We introduce a quantum-inspired approximation algorithm for MaxCut based on low-depth Clifford circuits. We start by showing that the solution unitaries found by the adaptive quantum approximation optimization algorithm (ADAPT-QAOA) for the MaxCut problem on weighted fully connected graphs are (almost) Clifford circuits. Motivated by this observation, we devise an approximation algorithm for MaxCut, ADAPT-Clifford, that searches through the Clifford manifold by combining a minimal set of generating elements of the Clifford group. Our algorithm finds an approximate solution of MaxCut on an $N$-vertex graph by building a depth $O\left(N\right)$ Clifford circuit. The algorithm has runtime complexity $O\left(N^2\right)$ and $O\left(N^3\right)$ for sparse and dense graphs, respectively, and space complexity $O\left(N^2\right)$, with improved solution quality achieved at the expense of more demanding runtimes. We implement ADAPT-Clifford and characterize its performance on graphs with positive and signed weights. The case of signed weights is illustrated with the paradigmatic Sherrington-Kirkpatrick model, for which our algorithm finds solutions with ground-state mean energy density corresponding to $\sim 94\%$ of the Parisi value in the thermodynamic limit. The case of positive weights is investigated by comparing the cut found by ADAPT-Clifford with the cut found with the Goemans-Williamson (GW) algorithm. For both sparse and dense instances we provide copious evidence that, up to hundreds of nodes, ADAPT-Clifford finds cuts of lower energy than GW.

We propose a method to trap polar molecules with the electric force induced by the surface acoustic wave (SAW) on piezoelectric materials. In this approach, the electric force is perpendicular to the moving direction of the polar molecules, and is used to control the positions of trapped polar molecules in the direction orthogonal to the acoustic transmission. By virtue of an external electric force, the SAW-induced electric field can trap the polar molecules into single-layer or multilayer lattices. The arrangement of molecules can affect the binding energy and localization of the molecule array. Then the one- or two-dimensional trapped polar molecule arrays can be used to construct the Bose-Hubbard (BH) model, whose energy and dynamics are affected by the localizations of the trapped molecules. We find that the phase transitions between the superfluid and Mott insulator based on trapped polar molecule BH model can be modulated by the SAW-induced electric potential.

We study the competition between disorder and singlet superconductivity in a quasi-one-dimensional (1D) system. We investigate the applicability of the Anderson theorem, namely that time-reversal conserving (nonmagnetic) disorder does not impact the critical temperature, by opposition to time-reversal breaking disorder (magnetic). To do so, we examine a quasi-1D system of spin 1/2 fermions with attractive interactions and forward scattering disorder using field theory (bosonization). By computing the superconducting critical temperature ($T_c$), we find that, for nonmagnetic disorder, the Anderson theorem also holds in the quasi-1D geometry. In contrast, magnetic disorder has an impact on the critical temperature, which we investigate by deriving renormalization group equations describing the competition between disorder and interactions. Computing the critical temperature as a function of disorder strength, we observe different regimes depending on the strength of interactions. We discuss possible platforms where this can be observed in cold atoms and condensed matter.

We explore the feasibility of fault-tolerant quantum computation using the bit-flip repetition code in a biased noise channel where only the bit-flip error can occur. While several logic gates can potentially produce phase-flip errors even in such a channel, we propose bias-preserving implementation of $S, H$, controlled-$Z$ (CZ), and $R_z$ gates. We demonstrate that our scheme improves the computational precision in several tasks such as the time evolution of quantum systems and variational quantum eigensolver.

A delicate tension complicates the relationship between the topological magnetoelectric effect (TME) in three-dimensional (3D) ${\mathbb{Z}}_2$ topological insulators (TIs) and time-reversal symmetry (TRS). TRS underlies a particular ${\mathbb{Z}}_2$ topological classification of the electronic ground state of crystalline band insulators and the associated quantization of the magnetoelectric response coefficient calculated using bulk linear-response theory but, according to standard symmetry arguments, simultaneously forbids a nonzero magnetoelectric coefficient in any physical finite-size system. This contrast between theories of magnetoelectric response in formal bulk models and in real finite-sized materials originates from the distinct approaches required to introduce notions of (electronic) polarization and orbital magnetization in these fundamentally different environments. In this work we argue for a modified interpretation of the bulk linear-response calculations in nonmagnetic ${\mathbb{Z}}_2$ TIs that is more plainly consistent with TRS and use this interpretation to discuss the effect's observation—still absent over a decade after its prediction. Our analysis is reinforced by microscopic bulk and thin-film calculations carried out using a simplified but still realistic effective model for the well established ${\mathrm{V}}_2{\mathrm{VI}}_3 [\text{V}=\text{(Sb,}\text{Bi)}$ and $\text{VI}=\text{(Se,}\text{Te)}]$ family of nonmagnetic ${\mathbb{Z}}_2$ TIs. When a uniform dc magnetic field is included in this model, the anomalous $n=0$ Landau levels (LLs) play the central role, both in thin films and in bulk. In the former case, only the $n=0$ LL eigenfunctions can support a dipole moment, which vanishes if there are no magnetic surface dopants and is quantized in the thick-film limit if magnetic dopants at the top and bottom surfaces have opposite orientation. In the latter case, the Hamiltonian projected into the $n=0$ LL subspace is a one-dimensional Su-Schrieffer-Heeger model with ground-state polarization that is quantized in accordance with the bulk linear-response coefficient calculated for (a lattice regularization of) the starting 3D model. Motivated by analytical results, we conjecture a type of microscopic bulk-boundary correspondence: a bulk insulator with (generalized) TRS supports a magnetoelectric coefficient that is purely itinerant (which is generically related to the geometry of the ground state) if and only if magnetic surface dopants are required for the TME to manifest in finite samples thereof. We conclude that in nonmagnetic ${\mathbb{Z}}_2$ TIs the TME is activated by magnetic surface dopants, that the charge-density response to a uniform dc magnetic field is localized at the surface and specified by the configuration of those dopants, and that the TME is qualitatively less robust against disorder than the integer quantum Hall effect.

Solid-state elastic-wave phonons are a promising platform for a wide range of quantum information applications including facilitating quantum transduction from microwave to optical electromagnetic fields, long-lived quantum memories, in addition to potentially acting as qubits themselves. An outstanding challenge and enabling capability in harnessing phonons for quantum information processing is achieving sufficiently strong nonlinear interactions between them. To this end, we propose a general architecture for generating strong quantum phononic nonlinearity using piezoelectric-semiconductor heterostructures consisting of a piezoelectric acoustic material hosting phononic modes that is in direct proximity to a two-dimensional electron gas (2DEG). Each phonon in the piezoelectric material carries an electric field, which extends into the 2DEG. The fields induce polarization of 2DEG electrons, which in turn interact with other piezoelectric phononic electric fields. The net result is coupling between the electric fields associated with the various phonon modes. We derive, from first principles, the nonlinear phononic susceptibility of a piezo-2DEG system and provide a prescription to calculate all orders of the susceptibility in a perturbative expansion. We show that many nonlinear processes are strongly favored at high electron mobility, motivating the use of the 2DEG to mediate the nonlinearities. We derive the first, second, and third-order susceptibilities and calculate them for the case of a lithium niobate surface acoustic wave interacting with a GaAs-AlGaAs heterostructure 2DEG. We show that, for this system, the strong third-order phononic nonlinearities generated could enable single-phonon Kerr shift in an acoustic cavity that exceeds realistic cavity linewidths, potentially leading to a new class of acoustic qubit. We further show that the strong second-order nonlinearity could be used to produce a high-gain, traveling-wave parametric amplifier to amplify—and ultimately detect—the outputs of the acoustic cavity qubits. Assuming favorable losses in such a system, the combination of these capabilities, combined with the ability to efficiently transduce phonons from microwave electromagnetic fields in transmission lines, thus hold promise for creating all-acoustic quantum information processors.

The Lieb-Robinson correlation function is the norm of a commutator between local operators acting on separate subsystems at different times. This provides a useful state-independent measure for characterizing the specifically quantum interaction between spatially separated qubits. The finite propagation velocity for this correlator defines a “light cone” of quantum influence. We calculate the Lieb-Robinson correlation function for one-dimensional qubit arrays described by the transverse-field Ising model. Direct calculations of this correlation function have been limited by the exponential increase in the size of the state space with the number of qubits. We introduce a technique that avoids this barrier by transforming the calculation to a sum over Pauli walks which results in linear scaling with system size. We can then explore propagation in arrays of hundreds of qubits and observe the effects of the quantum phase transition in the system. We observe the emergence of two distinct velocities of propagation: a correlation front velocity, which is affected by the phase transition, and the Lieb-Robinson velocity which is not. The correlation front velocity is equal to the maximum group velocity of single quasiparticle excitations. The Lieb-Robinson velocity describes the extreme leading edge of correlations when the value of the correlation function itself is still very small. For the semi-infinite chain of qubits at the quantum critical point, we derive an analytical result for the correlation function.

We use surface acoustic waves of 1 and 3 GHz in hybrid piezoelectric-magnetic systems with either nickel or cobalt as a magnetic layer to generate magnetoacoustic waves and directly image them using stroboscopic x-ray magnetic circular dichroism imaging. Our measurements visualize and quantify the amplitudes of both acoustic and magnetic components of the magnetoacoustic waves, which are generated in the ferromagnetic layer and can propagate over millimeter distances. Additionally, we quantified the magnetoelastic strain component for nickel and cobalt through micromagnetic simulations.

Topological defects are a universal concept across many disciplines, such as crystallography, liquid-crystalline physics, low-temperature physics, cosmology, and even biology. In nematic liquid crystals, topological defects called disclinations have been widely studied. For their three-dimensional (3D) dynamics, however, only recently have theoretical approaches dealing with fully 3D configurations been reported. Further, recent experiments have observed 3D disclination line reconnections, a phenomenon characteristic of defect line dynamics, but detailed discussions were limited to the case of approximately parallel defects. In this paper, we focus on the case of two disclination lines that approach at finite angles and lie in separate planes, a more fundamentally 3D reconnection configuration. Observing and analyzing such reconnection events, we find the square-root law of the distance between disclinations and the decrease of the interdisclination angle over time. We compare the experimental results with theory and find qualitative agreement on the scaling of distance and angle with time, but quantitative disagreement on distance and angle relative mobilities. To probe this disagreement, we derive the equations of motion for systems with reduced twist constant and also carry out simulations for this case. These, together with the experimental results, suggest that deformations of disclinations may be responsible for the disagreement.

The emerging field of stochastic thermodynamics extends classical ideas of entropy, heat, and work to nonequilibrium systems. One notable finding is that the second law of thermodynamics typically only holds after taking appropriate averages with respect to an ensemble of stochastic trajectories. The resulting average rate of entropy production then quantifies the degree of departure from thermodynamic equilibrium. In this paper we investigate how the presence of a semipermeable interface increases the average entropy production of a single diffusing particle. Starting from the Gibbs-Shannon entropy for the particle probability density, we show that a semipermeable interface or membrane $\mathcal{S}$ increases the average rate of entropy production by an amount that is equal to the product of the flux through the interface and the logarithm of the ratio of the probability density on either side of the interface, integrated along $\mathcal{S}$. The entropy production rate thus vanishes at thermodynamic equilibrium, but can be nonzero during the relaxation to equilibrium, or if there exists a nonzero stationary equilibrium state (NESS). We then give a probabilistic interpretation of the interfacial entropy production rate using so-called snapping out Brownian motion. This also allows us to construct a stochastic version of entropy production. Finally, we illustrate the theory using the example of diffusion with stochastic resetting on a circle, and find that the average rate of interfacial entropy production is a nonmonotonic function of the resetting rate and the permeability.

Anomalous topological phases, where edge states coexist with topologically trivial Chern bands, can only appear in periodically driven lattices. When the driving is smooth and continuous, the bulk-edge correspondence is guaranteed by the existence of a bulk invariant known as the winding number. However, in lattices subject to periodic discrete step walks the existence of edge states does not only depend on bulk invariants but also on the boundary. This is a consequence of the absence of an intrinsic time dependence or micromotion in discrete step walks. We report the observation of edge states and a simultaneous measurement of the bulk invariants in anomalous topological phases in a two-dimensional synthetic photonic lattice subject to discrete step walks. The lattice is implemented using time multiplexing of light pulses in two coupled fibre rings, in which one of the dimensions displays real-space dynamics and the other one is parametric. The presence of edge states is inherent to the periodic driving and depends on the properties of the boundary in the implemented two-band model with zero Chern number. We provide a suitable expression for the topological invariants whose calculation does not rely on micromotion dynamics.

Bound states in quantum dots coupled to superconductors can be in a coherent superposition of states with different electron number but with the same fermion parity. Electrostatic gating can tune this superposition to a sweet spot, where the quantum dot has the same mean electric charge independent of its electron-number parity. Here, we propose to encode quantum information in the local fermion parity of two tunnel-coupled quantum dots embedded in a Josephson junction. At the sweet spot, the qubit states have zero charge dipole moment. This protects the qubit from dephasing due to charge noise acting on the potential of each dot, as well as fluctuations of the (weak) interdot tunneling. At weak interdot tunneling, relaxation is suppressed because of disjoint qubit states. However, for strong interdot tunneling the system is protected against noise affecting each quantum dot separately (energy-level noise, dot-superconductor tunneling fluctuations, and hyperfine interactions). Finally, we describe initialization and readout as well as single-qubit and two-qubit gates by pulsing gate voltages.

We show that rotating two-dimensional Fermi gases possess a nonrelativistic scale and conformal invariance at weak but nonzero interactions, where the scale invariance of universal short-range interactions is not yet broken by quantum effects. We demonstrate the symmetry in the excitation spectrum of few-fermion ensembles in a harmonic trap obtained by exact diagonalization. The excitation spectrum is shown to split in a set of primary states and derived excited states that consist of breathing modes as well as two different center-of-mass excitations, which describe cyclotron and guiding-center excitations of the total particle cloud. Furthermore, the conformal symmetry is manifest in the many-body wave function, where it dictates the form of the hyperradial component, which we demonstrate using Monte Carlo sampling of few-body wave functions.

Quantum correlation functions are a natural way to encode multitime information, as they are ubiquitous in analysis from fluctuation theorems to information scrambling. Correlation functions can be identified with quasiprobabilities associated to quantum processes. In this work we show how these can be measured via error-cancellation techniques, using projective measurements only and no ancillae. The scheme is implemented in a nitrogen-vacancy center in diamond undergoing a unitary quantum work protocol. We reconstruct quantum-mechanical time correlations encoded in the Margenau-Hills quasiprobabilities by observing work extraction peaks five times those of sequential projective energy measurement schemes and in violation of newly derived stochastic bounds. We interpret the phenomenon via anomalous energy exchanges due to the underlying negativity of the quasiprobability distribution.

We exploit the coherent emission of Cherenkov diffraction radiation (ChDR) by a relativistic electron beam to sense its position even in the presence of other particle beams. ChDR is produced in alumina inserts embedded in the vacuum chamber walls and recorded in a narrow band centered at 30 GHz. This nontrivial solution has been implemented for plasma wakefield accelerators, where the electron beam to be sensed can copropagate with another high-energy proton beam that generates the plasma wakefield. In addition, at variance with most existing position detectors, this method is insensitive to spurious electric charges due to the presence of plasma. We present the overall design of the detector as well as experimental results obtained in the AWAKE facility at CERN.