In this work, we incorporate decoy-state analysis into a well-established numerical framework for key rate calculation, and we apply the numerical framework to decoy-state BB84 and measurement-device-independent (MDI) QKD protocols as examples. Additionally, we combine with these decoy-state protocols what is called “fine-grained statistics,” which is a variation of existing QKD protocols that makes use of originally discarded data to get a better key rate. We show that such variations can grant protocols resilience against any unknown and slowly changing rotation along one axis, similar to reference-frame-independent QKD, but without the need for encoding physically in an additional rotation-invariant basis. Such an analysis can easily be applied to existing systems, or even data already recorded in previous experiments, to gain a significantly higher key rate when considerable misalignment is present, extending the maximum distance for BB84 and MDI-QKD and reducing the need for manual alignment in an experiment.

We introduce the notion of “generalized bosons” whose exchange statistics resemble those of bosons, but the local bosonic commutator $[a,a^{†}]=1$ is replaced by an arbitrary single-mode operator that is diagonal in the generalized Fock basis. Examples of generalized bosons include boson pairs and spins. We consider the analog of the boson sampling task for these particles and observe that its output probabilities are still given by permanents, so that the results regarding hardness of sampling directly carry over. Finally, we propose implementations of generalized boson sampling in circuit-QED and ion-trap platforms.

Parafermion bound states (PBSs) are generalizations of Majorana bound states (MBSs) and have been predicted to exist as zero-energy eigenstates in proximitized fractional quantum Hall edge states. Similarly to MBSs, a finite distance between the PBS can split the ground-state degeneracy. However, parafermionic modes have a richer exchange statistics than MBSs, so several interaction terms are allowed by the underlying ${\mathbb{Z}}_{2n}$ symmetry, rendering the effective Hamiltonian governing a pair of PBSs at a finite distance nontrivial. Here, we use a combination of analytical techniques (semiclassical instanton approximation) and numerical techniques (quantum Monte Carlo simulations) to determine the effective coupling Hamiltonian. For this purpose, we go beyond the dilute one-instanton gas approximation and show how finite-size effects can give rise to higher-order parafermion interactions. We find good quantitative agreement between the analytical results and Monte Carlo simulations. We estimate that these finite-size corrections should be observable in some of the recently proposed experiments to observe PBSs in strongly correlated systems.

Spectroscopic and interferometric measurements complement each other in extracting the fundamental properties of quantum many-body systems. While spectroscopy provides precise measurements of equilibrated energies, interferometry can elucidate the dynamical evolution of the system. For an impurity immersed in a bosonic medium, both are equally important for understanding the quasiparticle physics of the Bose polaron. Here, we compare the interferometric and spectroscopic timescales to the underlying dynamical regimes of the impurity dynamics and the polaron lifetime, highlighting the capability of the interferometric approach to clearly resolve polaron dynamics. In particular, interferometric measurements of the coherence amplitude at strong interactions reveal faster quantum dynamics at large repulsive interaction strengths than at unitarity. These observations are in excellent agreement with a short-time theoretical prediction including both the continuum and the attractive polaron branch. For longer times, qualitative agreement with a many-body theoretical prediction which includes both branches is obtained. Moreover, the polaron energy is extracted from interferometric measurements of the observed phase velocity in agreement with previous spectroscopic results from weak to strong attractive interactions. Finally, the phase evolution allows for the measurement of an energetic equilibration timescale, describing the initial approach of the phase velocity to the polaron energy. Theoretically, this is shown to lie within the regime of universal dynamics revealing a fast initial evolution towards the formation of polarons. Our results give a comprehensive picture of the many-body physics governing the Bose polaron and thus validates the quasiparticle framework for further studies.

Modeling joint probability distributions is an important task in a wide variety of fields. One popular technique for this employs a family of multivariate distributions with uniform marginals called copulas. While the theory of modeling joint distributions via copulas is well understood, it gets practically challenging to accurately model real data with many variables. In this paper, we show that any copula can be naturally mapped to a multipartite maximally entangled state. Thus, the task of learning joint probability distributions becomes the task of learning maximally entangled states. We prove that a variational ansatz we christen as a “qopula” based on this insight leads to an exponential advantage over classical methods of learning some joint distributions. As an application, we train a quantum generative adversarial network (QGAN) and a quantum circuit Born machine (QCBM) using this variational ansatz to generate samples from joint distributions of two variables in historical data from the stock market. We demonstrate our generative learning algorithms on trapped ion quantum computers from IonQ for up to eight qubits. Our experimental results show interesting findings such as the resilience against noise, outperformance against equivalent classical models and 20–1000 times less iterations required to converge as compared to equivalent classical models.

We explore a mechanism of the anomalous rheology of active suspensions by hydrodynamic simulations using model pusher swimmers. Our simulations demonstrate that hydrodynamic interactions under shear flow systematically orient swimmers along the extension direction, which is responsible for determining the global swimming states and the resulting significant viscosity reduction. The present results indicate the essential role of hydrodynamic interactions in the elementary processes controlling the rheological properties in active suspensions. Furthermore, such processes may be the substance of the previously proposed scenario for anomalous rheology based on the interplay between the rotational diffusivities and the external shear flow.

The ability to solve differential equations represents a key step in the modeling and understanding of complex systems. There exist several analytical and numerical methods for solving differential equations, each with their own advantages and limitations. Physics-informed neural networks (PINNs) offer an alternative perspective. Although PINNs deliver promising results, many stones remain unturned about this method. In this paper, we introduce a method that improves the efficiency of PINNs in solving differential equations. Our method is related to the formulation of the problem: Instead of training a network to solve an $n\mathrm{th}$ order differential equation, we propose transforming the problem into the equivalent system of $n$ first-order equations in phase space. The target of the network is to solve all equations of the system simultaneously, effectively introducing a multitask optimization problem. We compare both approaches empirically on various problems, ranging from second-order differential equations with constant coefficients to higher-order and nonlinear problems. We also show that our approach is suited for solving partial differential equations. Our results show that the system approach performs equal or better in most experiments performed. We analyze the learning process for the few runs that did not perform well and show that the problem stems from conflicting gradients during training, effectively obstructing multitask learning. The result of this paper is a straightforward heuristic that can be incorporated into any subsequent research that builds on PINNs solving differential equations. Moreover, it also shows how to make PINNs even more efficient by implementing techniques from multitask learning literature.

Quantum computers have the potential to efficiently simulate the dynamics of nanoscale NMR systems. In this work, we demonstrate that a noisy intermediate-scale quantum computer can be used to simulate and predict nanoscale NMR resonances. In order to minimize the required gate fidelities, we propose a superconducting application-specific Co-Design quantum processor that reduces the number of SWAP gates by over 90% for chips with more than 20 qubits. The processor consists of transmon qubits capacitively coupled via tunable couplers to a central co-planar waveguide resonator with a quantum circuit refrigerator (QCR) for fast resonator reset. The QCR implements the nonunitary quantum operations required to simulate nuclear hyperpolarization scenarios.

Quantum error correction is one of the most important milestones for the realization of large-scale quantum computation. To achieve this, it is essential not only to integrate a large number of qubits with high fidelity but also to build a scalable classical system that can perform error correction. Here, we propose an efficient and scalable decoder for quantum error correction using “Fujitsu Digital Annealer” (DA). Specifically, the error correction problem of stabilizer codes is mapped into an Ising-type optimization problem, so-called quadratic unconstrained binary optimization (QUBO) problem, which is solved by DA. In particular, we implement the proposed DA decoder for the surface code and perform detailed numerical experiments for various code distances to see its performance and scalability. We observe that computational scaling for the DA decoder has a lower order of polynomials than the decoding methods using simulated annealing (SA) and minimum-weight perfect matching (MWPM) algorithm under all tested conditions. It is also shown that the DA decoder has advantages over the Union-Find (UF) decoder from a variety of perspectives including hardware implementation. Furthermore, the threshold behavior of the logical error probability for the DA decoder is analyzed and the resultant threshold lies between 9.4% and 9.8%, which is very close to that obtained by the MWPM decoder. This result clearly shows the high potential of the DA decoder for quantum error correction.

Topological transport of fermions is governed by the Chern numbers of the energy bands lying below the Fermi energy. For bosons, e.g., phonons and magnons in a crystal, topological transport is dominated by the Chern number of the lowest energy band when the bandgap is comparable with the thermal energy. Here, we demonstrate the presence of topological transport by bosonic magnons in a lattice of magnetic skyrmions—topological defects formed by a vortexlike texture of spins. We find a distinct thermal Hall signal in the magnetic skyrmion phase of an insulating polar magnet ${\mathrm{GaV}}_4{\mathrm{Se}}_8$, identified as the topological thermal Hall effect of magnons governed by the Chern number of the lowest energy band of the magnons in a triangular lattice of magnetic skyrmions. Our findings lay a foundation for studying topological phenomena of other bosonic excitations via thermal Hall probe.

Synthetic horizons in models for quantum matter provide an alternative route to explore fundamental questions of modern gravitational theory. Here we apply these concepts to the problem of emergence of thermal quantum states in the presence of a horizon, by studying ground-state thermalization due to instantaneous horizon creation in a gravitational setting and its condensed matter analog. By a sudden quench to position-dependent hopping amplitudes in a one-dimensional lattice model, we establish the emergence of a thermal state accompanying the formation of a synthetic horizon. The resulting temperature for long chains is shown to be identical to the corresponding Unruh temperature, provided that the postquench Hamiltonian matches the entanglement Hamiltonian of the prequench system. Based on detailed analysis of the outgoing radiation we formulate the conditions required for the synthetic horizon to behave as a purely thermal source, paving a way to explore this interplay of quantum-mechanical and gravitational aspects experimentally.

Ultracold atoms in optical lattices are pristine model systems with a tunability and flexibility that goes beyond solid-state analogies, e.g., dynamical lattice-geometry changes allow tuning a graphene lattice into a boron-nitride lattice. However, a fast change of the lattice geometry remains intrinsically difficult. Here we introduce a multifrequency lattice for fast and flexible lattice-geometry control and demonstrate it for a three-beam lattice, realizing the full dynamical tunability between honeycomb lattice, boron-nitride lattice, and triangular lattice on the microsecond scale, i.e., fast compared to the relevant energy scales. At the same time, the scheme ensures intrinsically high stability of the lattice geometry. We introduce the concept of a geometry phase as the parameter that fully controls the geometry and observe its signature as a staggered flux in a momentum space lattice. Tuning the geometry phase allows us to dynamically control the sublattice offset in the boron-nitride lattice. We use a fast sweep of the offset to transfer atoms into higher Bloch bands and perform a new type of Bloch band spectroscopy by modulating the sublattice offset. Finally, we generalize the geometry phase concept and the multifrequency lattice to three-dimensional optical lattices and quasiperiodic potentials. This scheme will allow further applications such as novel Floquet and quench protocols to create and probe, e.g., topological properties.

We address the problem of analytic continuation of imaginary-frequency Green's functions, which is crucial in many-body physics, using machine learning based on a multilevel residual neural network. We specifically address potential biases that can be introduced due to the use of artificially created spectral functions that are employed to train the neural network. We also implement an uncertainty estimation of the predicted spectral function, based on Monte Carlo dropout, which allows us to identify frequency regions where the prediction might not be accurate, and we study the effect of noise, in particular also for situations where the noise level during training is different from that in the actual data. Our analysis demonstrates that this method can indeed achieve a high quality of prediction, comparable to or better than the widely used maximum entropy method, but that further improvement is currently limited by the lack of true data that can be used for training. We also benchmark our approach by applying it to the case of ${\mathrm{SrVO}}_3$, where an accurate spectral function has been obtained from dynamical mean-field theory using a solver that works directly on the real frequency axis.

In a disordered environment, the average transmission of a propagating wave falls with increasing disorder. Beyond a crossover, transport is arrested because the wave is trapped in the bulk of the sample with exponentially decaying coupling to the boundaries due to Anderson localization. Here, we report the experimental demonstration of anomalous transport of hybrid particles under localizing disorder in a non-Hermitian setting. We create hybrid polariton-photon states in a one-dimensional copper sample with a comb-shaped periodic microstructure designed for microwave frequencies. Non-Hermiticity arises from multiple loss channels existing in the real experimental sample. Disorder is introduced by deliberate alterations of the periodic microstructure. Direct measurement of wave functions was achieved by a near-field probe. At a particular disorder, we observe the onset of Anderson localization of the hybrid states attested to by the exponential tails of the wave function. However, at stronger disorder and under conditions that support localization, an unexpected enhancement in the transmission was facilitated by an emergent miniband. The transmission was traced to the hopping of the hybrid particle over multiple coexisting localized resonances that exchange energy due to the nonorthogonality. These emergent states are manifested in all configurations under strong disorder, suggesting a novel transport regime. This is verified by measuring the averaged conductance which indicates an anomalous transport regime in the hybrid, non-Hermitian environment under strong disorder. These experimental observations open up new unexplored avenues in the ambit of disorder under non-Hermitian conditions.

A nonvanishing entropy production rate is one of the defining characteristics of any nonequilibrium system, and several techniques exist to determine this quantity directly from experimental data. The short-time inference scheme, derived from the thermodynamic uncertainty relation, is a recent addition to the list of these techniques. Here we apply this scheme to quantify the entropy production rate in a class of microscopic heat engine models called Brownian gyrators. In particular, we consider models with anharmonic confining potentials. In these cases, the dynamical equations are indelibly nonlinear, and the exact dependencies of the entropy production rate on the model parameters are unknown. Our results demonstrate that the short-time inference scheme can efficiently determine these dependencies from a moderate amount of trajectory data. Furthermore, the results show that the nonequilibrium properties of the gyrator model with anharmonic confining potentials are considerably different from its harmonic counterpart; especially in setups leading to a nonequilibrium dynamics and the resulting gyration patterns.