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We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of unitary operators. Hence, it allows for the direct implementation of a broad class of differential equations governing the dynamics of classical and quantum systems. The capabilities of the framework are demonstrated for an example system governed by Euler equations with absorbing boundaries., Comment: 5 pages + 5 supplemental, 4 figures + 1 supplemental

This paper presents the development and implementation of a versatile ad-hoc metropolitan-range Quantum Key Distribution (QKD) network. The approach presented integrates various types of physical channels and QKD protocols, and a mix of trusted and untrusted nodes. Unlike conventional QKD networks that predominantly depend on either fiber-based or free-space optical (FSO) links, the testbed presented amalgamates FSO and fiber-based links, thereby overcoming some inherent limitations. Various network deployment strategies have been considered, including permanent infrastructure and provisional ad-hoc links to eradicate coverage gaps. Furthermore, the ability to rapidly establish a network using portable FSO terminals and to investigate diverse link topologies is demonstrated. The study also showcases the successful establishment of a quantum-secured link to a cloud server.

This article proposes a Variational Quantum Algorithm (VQA) to solve linear and nonlinear thermofluid dynamic transport equations. The hybrid classical-quantum framework is applied to problems governed by the heat, wave, and Burgers' equation in combination with different engineering boundary conditions. Topics covered include the consideration of non-constant material properties and upwind-biased first- and higher-order approximations, widely used in engineering Computational Fluid Dynamics (CFD), by the use of a mask function. The framework is able to convert band matrices arising from Partial Differential Equations (PDEs) discretized on structured grids into quantum gates, thus contributing to the development of a modular library for quantum computing translations of CFD procedures. Verification examples demonstrate high predictive agreement with classical methods. Furthermore, the scalability analysis shows a $\textit{polylog}$ complexity in the number of qubits of the quantum circuits involved. Remaining challenges refer to the implicit construction of upwind schemes.

Continuous-variable (CV) quantum key distribution (QKD) allows for quantum secure communication with the benefit of being close to existing classical coherent communication. In recent years, CV QKD protocols using a discrete number of displaced coherent states have been studied intensively, as the modulation can be directly implemented with real devices with a finite digital resolution. However, the experimental demonstrations until now only calculated key rates in the asymptotic regime. To be used in cryptographic applications, a QKD system has to generate keys with composable security in the finite-size regime. In this paper, we present a CV QKD system using discrete modulation that is especially designed for urban atmospheric channels. For this, we use polarization encoding to cope with the turbulent but non-birefringent atmosphere. This will allow to expand CV QKD networks beyond the existing fiber backbone. In a first laboratory demonstration, we implemented a novel type of security proof allowing to calculate composable finite-size key rates against i.i.d. collective attacks without any Gaussian assumptions. We applied the full QKD protocol including a QRNG, error correction and privacy amplification to extract secret keys. In particular, we studied the impact of frame errors on the actual key generation.

Predicting the dynamics of turbulent fluid flows has long been a central goal of science and engineering. Yet, even with modern computing technology, accurate simulation of all but the simplest turbulent flow-fields remains impossible: the fields are too chaotic and multi-scaled to directly store them in memory and perform time-evolution. An alternative is to treat turbulence $\textit{probabilistically}$, viewing flow properties as random variables distributed according to joint probability density functions (PDFs). Turbulence PDFs are neither chaotic nor multi-scale, but are still challenging to simulate due to their high dimensionality. Here we show how to overcome the dimensionality problem by parameterising turbulence PDFs into an extremely compressed format known as a "tensor network" (TN). The TN paradigm enables simulations on single CPU cores that would otherwise be impractical even with supercomputers: for a $5+1$ dimensional PDF of a chemically reactive turbulent flow, we achieve reductions in memory and computational costs by factors of $\mathcal{O}(10^6)$ and $\mathcal{O}(10^3)$, respectively, compared to standard finite difference algorithms. A future path is opened towards something heretofore regarded as infeasible: directly simulating high-dimensional PDFs of both turbulent flows and other chaotic systems that are useful to describe probabilistically., Comment: Post peer-review version accepted for publication; link to data & code added

We present a Floquet Schrieffer Wolff transform (FSWT) to obtain effective Floquet Hamiltonians and micro-motion operators of periodically driven many-body systems for any non-resonant driving frequency. The FSWT perturbatively eliminates the oscillatory components in the driven Hamiltonian by solving operator-valued Sylvester equations with systematic approximations. It goes beyond various high-frequency expansion methods commonly used in Floquet theory, as we demonstrate with the example of the driven Fermi-Hubbard model. In the limit of high driving frequencies, the FSWT Hamiltonian reduces to the widely used Floquet-Magnus result. We anticipate this method will be useful for designing Rydberg multi-qubit gates, controlling correlated hopping in quantum simulations in optical lattices, and describing multi-orbital and long-range interacting systems driven in-gap., Comment: 20 pages, 9 figures

Despite its ubiquity, many-body dispersion remains poorly understood. Here we investigate the distribution of entanglement in quantum Drude oscillator assemblies, minimal models for dispersion bound systems. We analytically determine a relation between entanglement and energy, showing how the entanglement distribution governs dispersive bonding. This suggests that the monogamy of entanglement explains deviations of multipartite dispersive binding energies compared to the commonly used pairwise prediction. We illustrate our findings using examples of a trimer and extended crystal lattices.

A mathematical model is developed, to jointly analyze elastic and inelastic scattering data of fluctuating membranes within a single theoretical framework. The model builds on a non-homogeneously clipped time-dependent Gaussian random field. This specific approach provides one with general analytical expressions for the intermediate scattering function, for any number of sublayers in the membrane and arbitrary contrasts. The model is illustrated with the analysis of small-angle x-ray and neutron scattering as well as with neutron spin-echo data measured on unilamellar vesicles prepared from phospholipids extracted from porcine brain tissues. The parameters fitted on the entire dataset are the lengths of the chain and head of the molecules that make up the membrane, the amplitude and lateral sizes of the bending deformations, the thickness fluctuation, and a single parameter characterizing the dynamics.

We present an iterative generalisation of the quantum subspace expansion algorithm used with a Krylov basis. The iterative construction connects a sequence of subspaces via their lowest energy states. Diagonalising a Hamiltonian in a given Krylov subspace requires the same quantum resources in both the single step and sequential cases. We propose a variance-based criterion for determining a good iterative sequence and provide numerical evidence that these good sequences display improved numerical stability over a single step in the presence of finite sampling noise. Implementing the generalisation requires additional classical processing with a polynomial overhead in the subspace dimension. By exchanging quantum circuit depth for additional measurements the quantum subspace expansion algorithm appears to be an approach suited to near term or early error-corrected quantum hardware. Our work suggests that the numerical instability limiting the accuracy of this approach can be substantially alleviated beyond the current state of the art., Comment: 13+7 pages, 6 figures, updated references

Computing vacuum states of lattice gauge theories (LGTs) containing fermionic degrees of freedom can present significant challenges for classical computation using Monte-Carlo methods. Quantum algorithms may offer a pathway towards more scalable computation of groundstate properties of LGTs. However, a comprehensive understanding of the quantum computational resources required for such a problem is thus far lacking. In this work, we investigate using the quantum subspace expansion (QSE) algorithm to compute the groundstate of the Schwinger model, an archetypal LGT describing quantum electrodynamics in one spatial dimension. We perform numerical simulations, including the effect of measurement noise, to extrapolate the resources required for the QSE algorithm to achieve a desired accuracy for a range of system sizes. Using this, we present a full analysis of the resources required to compute LGT vacuum states using a quantum algorithm using qubitization within a fault tolerant framework. We develop of a novel method for performing qubitization of a LGT Hamiltonian based on a 'linear combination of unitaries' (LCU) approach. The cost of the corresponding block encoding operation scales as $\tilde{O}(N)$ with system size $N$. Including the corresponding prefactors, our method reduces the gate cost by multiple orders of magnitude when compared to previous LCU methods for the QSE algorithm, which scales as $\tilde{O}(N^2)$ when applied to the Schwinger model. While the qubit and single circuit T-gate cost resulting from our resource analysis is appealing to early fault-tolerant implementation, we find that the number of shots required to avoid numerical instability within the QSE procedure must be significantly reduced in order to improve the feasibility of the methodology we consider and discuss how this might be achieved., Comment: 19+19 pages, 7+4 figures, 0+5 tables. Fix typos, update format

The paper presents a variational quantum algorithm to solve initial-boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum hardware that is well suited for quantum computers of the current noisy intermediate-scale quantum era. The partial differential equation is initially translated into an optimal control problem with a modular control-to-state operator (ansatz). The objective function and its derivatives required by the optimizer can efficiently be evaluated on a quantum computer by measuring an ancilla qubit, while the optimization procedure employs classical hardware. The focal aspect of the study is the treatment of boundary conditions, which is tailored to the properties of the quantum hardware using a correction technique. For this purpose, the boundary conditions and the discretized terms of the partial differential equation are decomposed into a sequence of unitary operations and subsequently compiled into quantum gates. The accuracy and gate complexity of the approach are assessed for second-order partial differential equations by classically emulating the quantum hardware. The examples include steady and unsteady diffusive transport equations for a scalar property in combination with various Dirichlet, Neumann, or Robin conditions. The results of this flexible approach display a robust behavior and a strong predictive accuracy in combination with a remarkable polylog complexity scaling in the number of qubits of the involved quantum circuits. Remaining challenges refer to adaptive ansatz strategies that speed up the optimization procedure.

We study cavity-mediated interactions that are generated in a two-dimensional two-band Hubbard model coupled to an optical cavity, when it is driven in-gap by a strong laser. Starting from a Floquet description of the driven system, we derive effective low-energy Hamiltonians by projecting out the high-energy degrees of freedom and treating intrinsic interactions on a mean field level. We then investigate how the emergence of high-energy Frenkel excitons from the electronic interband coupling, which form near the upper electronic band, affects the interactions as well as the laser-induced Floquet renormalization of the electronic band structure. Cavity-mediated interactions are enhanced strongly when the light couples to an excitonic transition. Additionally, the interaction as well as the Floquet renormalization are strongly broadened in reciprocal space, which could further boost the impact of cavity-mediated interactions on the driven-dissipative steady state., Comment: 20 pages, 8 figures

Signal processing based on stimulated Brillouin scattering (SBS) is limited by the narrow linewidth of the optoacoustic response, which confines many Brillouin applications to continuous wave signals or optical pulses longer than several nanoseconds. In this work, we experimentally demonstrate Brillouin interactions at the 150 ps time scale and a delay for a record 15 ns which corresponds to a delay of 100 pulse widths. This breakthrough experimental result was enabled by the high local gain of the chalcogenide waveguides as the optoacoustic interaction length reduces with pulse width. We successfully transfer 150ps-long pulses to traveling acoustic waves within a Brillouin-based memory setup. The information encoded in the optical pulses is stored for 15 ns in the acoustic field. We show the retrieval of eight amplitude levels, multiple consecutive pulses and low distortion in pulse shape. The extension of Brillouin-based storage to the ultra-short pulse regime is an important step for the realisation of practical Brillouin-based delay lines and other optical processing applications., Comment: 6 pages, 6 figures

In this manuscript we describe the investigation of the SARS-CoV2 membrane fusion timescale by means of small-angle neutron scattering (SANS) using hydrogen/deuterium contrast variation. After the successful production of virus-like vesicles and human-host-cell-like vesicles we were able to follow the fusion of the respective vesicles in real-time. This was done using deuterated and protonated phospholipids in the vesicles in a neutron-contrast matched solvent. The vesicles were identical apart from either the presence or absence of the SARS-CoV2 spike protein. The human-host-cell-like vesicles were carrying an ACE2 receptor protein in all cases. In case of the absence of the spike protein a fusion over several hours was observed in agreement with literature, with a time constant of 4.5 h. In comparison, there was not time-evolution, but immediate fusion of the vesicles when the spike protein was present. Those two figures, fusion over several hours and fusion below 10 s corresponding to the absence or presence of the spike protein allow an upper-limit estimate for the fusion times of virus-like vesicles with the SARS-CoV2 spike protein of 10 s. This very fast fusion, when compared to the case without spike protein it is a factor of 2500, can also help to explain why infection with SARS-CoV2 can be so effective and fast. Studying spike protein variants using our method may explain differences in transmissibility between SARS-CoV2 strains. In addition, the model developed here can potentially be applied to any enveloped virus., Comment: 15 pages, 7 figures, 2 tables

We introduce a widely applicable tensor network-based framework for developing reduced order models describing wall-bounded fluid flows. As a paradigmatic example, we consider the incompressible Navier-Stokes equations and the lid-driven cavity in two spatial dimensions. We benchmark our solution against published reference data for low Reynolds numbers and find excellent agreement. In addition, we investigate the short-time dynamics of the flow at high Reynolds numbers for the lid driven and doubly-driven cavities. We represent the velocity components by matrix product states and find that the bond dimension grows logarithmically with simulation time. The tensor network algorithm requires at most a few percent of the number of variables parameterizing the solution obtained by direct numerical simulation, and approximately improves the runtime by an order of magnitude compared to direct numerical simulation on similar hardware. Our approach is readily transferable to other flows, and paves the way towards quantum computational fluid dynamics in complex geometries., Comment: 12 pages, 6 figures

With rapid progress in control and manipulation of ultracold magnetic atoms and dipolar molecules, the quantum simulation of lattice models with strongly interacting dipole-dipole interactions (DDI) and high densities is now within experimental reach. This rapid development raises the issue about the validity of quantum simulation in such regimes. In this study, we address this question by performing a full quantitative comparison between the continuum description of a one-dimensional gas of dipolar bosons in an optical lattice, and the single-band Bose-Hubbard lattice model that it quantum simulates. By comparing energies and density distributions, and by calculating direct overlaps between the continuum and lattice many-body wavefunctions, we demonstrate that in regimes of strong DDI and high densities the continuum system fails to recreate the desired lattice model. Two-band Hubbard models become necessary to reduce the discrepancy observed between continuum and lattice descriptions, but appreciable deviations in the density profile still remain. Our study elucidates the role of strong DDI in generating physics beyond lowest-band descriptions and should offer a guideline for the calibration of near-term dipolar quantum simulators., Comment: Fixed typos, added more references

Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required hardware, but also in identifying the most promising application areas and developing the corresponding quantum algorithms. The availability of intermediate-scale noisy quantum computers is now propelling the developments of novel algorithms, with applications across a variety of domains, including in aeroscience. Variational quantum algorithms are particularly promising since they are comparatively noise tolerant and aim to achieve a quantum advantage with only a few hundred qubits. Furthermore, they are applicable to a wide range of optimization problems arising throughout the natural sciences and industry. To demonstrate the possibilities for the aeroscience community, we give a perspective on how variational quantum algorithms can be utilized in computational fluid dynamics. We discuss how classical problems are translated into quantum algorithms and their logarithmic scaling with problem size. As an explicit example we apply this method to Burgers' Equation in one spatial dimension. We argue that a quantum advantage over classical computing methods could be achieved by the end of this decade if quantum hardware progresses as currently envisaged and emphasize the importance of joining up development of quantum algorithms with application-specific expertise to achieve real-world impact., Comment: 22 pages, 5 figures, submitted to AIAA Virtual collection "Short Surveys of Quantum Information Science and Technology for Aerospace Research"

A large class of optimisation problems can be mapped to the Ising model where all details are encoded in the coupling of spins. The task of the original mathematical optimisation is then equivalent to finding the ground state of the corresponding spin system which can be achieved via quantum annealing relying on the adiabatic theorem. Some of the inherent disadvantages of this procedure can be alleviated or resolved using a stochastic approach, and by coupling to the external environment. We show that careful engineering of the system-bath coupling at an individual spin level can further improve annealing.

Theoretical research into many-body quantum systems has mostly focused on regular structures which have a small, simple unit cell and where a vanishingly small number of pairs of the constituents directly interact. Motivated by advances in control over the pairwise interactions in many-body simulators, we determine the fate of spin systems on more general, arbitrary graphs. Placing the minimum possible constraints on the underlying graph, we prove how, with certainty in the thermodynamic limit, such systems behave like a single collective spin. We thus understand the emergence of complex many-body physics as dependent on `exceptional', geometrically constrained structures such as the low-dimensional, regular ones found in nature. Within the space of dense graphs we identify hitherto unknown exceptions via their inhomogeneity and observe how complexity is heralded in these systems by entanglement and highly non-uniform correlation functions. Our work paves the way for the discovery and exploitation of a whole class of geometries which can host uniquely complex phases of matter., Comment: Published Version

We propose an experiment with a driven quantum gas coupled to a dissipative optical cavity that realizes a novel kind of far-from-equilibrium phase transition between spatial and temporal order. The control parameter of the transition is the detuning between the drive frequency and the cavity resonance. For negative detunings, the system features a spatially ordered phase, while positive detunings lead to a phase with both spatial order and persistent oscillations, which we call dissipative spatio-temporal lattice. We give numerical and analytical evidence for this superradiant phase transition and show that the spatio-temporal lattice originates from cavity dissipation. In both regimes the atoms are subject to an accelerated transport, either via a uniform acceleration or via abrupt transitions to higher momentum states. Our work provides perspectives for temporal phases of matter that are not possible at equilibrium., Comment: 5+6 pages, 4+3 figures

Recently, several studies involving open quantum systems which possess a strong symmetry have observed that every individual trajectory in the Monte Carlo unravelling of the master equation will dynamically select a specific symmetry sector to freeze into in the long-time limit. This phenomenon has been termed dissipative freezing, and in this paper we argue, by presenting several simple mathematical perspectives on the problem, that it is a general consequence of the presence of a strong symmetry in an open system with only a few exceptions. Using a number of example systems we illustrate these arguments, uncovering an explicit relationship between the spectral properties of the Liouvillian in off-diagonal symmetry sectors and the time it takes for freezing to occur. In the limiting case that eigenmodes with purely imaginary eigenvalues are manifest in these sectors, freezing fails to occur. Such modes indicate the preservation of information and coherences between symmetry sectors of the system and can lead to phenomena such as non-stationarity and synchronisation. The absence of freezing at the level of a single quantum trajectory provides a simple, computationally efficient way of identifying these traceless modes., Comment: Version 4 (mostly grammatical changes from previous version): 21 Pages, 4 Figures, 1 Table

Simulating quantum systems is believed to be one of the first applications for which quantum computers may demonstrate a useful advantage. For many problems in physics, we are interested in studying the evolution of the electron-phonon Hamiltonian, for which efficient digital quantum computing schemes exist. Yet to date, no accurate simulation of this system has been produced on real quantum hardware. In this work, we consider the absolute resource cost for gate-based quantum simulation of small electron-phonon systems as dictated by the number of Trotter steps and bosonic energy levels necessary for the convergence of dynamics. We then apply these findings to perform experiments on IBM quantum hardware for both weak and strong electron-phonon coupling. Despite significant device noise, through the use of approximate circuit recompilation we obtain electron-phonon dynamics on current quantum computers comparable to exact diagonalisation. Our results represent a significant step in utilising near term quantum computers for simulation of quantum dynamics and highlight the novelty of approximate circuit recompilation as a tool for reducing noise., Comment: 19 pages, 8 figures. Published version with new Appendix F

Multigrid has become a popular method for solving some of the most challenging real-world computational problems, such as computational fluid dynamics (CFD). The reason for this is the very good scaling properties of multigrid, which is often linear, or close to linear, with respect to problem size. In this paper a method is presented, which can be used to implement a quantum version of the multigrid algorithm. The method relies upon a quantum state that is maintained in a equal superposition throughout the calculation, and where information is encoded digitally in the qubits in a way more similar to a classical computer. This differs from many existing quantum algorithms where information is encoded in the amplitudes of the quantum states in the superposition. At the core of the method is an algorithm for sharing information between the states in the superposition. An exponential speedup is provided for classes of problems where the solution vector can be compressed efficiently, and where a quantum compiler can reduce the quantum circuit depth efficiently.

Recent experimental progress in magnetic atoms and polar molecules has created the prospect of simulating dipolar Hubbard models with off-site interactions. When applied to real-space cylindrical optical lattices, these anisotropic dipole-dipole interactions acquire a tunable spatially-dependent component while they remain translationally-invariant in the axial direction, creating a sublattice structure in the azimuthal direction. We numerically study how the coexistence of these classes of interactions affects the ground state of hardcore dipolar bosons at half-filling in a finite-size cylindrical optical lattice with octagonal rings. When these two interaction classes cooperate, we find a solid state where the density order is determined by the azimuthal sublattice structure and builds smoothly as the interaction strength increases. For dipole polarisations where the axial interactions are sufficiently repulsive, the repulsion competes with the sublattice structure, significantly increasing entanglement and creating two distinct ordered density patterns. The spatially-varying interactions cause the emergence of these ordered states in small lattices as a function of interaction strength to be staggered according to the azimuthal sublattices., Comment: 14 pages, 10 figures

Variational quantum algorithms (VQAs) are increasingly being applied in simulations of strongly-bound (covalently bonded) systems using full molecular orbital basis representations. The application of quantum computers to the weakly-bound intermolecular and non-covalently bonded regime however has remained largely unexplored. In this work, we develop a coarse-grained representation of the electronic response that is ideally suited for determining the ground state of weakly interacting molecules using a VQA. We require qubit numbers that grow linearly with the number of molecules and derive scaling behaviour for the number of circuits and measurements required, which compare favourably to traditional variational quantum eigensolver methods. We demonstrate our method on IBM superconducting quantum processors and show its capability to resolve the dispersion energy as a function of separation for a pair of non-polar molecules - thereby establishing a means by which quantum computers can model Van der Waals interactions directly from zero-point quantum fluctuations. Within this coarse-grained approximation, we conclude that current-generation quantum hardware is capable of probing energies in this weakly bound but nevertheless chemically ubiquitous and biologically important regime. Finally, we perform experiments on simulated and real quantum computers for systems of three, four and five oscillators as well as oscillators with anharmonic onsite binding potentials; the consequences of the latter are unexamined in large systems using classical computational methods but can be incorporated here with low computational overhead., Comment: 28 pages, 12 figures. Published version. Additional experimental results

We study a one-dimensional array of bosons with infinite-range interactions mediated by a laser-driven dissipative optical cavity. The cavity-mediated infinite-range interactions open up a new pathway to fermionization, hitherto only known for dipolar bosons due to their long-range interactions. In parameter ranges attainable in state-of-the-art experiments, we systematically compare observables for bosons and fermions with infinite-range interactions. At large enough laser pump power, many observables, including density distributions in real and momentum space, correlation functions, eigenvalues of the one-body density matrix, and superradiance order parameter, become identical for bosons and fermions. We map out the emergence of this cavity-induced fermionization as a function of pump power and contact interactions. We discover that cavity-mediated interactions can compensate a reduction by several orders of magnitude in the strength of the contact interactions needed to trigger fermionization., Comment: main text: 7 pages, 3 figures - supplement: 7 pages, 4 figures

Converting neutron scattering data to real-space time-dependent structures can only be achieved through suitable models, which is particularly challenging for geometrically disordered structures. We address this problem by introducing time-dependent clipped Gaussian field models. General expressions are derived for all space- and time-correlation functions relevant to coherent inelastic neutron scattering, for multiphase systems and arbitrary scattering contrasts. Various dynamic models are introduced that enable one to add time-dependence to any given spatial statistics, as captured e.g. by small-angle scattering. In a first approach, the Gaussian field is decomposed into localised waves that are allowed to fluctuate in time or to move, either ballistically or diffusively. In a second approach, a dispersion relation is used to make the spectral components of the field time-dependent. The various models lead to qualitatively different dynamics, which can be discriminated by neutron scattering. The methods of the paper are illustrated with oil/water microemulsion studied by small-angle scattering and neutron spin-echo. All available data - in both film and bulk contrasts, over the entire range of $q$ and $\tau$- are analyzed jointly with a single model. The analysis points to static large-scale structure of the oil and water domains, while the interfaces are subject to thermal fluctuations. The fluctuations have an amplitude around 6 nm and contribute to 30 % of the total interface area., Comment: The following article has been accepted by Journal of Chemical Physics. After it is published, it will be found at https://aip.scitation.org/journal/jcp/

Understanding turbulence is the key to our comprehension of many natural and technological flow processes. At the heart of this phenomenon lies its intricate multi-scale nature, describing the coupling between different-sized eddies in space and time. Here we introduce a new paradigm for analyzing the structure of turbulent flows by quantifying correlations between different length scales using methods inspired from quantum many-body physics. We present results for interscale correlations of two paradigmatic flow examples, and use these insights along with tensor network theory to design a structure-resolving algorithm for simulating turbulent flows. With this algorithm, we find that the incompressible Navier-Stokes equations can be accurately solved within a computational space reduced by over an order of magnitude compared to direct numerical simulation. Our quantum-inspired approach provides a pathway towards conducting computational fluid dynamics on quantum computers., Comment: Newest and final version of our article

We show that low-lying excitations of a 2D BCS superconductor are significantly altered when coupled to an externally driven cavity, which induces controllable long-range attractive interactions between the electrons. We find that they combine non-linearly with intrinsic local interactions to increase the Bogoliubov quasiparticle excitation energies, thus enlarging the superconducting gap. The long-range nature of the driven-cavity-induced attraction qualitatively changes the collective excitations of the superconductor. Specifically, they lead to the appearance of additional collective excitations of the excitonic modes. Furthermore, the Higgs mode is pushed into the gap and now lies below the Bogoliubov quasiparticle continuum such that it cannot decay into quasiparticles. This way, the Higgs mode's lifetime is greatly enhanced.

Many complex systems can spontaneously oscillate under non-periodic forcing. Such self-oscillators are commonplace in biological and technological assemblies where temporal periodicity is needed, such as the beating of a human heart or the vibration of a cello string. While self-oscillation is well understood in classical non-linear systems and their quantized counterparts, the spontaneous emergence of periodicity in quantum systems without a semi-classical limit is more elusive. Here, we show that this behavior can emerge within the repeated-interaction description of open quantum systems. Specifically, we consider a many-body quantum system that undergoes dissipation due to sequential coupling with auxiliary systems at random times. We develop dynamical symmetry conditions that guarantee an oscillatory long-time state in this setting. Our rigorous results are illustrated with specific spin models, which could be implemented in trapped-ion quantum simulators., Comment: 5+5 pages; 3 figures

The resurgence of self-supervised learning, whereby a deep learning model generates its own supervisory signal from the data, promises a scalable way to tackle the dramatically increasing size of real-world data sets without human annotation. However, the staggering computational complexity of these methods is such that for state-of-the-art performance, classical hardware requirements represent a significant bottleneck to further progress. Here we take the first steps to understanding whether quantum neural networks could meet the demand for more powerful architectures and test its effectiveness in proof-of-principle hybrid experiments. Interestingly, we observe a numerical advantage for the learning of visual representations using small-scale quantum neural networks over equivalently structured classical networks, even when the quantum circuits are sampled with only 100 shots. Furthermore, we apply our best quantum model to classify unseen images on the ibmq\_paris quantum computer and find that current noisy devices can already achieve equal accuracy to the equivalent classical model on downstream tasks., Comment: 13 pages, 10 figures. Additional results and discussion

Coherent driving has established itself as a powerful tool for guiding a many-body quantum system into a desirable, coherent non-equilibrium state. A thermodynamically large system will, however, almost always saturate to a featureless infinite temperature state under continuous driving and so the optical manipulation of many-body systems is considered feasible only if a transient, prethermal regime exists, where heating is suppressed. Here we show that, counterintuitively, in a broad class of lattices Floquet heating can actually be an advantageous effect. Specifically, we prove that the maximum entropy steady states which form upon driving the ground state of the Hubbard model on unbalanced bi-partite lattices possess uniform off-diagonal long-range order which remains finite even in the thermodynamic limit. This creation of a `hot' condensate can occur on \textit{any} driven unbalanced lattice and provides an understanding of how heating can, at the macroscopic level, expose and alter the order in a quantum system. We discuss implications for recent experiments observing emergent superconductivity in photoexcited materials., Comment: 10 pages, 3 figures

Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been found. We develop such a general theory based on novel necessary and sufficient algebraic criteria for persistently oscillating eigenmodes (limit cycles) of time-independent quantum master equations. We show these eigenmodes must be quantum coherent and give an exact analytical solution for all such dynamics in terms of a dynamical symmetry algebra. Using our theory, we study both stable synchronization and metastable/transient synchronization. We use our theory to fully characterise spontaneous synchronization of autonomous systems. Moreover, we give compact algebraic criteria that may be used to prove absence of synchronization. We demonstrate synchronization in several systems relevant for various fermionic cold atom experiments., Comment: Resubmission to SciPost. 58 pages, 8 figures. Comments are welcome

Under the action of coherent periodic driving a generic quantum system will undergo Floquet heating and continously absorb energy until it reaches a featureless thermal state. The phase-space constraints induced by certain symmetries can, however, prevent this and allow the system to dynamically form robust steady states with off-diagonal long-range order. In this work, we take the Hubbard model on an arbitrary lattice with arbitrary filling and, by simultaneously diagonalising the two possible SU(2) symmetries of the system, we analytically construct the correlated steady states for different symmetry classes of driving. This construction allows us to make verifiable, quantitative predictions about the long-range particle-hole and spin-exchange correlations that these states can possess. In the case when both SU(2) symmetries are preserved in the thermodynamic limit we show how the driving can be used to form a unique condensate which simultaneously hosts particle-hole and spin-wave order., Comment: 9 pages, 5 figures

Single-shot images are the standard readout of experiments with ultracold atoms -- the tarnished looking glass into their many-body physics. The efficient extraction of observables from single-shot images is thus crucial. Here, we demonstrate how artificial neural networks can optimize this extraction. In contrast to standard averaging approaches, machine learning allows both one- and two-particle densities to be accurately obtained from a drastically reduced number of single-shot images. Quantum fluctuations and correlations are directly harnessed to obtain physical observables for bosons in a tilted double-well potential at an unprecedented accuracy. Strikingly, machine learning also enables a reliable extraction of momentum-space observables from real-space single-shot images and vice versa. This obviates the need for a reconfiguration of the experimental setup between in-situ and time-of-flight imaging, thus potentially granting an outstanding reduction in resources., Comment: 7+8 pages, 3+8 figures, software available at http://ultracold.org

The response of a position-sensitive Li-glass scintillator detector being developed for thermal-neutron detection with 6 mm position resolution has been investigated using collimated beams of thermal neutrons. The detector was moved perpendicularly through the neutron beams in 0.5 to 1.0 mm horizontal and vertical steps. Scintillation was detected in an 8 X 8 pixel multi-anode photomultiplier tube on an event-by-event basis. In general, several pixels registered large signals at each neutron-beam location. The number of pixels registering signal above a set threshold was investigated, with the maximization of the single-hit efficiency over the largest possible area of the detector as the primary goal. At a threshold of ~50% of the mean of the full-deposition peak, ~80% of the events were registered in a single pixel, resulting in an effective position resolution of ~5 mm in X and Y. Lower thresholds generally resulted in events demonstrating higher pixel multiplicities, but these events could also be localized with ~5 mm position resolution., Comment: 23 pages, 8 figures

Dynamical symmetries are algebraic constraints on quantum dynamical systems, which are often responsible for persistent temporal periodicity of observables. In this work, we discuss how an extensive set of strictly local dynamical symmetries can exist in an interacting many-body quantum system. These strictly local dynamical symmetries lead to spontaneous breaking of continuous time-translation symmetry, i.e. the formation of extremely robust and persistent oscillations when an infinitesimal time-dependent perturbation is applied to an arbitrary initial (stationary) state. Observables which do not overlap with the local (dynamical) symmetry operators can relax, losing memory of their initial conditions. The remaining observables enter highly robust non-equilibrium limit cycles, signaling the emergence of a non-trivial \emph{quantum many-body attractor}. We provide an explicit recipe for constructing Hamiltonians featuring local dynamical symmetries. As an example, we introduce the XYZ spin-lace model, which is a model of a quasi-1D quantum magnet., Comment: are very welcome

We introduce the concept of a squeezed laser, in which a squeezed cavity mode develops a macroscopic photonic occupation due to stimulated emission. Above the lasing threshold, the emitted light retains both the spectral purity inherent of a laser and the photon correlations characteristic of a photonic mode with squeezed quadratures. Our proposal, which can be implemented in optical setups, relies on the parametric driving of the cavity and dissipative stabilization by a broadband squeezed vacuum. The squeezed laser can find applications that go beyond those of standard lasers thanks to the squeezed character, such as the direct application in Michelson interferometry beyond the standard quantum limit, or its use in atomic metrology., Comment: Additions to second version: effects of intra-cavity losses; symmetry-broken solutions; spectrum of squeezing; operation in a Michelson interferometer

The response of a position-sensitive Li-glass based scintillation detector to focused beams of 2.5 MeV protons and deuterons has been investigated. The beams were scanned across the detector in 0.5 mm horizontal and vertical steps perpendicular to the beams. Scintillation light was registered using an 8 by 8 pixel multi-anode photomultiplier tube. The signal amplitudes were recorded for each pixel on an event-by-event basis. Several pixels generally registered considerable signals at each beam location. The number of pixels above set thresholds were investigated, with the optimization of the single-hit efficiency over the largest possible area as the goal. For both beams, at a threshold of ~50% of the mean of the full-deposition peak, ~80% of the events were registered in a single pixel, resulting in an effective position resolution of ~5 mm in X and Y., Comment: 22 pages, 8 figures, to be submitted to Nucl. Instr. and Meth. in Phys. Res. A

In triangular lattice structures, spatial anisotropy and frustration can lead to rich equilibrium phase diagrams with regions containing complex, highly entangled states of matter. In this work we study the driven two-rung triangular Hubbard model and evolve these states out of equilibrium, observing how the interplay between the driving and the initial state unexpectedly shuts down the particle-hole excitation pathway. This restriction, which symmetry arguments fail to predict, dictates the transient dynamics of the system, causing the available particle-hole degrees of freedom to manifest uniform long-range order. We discuss implications of our results for a recent experiment on photo-induced superconductivity in ${\rm \kappa - (BEDT-TTF)_{2}Cu[N(CN)_{2}]Br}$ molecules., Comment: Main Text: 7 Pages, 4 Figures, Supplementary: 4 Pages, 3 Figures

Spin-charge separation (SCS) is a striking manifestation of strong correlations in low-dimensional quantum systems, whereby a fermion splits into separate spin and charge excitations that travel at different speeds. Here, we demonstrate that periodic driving enables control over SCS in a Hubbard system near half-filling. In one dimension, we predict analytically an exotic regime where charge travels slower than spin and can even become 'frozen', in agreement with numerical calculations. In two dimensions, the driving slows both charge and spin, and leads to complex interferences between single-particle and pair-hopping processes., Comment: arXiv admin note: text overlap with arXiv:2002.02312

We discuss the emergence of non-stationarity in open quantum many-body systems. This leads us to the definition of dissipative time crystals which display experimentally observable, persistent, time-periodic oscillations induced by noisy contact with an environment. We use the Loschmidt echo and local observables to indicate the presence of a finite sized dissipative time crystal. Starting from the closed Hubbard model we then provide examples of dissipation mechanisms that yield experimentally observable quantum periodic dynamics and allow analysis of the emergence of finite sized dissipative time crystals. For a disordered Hubbard model including two-particle loss and gain we find a dark Hamiltonian driving oscillations between GHZ states in the long-time limit. Finally, we discuss how the presented examples could be experimentally realized., Comment: 31 pages, 5 figures. Accepted in NJP: Focus on Time Crystals. Added previously omitted relevant references

We use the Bethe Ansatz technique to study dissipative systems experiencing loss. The method allows us to exactly calculate the Liouvillian spectrum. This opens the possibility of analytically calculating the dynamics of a wide range of experimentally relevant models including cold atoms subjected to one and two body losses, coupled cavity arrays with bosons escaping the cavity, and cavity quantum electrodynamics. As an example of our approach we study the relaxation properties in a boundary driven XXZ spin chain. We exactly calculate the Liouvillian gap and find different relaxation rates with a novel type of dynamical dissipative phase transition. This physically translates into the formation of a stable domain wall in the easy-axis regime despite the presence of loss. Such analytic results have previously been inaccessible for systems of this type., Comment: 11 pages, 4 figures

The light-matter interaction can be utilized to qualitatively alter physical properties of materials. Recent theoretical and experimental studies have explored this possibility of controlling matter by light based on driving many-body systems via strong classical electromagnetic radiation, leading to a time-dependent Hamiltonian for electronic or lattice degrees of freedom. To avoid inevitable heating, pump-probe setups with ultrashort laser pulses have so far been used to study transient light-induced modifications in materials. Here, we pursue yet another direction of controlling quantum matter by modifying quantum fluctuations of its electromagnetic environment. In contrast to earlier proposals on light-enhanced electron-electron interactions, we consider a dipolar quantum many-body system embedded in a cavity composed of metal mirrors, and formulate a theoretical framework to manipulate its equilibrium properties on the basis of quantum light-matter interaction. We analyze hybridization of different types of the fundamental excitations, including dipolar phonons, cavity photons, and plasmons in metal mirrors, arising from the cavity confinement in the regime of strong light-matter interaction. This hybridization qualitatively alters the nature of the collective excitations and can be used to selectively control energy-level structures in a wide range of platforms. Most notably, in quantum paraelectrics, we show that the cavity-induced softening of infrared optical phonons enhances the ferroelectric phase in comparison with the bulk materials. Our findings suggest an intriguing possibility of inducing a superradiant-type transition via the light-matter coupling without external pumping. We also discuss possible applications of the cavity-induced modifications in collective excitations to molecular materials and excitonic devices., Comment: 30 pages, 14 figures, to appear in PRX