We present a systematic approach for the semiclassical treatment of many-body dynamics of interacting, open spin systems. Our approach overcomes some of the shortcomings of the recently developed discrete truncated Wigner approximation (DTWA) based on Monte Carlo sampling in a discrete phase space that improves the classical treatment by accounting for lowest-order quantum fluctuations. We provide a rigorous derivation of the DTWA by embedding it in a continuous phase space, thereby introducing a hybrid discrete-continuous truncated Wigner approximation . We derive a set of operator-differential mappings that yield an exact equation of motion (EOM) for the continuous SU(2) Wigner function of spins. The standard DTWA is then recovered by a systematic neglection of specific terms in this exact EOM. The hybrid approach permits us to determine the validity conditions and to gain a detailed understanding of the quality of the approximation, paving the way for systematic improvements. Furthermore, we show that the continuous embedding allows for a straightforward extension of the method to open spin systems subject to dephasing, losses, and incoherent drive, while preserving the key advantages of the discrete approach, such as a positive definite Wigner distribution of typical initial states. We derive exact stochastic differential equations for processes which cannot be described by the standard DTWA due to the presence of nonclassical noise. We illustrate our approach by applying it to the dissipative dynamics of Rydberg excitation of one-dimensional arrays of laser-driven atoms and compare it to exact results for small systems.

Quantum systems displaying many accessible levels could be very powerful units of forthcoming quantum computing architectures. Indeed, the large number of available states could significantly simplify the actual implementation of several algorithms. Here we show that artificial molecular spins are particularly suitable to realize such a platform. In particular, multispin molecules with competing interactions provide a large number of low-energy multiplets in which decoherence is strongly suppressed compared to a single spin $S$ and does not increase with the system size. This feature, combined with the proper connectivity between the multiplets, enables the implementation of complex operations with remarkable fidelity, thus fully unleashing the potential of the molecular approach. We demonstrate the power of this approach by numerically simulating the implementation of one- and two-qudit gates on realistic molecular systems.

We demonstrate that the three-dimensional $e_g$ orbital Hubbard model can be generalized to arbitrary dimension $d$, and that the form of the result is determined uniquely by the requirements that (i) the twofold degeneracy of the $e_g$ orbital be retained, and (ii) the cubic lattice be turned into a hypercubic lattice. While the local Coulomb interaction $U$ is invariant for each basis of orthogonal orbitals, the form of the kinetic energy depends on the orbital basis and takes the most symmetric form for the so-called complex-orbital basis. Characteristically, with respect to this basis, the model has two hopping channels: one that is orbital-flavor conserving, and a second one that is orbital-flavor nonconserving. We show that the noninteracting electronic structure consists of two nondegenerate bands of plane-wave real-orbital single-particle states for which the orbital depends on the wave vector. Due to the latter feature each band is unpolarized at any filling, and has a non-Gaussian density of states at $d=\infty$. The orbital liquid state is obtained by filling these two bands up to the same Fermi energy. We investigate the $e_g$ orbital Hubbard model in the limit $d\to \infty$, treating the on-site Coulomb interaction $U$ within the Gutzwiller approximation, thus determining the correlation energy of the orbital liquid and the (disordered) paraorbital states. In perfect analogy with the case of the spin Hubbard model, the Gutzwiller approximation is demonstrated to be exact at $d=\infty$ for the orbital Hubbard model, because of the collapse of electron correlations to a single site. At half-filling (one electron per site on average, $n=1$) one finds a Brinkman-Rice type “metal-insulator” transition in the orbital liquid, which is analogous to the transition for a paramagnetic state in the spin model, but occurs at stronger Hubbard interaction $U$ due to the enhanced kinetic energy provided by the nonconserving hopping channel. We show that the orbital liquid is the ground state everywhere in the $(n,U)$ phase diagram except close to half-filling at sufficiently large $U$, where ferro-orbital order with real orbitals occupied is favored. The latter feature is shown to be specific for $d=\infty$, being of mathematical nature due to the exponential tails in the density of states.

We revisit the lattice formulation of the Schwinger model using the Kogut-Susskind Hamiltonian approach with staggered fermions. This model, introduced by Banks et al. Phys. Rev. D 13, 1043 (1976), contains the mass term $m_{\mathrm{lat}}{\sum }_n{(-1)}^n{\chi }_n^{†}{\chi }_n$, and setting it to zero is often assumed to provide the lattice regularization of the massless Schwinger model. We instead argue that the relation between the lattice and continuum mass parameters should be taken as $m_{\mathrm{lat}}=m-\frac{1}{8}{e}^{2}a$. The model with $m=0$ is shown to possess a discrete chiral symmetry that is generated by the unit lattice translation accompanied by the shift of the $\theta$ angle by $\pi$. While the mass shift vanishes as the lattice spacing $a$ approaches zero, we find that including this shift greatly improves the rate of convergence to the continuum limit. We demonstrate the faster convergence using both numerical diagonalizations of finite lattice systems, as well as extrapolations of the lattice strong coupling expansions.

Time-correlated photon pairs are generated by triply resonant four-wave-mixing in an ${\mathrm{In}}_{0.5}{\mathrm{Ga}}_{0.5}\mathrm{P}$ photonic crystal cavity. Maximal efficiency is reached by actively compensating for the residual spectral misalignment of the cavity modes. The generation rate reaches 5 MHz in cavities with a $Q$-factor $\approx 4\times {10}^4$, more than one order of magnitude larger than what is measured using ring resonators with similar $Q$ factors fabricated on the same chip. The photonic crystal source is integrated on a Si photonic circuit, an important asset for applications in quantum technologies.

We show how graph neural networks can be used to solve the canonical graph coloring problem. We frame graph coloring as a multiclass node classification problem and utilize an unsupervised training strategy based on the statistical physics Potts model. Generalizations to other multiclass problems such as community detection, data clustering, and the minimum clique cover problem are straightforward. We provide numerical benchmark results and illustrate our approach with an end-to-end application for a real-world scheduling use case within a comprehensive encode-process-decode framework. Our optimization approach performs on par or outperforms existing solvers, with the ability to scale to problems with millions of variables.

We optimize finite-time stochastic heat engines with a periodically scaled Hamiltonian under experimentally motivated constraints on the bath temperature $T$ and the scaling parameter $\lambda$. We present a general geometric proof that maximum-efficiency protocols for $T$ and $\lambda$ are piecewise constant, alternating between the maximum and minimum allowed values. When $\lambda$ is restricted to a small range and the system is close to equilibrium at the ends of the isotherms, a similar argument shows that this protocol also maximizes output power. These results are valid for arbitrary dynamics. We illustrate them for an overdamped Brownian heat engine, which can experimentally be realized using optical tweezers with stiffness $\lambda$.

We present a density-functional theory (DFT) study of the structural, electronic, and chemical bonding behavior in germanium (Ge)-doped vanadium dioxide $\left({\mathrm{VO}}_2\right)$. Our motivation is to explain the reported increase of the metal-insulator transition temperature under Ge doping and to understand how much of the fundamental physics and chemistry behind it can be captured at the conventional DFT level. We model doping using a supercell approach, with various concentrations and different spatial distributions of Ge atoms in ${\mathrm{VO}}_2$. Our results suggest that the addition of Ge atoms strongly perturbs the high-symmetry metallic rutile phase and induces structural distortions that partially resemble the dimerization of the experimental insulating structure. Our work, therefore, hints at a possible explanation of the observed increase in transition temperature under Ge doping, motivating further studies into understanding the interplay of structural and electronic transitions in ${\mathrm{VO}}_2$.

Antibubbles, which consist of a shell of a low-density fluid inside a high-density fluid, have several promising applications. We show, via extensive direct numerical simulations (DNSs), in both two and three dimensions, that the spatiotemporal evolution of antibubbles can be described naturally by the coupled Cahn-Hilliard-Navier-Stokes (CHNS) equations for a binary fluid. Our DNSs capture elegantly the gravity-induced thinning and breakup of an antibubble via the time evolution of the Cahn-Hilliard scalar-order-parameter field $\varphi$, which varies continuously across interfaces, so we do not have to enforce complicated boundary conditions at the moving antibubble interfaces. To ensure that our results are robust, we supplement our CHNS simulations with sharp-interface volume-of-fluid DNSs. We track the thickness of the antibubble and calculate the dependence of the lifetime of an antibubble on several parameters; we show that our DNS results agree with various experimental results; in particular, the velocity with which the arms of the antibubble retract after breakup scales as ${\sigma }^{1/2}$, where $\sigma$ is the surface tension.

We propose and analyze two types of microwave-activated gates between a fluxonium and a transmon qubit, namely a cross-resonance (CR) and a CPHASE gate. The large frequency difference between a transmon and a fluxonium makes the realization of a two-qubit gate challenging. For a medium-frequency fluxonium qubit, the transmon-fluxonium system allows for a cross-resonance effect mediated by the higher levels of the fluxonium over a wide range of transmon frequencies. This allows one to realize the cross-resonance gate by driving the fluxonium at the transmon frequency, mitigating typical problems of the cross-resonance gate in transmon-transmon chips related to frequency targeting and residual $ZZ$ coupling. However, when the fundamental frequency of the fluxonium enters the low-frequency regime below $100\mathrm{MHz}$, the cross-resonance effect decreases leading to long gate times. For this range of parameters, a fast microwave CPHASE gate can be implemented using the higher levels of the fluxonium. In both cases, we perform numerical simulations of the gate showing that a gate fidelity above $99\%$ can be obtained with gate times between 100 and $300\mathrm{ns}$. Next to a detailed gate analysis, we perform a study of chip yield for a surface code lattice of fluxonia and transmons interacting via the proposed cross-resonance gate. We find a much better yield as compared to a transmon-only architecture with the cross-resonance gate as native two-qubit gate.

We study the electronic structure of hole-doped transition metal dichalcogenides for small twist angles, where the on-site repulsion is extremely strong. Using unbiased diagrammatic Monte Carlo simulations, we find evidence for magnetic correlations which are driven by delocalization, and can be controlled in situ via the dielectric environment. For weak spin-orbit coupling we find that the moderately doped system becomes antiferromagnetic, while the regime of strong spin-orbit coupling features ferromagnetic correlations. We show that this behavior is accurately predicted by an analytical theory based on moment expansion of the Hamiltonian, and an analysis of corresponding particle trajectories.

We construct a unified theory of thermodynamics and stochastic thermodynamics for classical nonequilibrium systems driven by non-conservative forces, using the recently developed covariant Ito-Langevin theory. The thermodynamic forces are split into a conservative part and a non-conservative part. Thermodynamic functions are defined using the reference conservative system. Work and heat are partitioned into excess parts and house-keeping parts, which are due to, respectively, conservative forces and non-conservative forces. Excess entropy production (EP) and house-keeping EP are analogously defined. The splitting of thermodynamic forces is subjected to an arbitrariness resembling a gauge symmetry, with each gauge defining a reference conservative Langevin system. In the special Gibbs gauge, the nonequilibrium steady state (NESS) is characterized by Gibbs canonical distribution, the excess heat agrees with that defined by Hatano and Sasa, and the excess EP agrees with that of Glansdorff and Prigogine, i.e., it is the time rate of the second-order variation of system entropy near the NESS. Adopting the Gibbs gauge, and focusing on the excess parts of thermodynamic quantities, a complete analogy between thermodynamics of non-conservative systems and that of conservative systems is established. One important consequence of this analogy is that both the free energy and excess EP are minimized at NESS. Our theory therefore constitutes a statistical foundation both for the steady-state thermodynamics theory due to Sasa and Tasaki and for the stability theory of NESS due to Glansdorff and Prigogine. These results are valid even if the system is far from equilibrium. By studying detailed fluctuation theorem, we find striking differences between systems with symmetric kinetic matrices and those with asymmetric kinetic matrices. For systems with asymmetric kinetic matrices, the total EP is the sum of house-keeping EP, excess EP, and pumped entropy. Entropy pumping is an exchange of entropy between the system and environment without necessarily involving dissipation. In the presence of entropy pumping, the system may behave as either a demon or an antidemon. Fluctuation theorems and work relations are derived both for total work and for excess work. For systems with symmetric kinetic matrices, there is no entropy pumping, yet in the Gibbs gauge, the excess work and house-keeping work each satisfies a separate fluctuation theorem. We illustrate our theory using many concrete examples.

We investigate the quench dynamics of quasi-one- and two-dimensional dipolar Bose-Einstein condensates of ${}^{164}\mathrm{Dy}$ atoms under the influence of a fast rotating magnetic field. The magnetic field thus controls both the magnitude and sign of the dipolar potential. We account for quantum fluctuations, critical to formation of exotic quantum droplet and supersolid phases in the extended Gross-Pitaevskii formalism, which includes the so-called Lee-Huang-Yang correction. An analytical variational ansatz allows us to obtain the phase diagrams of the superfluid and droplet phases. The crossover from the superfluid to the supersolid phase and to single and droplet arrays is probed with particle number and dipolar interaction. The dipolar strength is tuned by rotating the magnetic field with subsequent effects on phase boundaries. Following interaction quenches across the aforementioned phases, we monitor the dynamical formation of supersolid clusters or droplet lattices. We include losses due to three-body recombination over the crossover regime, where the three-body recombination rate coefficient scales with the fourth power of the scattering length $(a_s)$ or the dipole length $\left(a_{dd}\right)$. For fixed values of the dimensionless parameter, ${\epsilon }_{dd}=a_{dd}/a_s$, tuning the dipolar anisotropy leads to an enhancement of the droplet lifetimes.

Superconductivity in FeSe is strongly enhanced under applied pressure and it is proposed to emerge from anomalously coupled structural and magnetic phases. Small impurities inside the Fe plane can strongly disrupt the pair formation in FeSe at ambient pressure and can also reveal the interplay between normal and superconducting phases. Here, we investigate how an impurity inside the Fe plane induced by the Cu substitution can alter the balance between competing electronic phases of FeSe at high pressures. In the absence of an applied magnetic field, at low pressures the nematic and superconducting phases are suppressed by a similar factor. On the other hand, at high pressures, above 10 kbar, the superconductivity remains unaltered despite the lack of any signature in transport associated to a magnetic phase in zero-magnetic field. However, by applying a magnetic field, the resistivity displays an anomaly preceding the activated behavior in temperature, assigned to a magnetic anomaly. We find that the high-pressure superconducting phase of FeSe is robust and remains enhanced in the presence of Cu impurity, whereas the magnetic phase is not. This could suggest that high-$T_{\mathrm{c}}$ superconductivity has a sign-preserving order parameter in the presence of a rather glassy magnetic phase.

We theoretically demonstrate that the vortex supercurrent can be reversed by the frequency-symmetry conversion among Cooper pairs by surface Andreev bound states. The surface of a three-dimensional superconductor pierced by a flux quantum is considered. We compare the vortex supercurrents near the surface of the spin-singlet $s$-wave and spin-triplet $p_z$-wave superconductors using quasiclassical Eilenberger theory, where the surface is perpendicular to the $z$ direction. We demonstrate that the vortex supercurrent near the surface of a $p_z$-wave superconductor is reversed compared to those far from the surface, whereas that of an $s$-wave superconductor is not. The splitting of the zero-energy states caused by the interference of the surface Andreev bound states and Caroli-de Gennes-Matricon modes is demonstrated.