We discuss a microswimmer model made of three spheres actuated by an internal active time-periodic force, tied by an elastic potential, and submitted to hydrodynamic interactions with thermal noise. The dynamical approach we use, replacing the more common kinematic one, shows the instability of the original model and the need of a confining potential to prevent the evaporation of the swimmer. We investigate the effect of the main parameters of the model, such as the frequency and phase difference of the periodic active force, the stiffness of the confining potential, the length of the swimmer and the temperature and viscosity of the fluid. Our observables of interest are the averages of the swim velocity, the energy consumption rate, the diffusion coefficient, and the swimming precision, which is limited by the energy consumption through the celebrated thermodynamic uncertainty relations. An optimum for velocity and precision is found for an intermediate frequency. Reducing the potential stiffness, the viscosity, or the length is also beneficial for the swimming performance, but these parameters are limited by the consistency of the model. Analytical approximation for many of the relevant observables is obtained for small deformations of the swimmer. We also discuss the efficiency of the swimmer in terms of its maximum precision and of the hydrodynamic, or Lighthill, criterion, and how they are connected.

We study the interplay between the anisotropy of the dipole-dipole interaction and confinement in a curved geometry by means of the extended Gross-Pitaevskii equation, which allows us to characterize the ground state of a dipolar Bose gas under the confinement of a bubble trapping potential. We do so in terms of the scattering length $a$ and the number of particles. We observe the emergence of a wide variety of dipolar solids, consisting on arrangements of different number of droplets along a ring over the equator of the spherical shell confinement. We also show that the transition between the different phases of the system can be engineered by varying $a$, the number of particles or the radius of the trap, parameters, which can be experimentally tuned. Finally, we show the importance of working in microgravity conditions as gravity unstabilizes the observed dipolar solids.

We design, fabricate, and test a double-gap bicone magnetorheological (MR) device to measure steady shear rheological properties of MR fluids under saturating magnetic fields (i.e., large enough to saturate the MR fluids). The device is optimized using finite element method and computational fluid dynamics simulations so that homogeneous, saturating field strengths are reached while keeping a constant shear rate within the main shearing gaps. Experiments demonstrate that the flow curves in the saturation regime can be fitted to a viscoplastic Casson model in good agreement with MR fluids under much lower (nonsaturating) fields. Moreover, yield stress data follow a linear dependence on volume fraction at low particle loadings, in agreement with existing theoretical models.

We show that a single nonlinear defect can thermalize an initial excitation towards a Rayleigh-Jeans (RJ) state in complex multimoded systems. The thermalization can be hindered by disorder-induced localization phenomena, which drive the system into a metastable RJ state. It can differ dramatically from the thermal RJ and it involves only a (quasi)isolated set of prethermal modes whose density can be predicted using a renormalization group theory. Importantly, we establish a connection between the modal relaxation rates that dictate the dynamics towards (quasi)equilibrium and the Thouless conductance. This connection allows us to derive the whole modal relaxation rate distribution. Our results are relevant to photonics, optomechanics, and cold atoms.

A quasi-one-dimensional Bose-Einstein condensate loaded into a quasi-periodic potential created by two sublattices of comparable amplitudes and incommensurate periods is considered. Although the conventional tight-binding approximation is not applicable in this setting, the description can still be reduced to a discrete model that accounts for the modes below the mobility edge. In the respective discrete lattice, where no linear hopping exists, solutions and their dynamics are governed solely by nonlinear interactions. Families of nonlinear modes, including those with no linear limit, are described with a special focus on dimers, which correspond to breather solutions of the Gross-Pitaevskii equation with a quasi-periodic potential. The breathers are found to be stable for negative scattering lengths. Localization and stable propagation of breathers are also observed for positive scattering lengths at relatively weak and moderate nonlinearities.

Protein folding processes are a vital aspect of molecular biology that is hard to simulate with conventional computers. Quantum algorithms have been proven superior for certain problems and may help tackle this complex life science challenge. We analyze the resource requirements for simulating simplified yet computationally challenging protein folding models on a quantum computer, assessing the feasibility of these existing approaches in the current and near-future technological landscape. We calculate the minimum number of qubits, interactions, and two-qubit gates necessary to build a heuristic quantum algorithm with the specific information of a folding problem. Particularly, we focus on the resources needed to build quantum operations based on the Hamiltonian linked to the protein folding models for a given amino acid count. Such operations are a fundamental component of these quantum algorithms, guiding the evolution of the quantum state for efficient computations. Specifically, we study coarse-grained folding models on the lattice and the fixed backbone side-chain conformation model and assess their compatibility with the constraints of existing quantum hardware given different bit encodings. We conclude that the number of qubits required falls within current technological capabilities. However, the limiting factor is the high number of interactions in the Hamiltonian, resulting in a quantum gate count unavailable today.

The analysis of noisy quantum states prepared on current quantum computers is getting beyond the capabilities of classical computing. Quantum neural networks based on parametrized quantum circuits, measurements and feed-forward can process large amounts of quantum data to reduce measurement and computational costs of detecting nonlocal quantum correlations. The tolerance of errors due to decoherence and gate infidelities is a key requirement for the application of quantum neural networks on near-term quantum computers. Here we construct quantum convolutional neural networks (QCNNs) that can, in the presence of incoherent errors, recognize different symmetry-protected topological phases of generalized cluster-Ising Hamiltonians from one another as well as from topologically trivial phases. Using matrix product state simulations, we show that the QCNN output is robust against symmetry-breaking errors below a threshold error probability and against symmetry-preserving errors provided the error channel is invertible. This is in contrast to string order parameters and the output of previously designed QCNNs, which vanish in the presence of any symmetry-breaking errors. To facilitate the implementation of the QCNNs on near-term quantum computers, the QCNN circuits can be shortened from logarithmic to constant depth in system size by performing a large part of the computation in classical postprocessing. These constant-depth QCNNs reduce sample complexity exponentially with system size in comparison to the direct sampling using local Pauli measurements.

Besides the exactly solvable spin-1/2 Kitaev model, higher spin-$S$ ones, not exactly solvable, are promising playgrounds for researches on the quantum spin liquid as well. One of the main interests in higher spin-$S$ cases is the interplay between the Kitaev spin liquid (KSL) and spin nematics. We probe this interplay in a spin-1 model on the honeycomb lattice with competing bilinear-biquadratic and Kitaev interactions. Utilizing the 2D infinite projected entangled-pair state (iPEPS), we map out the phase diagram for the ferro-biquadratic interaction. In the phase diagram, we discover the direct phase transitions between the KSL phases and ferro-quadrupolar ordered spin nematic phase, which we call the FQ phase. It has been revealed that the ferro KSL exhibits robustness against perturbations from ferro-quadrupolar interactions. Also, the FQ phase is extended to the parameter region near the antiferro-Kitaev limit.

The wave nature of matter is a cornerstone of modern physics and has been demonstrated for a wide range of fundamental and composite particles. While diffraction at nanomechanical masks is usually regarded to be independent of internal atomic or molecular states, the particles' polarizabilities and dipole moments lead to dispersive interactions with the grating surface. In prior experiments, such forces largely prevented coherent diffraction of polar molecules as they induce dephasing of the matter wave in the presence of randomly distributed charges inside the grating. Here, we show that surface milling using neon ions facilitates the fabrication of lowly charged nanomasks in gold-capped silicon nitride membranes. This allows us to observe diffraction of polar molecules with over four times larger electric dipole moment than in previous experiments, opening a path towards distinction of structural conformers in matter-wave experiments.

We envisage many-body systems described by quantum spin-chain Hamiltonians featuring a trivial separable eigenstate. For generic Hamiltonians, such a state represents a quantum scar. We show that, typically, a macroscopically entangled state naturally grows after a single projective measurement of just one spin in the quantum scar. Moreover, we identify a condition under which what is growing is a “Schrödinger's cat state.” Our analysis does not reveal any particular requirement for the entangled state to develop, provided that the quantum scar does not minimize/maximize a local conservation law. We study two explicit examples: systems described by generic Hamiltonians where spins interact in pairs, and models that exhibit a $\text{U}\left(1\right)$ hidden symmetry. The latter can be reinterpreted as a two-leg ladder in which the interactions along the legs are controlled by the local state on the other leg through transistorlike building blocks.

We present the quantum simulation of the frustrated quantum spin-$\frac{1}{2}$ antiferromagnetic Heisenberg spin chain with competing nearest-neighbor $\left(J_1\right)$ and next-nearest-neighbor $\left(J_2\right)$ exchange interactions in the real superconducting quantum computer with qubits ranging up to 100. In particular, we implement the Hamiltonian with the next-nearest neighbor exchange interaction in conjunction with the nearest-neighbor interaction on IBM's superconducting quantum computer and carry out the time evolution of the spin chain by employing the first-order Trotterization. Furthermore, our implementation of the second-order Trotterization for the isotropic Heisenberg spin chain, involving only nearest-neighbor exchange interaction, enables precise measurement of the expectation values of staggered magnetization observable across a range of up to 100 qubits. Notably, in both cases, our approach results in a constant circuit depth in each Trotter step, independent of the number of qubits. Our demonstration of the accurate measurement of expectation values for the large-scale quantum system using superconducting quantum computers designates the quantum utility of these devices for investigating various properties of many-body quantum systems. This will be a stepping stone to achieving the quantum advantage over classical ones in simulating quantum systems before the fault tolerance quantum era.

Open quantum systems with nearly degenerate energy levels have been shown to exhibit long-lived metastable states in the approach to equilibrium, even when modelled with certain Lindblad-form quantum master equations. This is a result of dramatic separation of timescales due to differences between Liouvillian eigenvalues. These metastable states often have nonzero coherences that die off only in the long-time limit once the system reaches thermal equilibrium. We examine two distinct situations that give rise to this effect: one in which dissipative dynamics couple together states only within a nearly degenerate subspace, and one in which they give rise to jumps over finite-energy splittings, between separate nearly degenerate subspaces. We find, in each case, that a change of basis can often lead to a representation that more naturally captures the impact of the system-bath interaction than does the energy eigenbasis, revealing that separate timescales are associated with separate processes (e.g., decoherence into a nonenergy eigenbasis, decay of population correlations to the initial state). This approach is paired with the inspection of quantum trajectories, which further provide intuition as to how open system evolution is characterized when coherent oscillations, thermal relaxation, and decoherence all occur simultaneously.

Quantum computation is expected to accelerate certain computational tasks over classical counterparts. Its most primitive advantage is its ability to sample from classically intractable probability distributions. A promising approach to make use of this fact is the so-called quantum-enhanced Markov-chain Monte Carlo (qe-MCMC) method [D. Layden et al., Nature (London) 619, 282 (2023)], which uses outputs from quantum circuits as the proposal distributions. In this paper, we propose the use of a quantum alternating operator ansatz (QAOA) for qe-MCMC and provide a strategy to optimize its parameters to improve convergence speed while keeping its depth shallow. The proposed QAOA-type circuit is designed to satisfy the specific constraint which qe-MCMC requires with arbitrary parameters. Through our extensive numerical analysis, we find a correlation in a certain parameter range between an experimentally measurable value, acceptance rate of MCMC, and the spectral gap of the MCMC transition matrix, which determines the convergence speed. This allows us to optimize the parameter in the QAOA circuit and achieve quadratic speedup in convergence. Since MCMC is used in various areas such as statistical physics and machine learning, this paper represents an important step toward realizing practical quantum advantage with currently available quantum computers through qe-MCMC.

Scaling the size of assembled neutral-atom arrays trapped in optical lattices or optical tweezers is an enabling step for a number of applications ranging from quantum simulations to quantum metrology. However, preparation times increase with system size and constitute a severe bottleneck in the bottom-up assembly of large ordered arrays from stochastically loaded optical traps. Here we demonstrate a method to circumvent this bottleneck by recycling atoms from one experimental run to the next, while continuously reloading and adding atoms to the array. Using this approach, we achieve densely packed arrays with more than 1000 atoms stored in an optical lattice, continuously refilled with a 3.5 s cycle time and about 130 atoms reloaded during each cycle. Furthermore, we show that we can continuously maintain such large arrays by simply reloading atoms that are lost from one cycle to the next. Our approach paves the way towards quantum science with large ordered atomic arrays containing thousands of atoms in continuous operation.

We investigate the stationary (late-time) training regime of single- and two-layer underparameterized linear neural networks within the continuum limit of stochastic gradient descent (SGD) for synthetic Gaussian data. In the case of a single-layer network in the weakly underparameterized regime, the spectrum of the noise covariance matrix deviates notably from the Hessian, which can be attributed to the broken detailed balance of SGD dynamics. The weight fluctuations, are in this case, generally anisotropic but effectively experience an isotropic loss. For an underparameterized two-layer network, we describe the stochastic dynamics of the weights in each layer and analyze the associated stationary covariances. We identify the interlayer coupling as a distinct source of anisotropy for the weight fluctuations. In contrast to the single-layer case, the weight fluctuations are effectively subject to an anisotropic loss, the flatness of which is inversely related to the fluctuation variance. We thereby provide an analytical derivation of the recently observed inverse-variance flatness relation in a model of a deep linear neural network.