-to-all $p$-body interactions. Given the mean-field nature of these models, we treat the problem exactly in the thermodynamic limit and show that, for a given $p$, these systems can host various robust time-crystalline responses with period $nT$, where $T$ is the period of the drive and $n$ an integer between 2 and $p$. In particular, the case of four-body interactions ($p=4$) gives rise to both a usual period-doubling crystal and also a period-quadrupling phase. We develop a comprehensive framework to predict robust subharmonic response in classical area-preserving maps, and use this as a basis to predict the occurrence and characterize the stability of the resulting mean-field FTC phases in the quantum regime. Our analysis reveals that the robustness of the time-crystal behavior is reduced as their period increases, and establishes a connection between the emergence of time crystals, described by eigenstate ordering and robust subharmonic response, and the phenomenology of excited state and dynamical quantum phase transitions. Finally, for the models hosting two or more coexisting time crystal phases, we define protocols where the periodic subharmonic response of the system can be varied in time via the nonperiodic modulation of an external control parameter.

Variational algorithms have particular relevance for near-term quantum computers but require nontrivial parameter optimizations. Here we propose analytic descent: Given that the energy landscape must have a certain simple form in the local region around any reference point, it can be efficiently approximated in its entirety by a classical model—we support these observations with rigorous, complexity-theoretic arguments. One can classically analyze this approximate function to directly jump to the (estimated) minimum before determining a more refined function, if necessary. We derive an optimal measurement strategy and generally prove that the asymptotic resource cost of a jump corresponds to only a single gradient vector evaluation.

We embedded an all-hydrocarbon-based carbocation in a metallic microcavity that was tuned to resonance with an electronic transition of the carbocation. The measured Rabi splitting was 41% of the excitation energy, putting the system well into the ultrastrong coupling regime. Importantly, due to the intrinsic charge on the carbocation, the polaritons that form carry a significant charge fraction (0.55 $e_0$) and a large charge-to-mass ratio ($\sim 2400$ $e_0/m_0$). Moreover, the ground state of the ultrastrongly coupled system is calculated to carry about 1% of one elementary charge. These unique properties of our system, together with its convenient preparation, provide a practical platform to study charged polaritons in the ultrastrong coupling regime.

We generalize the recently proposed $\mathcal{PT}$-symmetric axion haloscope to a larger array with more $\mathcal{PT}$-symmetric structures. By broadening the response bandwidth of the signal without increasing the readout noise, the optimized scan rate of the axion haloscope is significantly enhanced, as well as is the signal power. Furthermore, we show that the robustness of the detector towards the variations of the array coupling is the strongest when a binary tree structure is introduced which contains a largely enhanced $\mathcal{PT}$ symmetry. The multiple allowed probing sensors can further increase the scan rate by a factor of the sensors' number due to the correlation of the signals. This type of array can strongly boost the search for an axion compared to single-mode resonant detection. The enhancement to the scan rate becomes the most manifest when applied to the proposed detection using a superconducting radio-frequency cavity with an ac magnetic field where most of the parameter space of the QCD axion above kHz can be probed.

Many synthetic quantum systems allow particles to have dispersion relations that are neither linear nor quadratic functions. Here, we explore single-particle scattering in general spatial dimension $D\ge 1$ when the density of states diverges at a specific energy. To illustrate the underlying principles in an experimentally relevant setting, we focus on waveguide quantum electrodynamics (QED) problems (i.e., $D=1$) with dispersion relation $\epsilon \left(k\right)=\pm \left|d\right|k^m$, where $m\ge 2$ is an integer. For a large class of these problems for any positive integer $m$, we rigorously prove that when there are no bright zero-energy eigenstates, the $S$ matrix evaluated at an energy $E\to 0$ converges to a universal limit that is only dependent on $m$. We also give a generalization of a key index theorem in quantum scattering theory known as Levinson's theorem—which relates the scattering phases to the number of bound states—to waveguide QED scattering for these more general dispersion relations. We then extend these results to general integer dimensions $D\ge 1$, dispersion relations $\epsilon \left(\mathit{k}\right)={\left|\mathit{k}\right|}^a$ for a $D$-dimensional momentum vector $\mathit{k}$ with any real positive $a$, and separable potential scattering.

Using tools from representation theory, we derive expressions for the coincidence rate of partially-distinguishable particles in an interferometry experiment. Our expressions are valid for either bosons or fermions, and for any number of particles. In an experiment with $n$ particles the expressions we derive contain a term for each partition of the integer $n$; Gamas's theorem is used to determine which of these terms are automatically zero based on the pairwise level of distinguishability between particles. Most sampling schemes (such as “boson sampling”) are limited to completely indistinguishable particles; our paper aids in the understanding of systems where an arbitrary level of distinguishability is permitted. As an application of our paper we introduce a sampling scheme with partially-distinguishable fermions, which we call “generalized fermion sampling”.