We study the thermalization dynamics of a quantum system embedded in an incommensurate potential and coupled to a Markovian thermal reservoir. The dephasing induced by the bath drives the system toward an infinite-temperature steady state, erasing all initial information-including signatures of localization. We find that initially localized states can relax to the homogeneous steady state faster than delocalized states. Moreover, low-temperature initial states thermalize to infinite temperature more rapidly than high-temperature states—a phenomenon reminiscent of the Mpemba effect, in which hotter liquids freeze faster than colder ones. The slowest relaxation mode in the Liouvillian spectrum plays a critical role in the expedited thermalization for localized or cold initial states. Our results reveal that the combination of disordered structure and environmental dissipation may lead to nontrivial thermalization behavior, which advances both the conceptual framework of the Mpemba effect and the theoretical understanding of nonequilibrium processes in dissipative disordered systems.

We consider the problem of mutually unbiased bases as a polynomial optimization problem over the reals. After greatly reducing it by using known symmetries, we then explore it using two methods, combining a number of optimization techniques. The first of these is a search for bases using Lagrange multipliers that converges rapidly in case of mutually unbiased bases' (MUB) existence, while the second combines a hierarchy of semidefinite programs with branch-and-bound techniques to perform a global search. We demonstrate that such an algorithm would eventually solve the open question in dimension six with finite memory, although it still remains intractable. We then investigate the idea that, to show the inexistence of bases, it often suffices to search for orthonormal vector sets of smaller sizes, rather than full bases (an idea sometimes referred to as “constellations” in the literature). We use our two methods to conjecture the minimum set sizes required to show infeasibility, as well as proving it via global search for dimension three . The fact that such subproblems seem to also be infeasible heavily reduces the number of variables, by 66% in the case of the open problem, potentially providing a significant speedup for other algorithms and bringing them into the realm of tractability.

Photon loss is the dominant source of noise in optical quantum systems. The Gottesman-Kitaev-Preskill (GKP) bosonic code provides significant protection; however, even low levels of loss can generate uncorrectable errors that another concatenated code must handle. In this work, we characterize these errors by deriving analytic expressions for the logical channel that arises from pure loss acting on approximate GKP qubits. Unlike random displacement noise, we find that the loss-induced logical channel is not a stochastic Pauli channel. We also provide analytic expressions for the logical channel for “heralded loss,” when the light scattered out of the signal mode is measured either by photon number counting, i.e., photon subtraction, or heterodyne detection. These expressions offer a pathway to intentionally inducing non-Pauli channels for, e.g., magic-state production.

Error filtration is a hardware scheme that mitigates noise by exploiting auxiliary qubits and entangling gates. Although both the signal and ancillae are subject to local noise, constructive interference and postselection allow us to reduce the noise level in the signal qubit. Here we highlight the relation between error filtration and error detection codes and determine the optimal codes that make the qubits interfere most effectively. We examine our optimized scheme under imperfect implementation, where ancillary qubits may be noisy or subject to crosstalk. Even with these imperfections, we find that adding more ancillary qubits helps to protect quantum information. We benchmark our approach against figures of merit that correspond to different applications, including entanglement fidelity, quantum Fisher information (for applications in quantum sensing), and the Clauser-Horne-Shimony-Holt value (for cryptographic applications), with one, two, and three ancillary qubits. By using the entanglement fidelity as a figure of merit, we suggest a general condition for error filtration, and for one and two ancillae, we obtain some explicit expressions for the optimal codes. We also compare our method with the recently introduced superposed quantum error mitigation (SQEM) scheme based on superposition of causal orders and show that, for a wide range of noise strengths, our approach may outperform SQEM in terms of effectiveness and robustness.

We present four quantum algorithms for solving a multidimensional drift-diffusion equation. They rely on a quantum linear system solver, a quantum Hamiltonian simulation, a quantum random walk, and the quantum Fourier transform. We compare the complexities of these methods to their classical counterparts, finding that diagonalization via the quantum Fourier transform offers a quantum computational advantage for solving linear partial differential equations at a fixed final time. We employ a multidimensional amplitude estimation process to extract the full probability distribution from the quantum computer.

Optimization problems in finance, physics, and computer science are typically very hard to tackle in classical computing; quantum computing could help speed up computations and provide efficient methods for tackling large problems. Typically, to treat a problem with a quantum computer, the optimal solution is cast as the ground state of a diagonal Hamiltonian. We develop a method, called imaginary-time evolution block encoding (ITE-BE), based on a recent imaginary-time algorithm, which requires no variational parameter optimization, as all parameters can be derived analytically from the target Hamiltonian. We also demonstrate that our method can be successfully combined with other quantum algorithms such as the quantum approximate optimization algorithm (QAOA). For illustration, here we study the MaxCut problem. We find that the QAOA ansatz increases the postselection success of ITE-BE, and shallow QAOA circuits, when boosted with ITE-BE, achieve better performance than deeper QAOA circuits. For the special case of the transverse initial state, we adapt our block-encoding scheme to allow for a deterministic application of the first layer of the circuit.

Bargmann invariants, also known as multivariate traces of quantum states $\mathrm{Tr}({\rho }_1{\rho }_2\cdots {\rho }_n)$, are unitary invariant quantities used to characterize weak values, Kirkwood-Dirac quasiprobabilities, out-of-time-order correlators, and geometric phases. Here we give a complete characterization of the set $B_n$ of complex values that $n\mathrm{th}$-order invariants can take, resolving some recently proposed conjectures. We show that $B_n$ is equal to the range of invariants arising from pure states described by Gram matrices of circulant form. We show that both ranges are equal to the $n\mathrm{th}$ power of the complex unit $n$-gon and are therefore convex, which provides a simple geometric intuition. Finally, we show that any Bargmann invariant of order $n$ is realizable using either qubit states or circulant qutrit states.

We propose a new method for identifying cutting locations for quantum circuit cutting, with a primary focus on partitioning circuits into three or more parts. Under the assumption that the classical postprocessing function is decomposable, we derive a new upper bound on the sampling overhead resulting from both timelike and spacelike cuts. We show that this bound improves upon the previously known bound by orders of magnitude in cases of three or more partitions. Based on this bound, we formulate an objective function $L_Q$ and present a method to determine cutting locations that minimize it. Our method is shown to outperform a previous approach in terms of computation time. Moreover, the quality of the obtained partitioning is found to be comparable to or better than that of the baseline in all but a few cases, as measured by $L_Q$. These results are obtained by identifying cutting locations in a number of benchmark circuits of the size and type expected in quantum computations that outperform classical computers.

We numerically investigate the generation and dynamics of tripartite entanglement among qubits (quantum emitters or atoms) in multimode cavity quantum electrodynamics (cQED). Our cQED architecture features three initially unentangled excited two-level quantum emitters confined within a triangle-shaped multimode optical cavity, which later become entangled due to a Jaynes-Cummings-like interaction. Using the tripartite negativity measure of entanglement and fidelity with respect to the genuine tripartite entangled state (Greenberger-Horne-Zeilinger state, to be precise), we analyze the impact of the number of cavity modes, qubit locations, and losses (spontaneous emission from qubits and photon leakage from the cavity mirrors) on the generated entanglement. Our key results include the presence of two kinds of retardation effects: one resulting from the time it takes for photons to propagate from one qubit to another, and the other to complete one round trip in the cavity. We observed these retardation effects only in multimode cavities, with the exciting possibility of controlling the collapse and revival patterns of tripartite entanglement by altering the qubit locations in the cavity. Furthermore, the impact of losses on the generated entanglement and the dependence of maximum entanglement on the total number of modes yield results that surpass those reported for single and two excitations. With recent advances in circuit quantum electrodynamics, these findings hold promise for the development of entanglement-based quantum networking protocols and quantum memories.

We present a protocol for the generation of NOON states with ultracold atoms, leveraging the Bose-Hubbard model in the self-trapping regime. By means of an optimized adiabatic protocol, we achieve a significant reduction in the time required for the preparation of highly entangled NOON states, involving two or more modes. Our method saturates the quantum speed limit, ensuring both efficiency and high fidelity in state preparation. A detailed analysis of the geodesic counterdiabatic driving protocol and its application to the Bose-Hubbard system highlights its ability to expand the energy gap, facilitating faster adiabatic evolution. Through perturbation theory, we derive effective parameters that emulate the counterdiabatic Hamiltonian, enabling experimentally viable implementations with constant physical parameters. This approach is demonstrated to yield exponential time savings compared with standard geodesic driving, making it a powerful tool for creating complex entangled states for applications in quantum metrology and quantum information. Our findings pave the way for scalable and precise quantum state control in ultracold atomic systems.

The complete classification of the saddle-point solutions for high-order above-threshold ionization, presented in Phys. Rev. A 111, 023103 (2025) and Phys. Rev. A 111, 053110 (2025) for a linearly polarized laser field, is generalized to the case of an arbitrary bichromatic elliptically polarized field. We first present the classification of the saddle-point solutions for the case of a monochromatic elliptically polarized driving field, which is the simplest example of the field that has two components, i.e., that evolves in the plane. For a bichromatic laser field whose elliptically polarized components have the frequencies $r\omega$ and $s\omega$ ($r$ and $s$ are integers, $s>r$, and $\omega$ is the fundamental frequency), the system of the saddle-point equations has $8s^2$ solutions per optical cycle. One-half of these solutions are the so-called backward-scattering solutions for which the direction of the electron motion is significantly affected by the rescattering. The other half are the forward-scattering solutions for which the electron is only slightly deflected during the rescattering event. For some specific field configurations, the number of saddle-point solutions can be smaller. For example, for a bicircular field, which consists of two counterrotating circularly polarized components, there are $4s(r+s)$ solutions, while for the corotating configuration there are $4s^2$ solutions. As an application, we have shown that for a monochromatic elliptically polarized laser field, all four threshold anomalies appear in the spectra of the rescattered photoelectrons.

We theoretically investigate the enhancement of extreme-ultraviolet-radiation (XUV) generation by orthogonally polarized laser-controlled spontaneous emission of Ar atoms. The three-dimensional time-dependent Schrödinger equation is solved numerically using the generalized pseudospectral method. Applying an intense third-harmonic field of 1030-nm laser results in a series of spectral lines appearing in the harmonic spectrum between 13.5  and 15.8 eV. These lines correspond to field-free transitions between the ground state and $3s^{2}3p^{5}nd$ ($n=3,4,5,...$) excited states of argon. Introducing a weak multicycle fundamental laser pulse perpendicular to the third-harmonic field leads to a narrowband XUV emission centered at 14.15 eV, corresponding to the transition from the $3s^{2}3p^{5}3d$ excited state to the ground state. Combining population analysis with the synchrosqueezed transform time-frequency spectra, we attribute those emissions to free induction decay from the coherently excited states. The perpendicular fundamental field will cause the ionization of excited states, leading to the depletion of those states and the generation of excited states' high-order harmonics, which suppress the free induction decay emission. For higher excited states, the fundamental field alters the excitation pathways, significantly reducing state populations. The use of orthogonally polarized laser fields enables selective excitation of specific electronic states, enhancing the spectral purity. Our findings demonstrate the potential of orthogonal two-color laser pulses in generating bright, narrowband XUV radiation. This research provides new insights for developing XUV and soft x-ray light sources, offering promising applications in various fields requiring precise and intense XUV radiation.

We reveal a feature of quantum scarring in systems with many particles: quantum scars, living densely near an unstable periodic orbit, must be compensated by corresponding antiscarred states suppressed there to establish the uniformity of the whole. The uniformity of the underlying phase space is linked to early-time dynamics—a regime beyond the predictions of random matrix theory and encapsulated in the eigenstate stacking theorem. By extending the domain of the stacking theorem, we apply our theory to a chaotic spinor Bose-Einstein condensate, whose quantum scar dynamics have recently been observed in the laboratory. Our work uncovers how scarring of some eigenstates affects the rest of the chaotic and thermal spectrum in quantum systems with many particles.

We investigate the collective excitation spectrum of a quasi-two-dimensional Bose-Einstein condensate trapped in a harmonic confinement with nonlinear rotation induced by a density-dependent gauge potential. Using a Bogoliubov–de Gennes (BdG) analysis, we show that the dipole mode frequency depends strongly on the nonlinear interaction strength, violating Kohn's theorem which is also well complemented by the analytical expression for the dipole and breathing modes obtained employing a variational analysis. We identify four different vortex displacement modes, Tkachenko, circular, quadratic, and rational, whose frequencies are rotation sensitive. An analytical Tkachenko mode frequency from a hydrodynamic approach agrees well with that computed using BdG and Fourier analysis. The excitation spectrum remains symmetric around the angular quantum number $l=0$, but energy splitting between $l$ and $-l$ varies with the sign and strength of the nonlinear rotation. Finally, we demonstrate that the surface mode excitation frequency increases (decreases) with an increase in the positive (negative) nonlinear rotation strength.

We compute the complete set of second-order transport coefficients of the unitary Fermi gas, a dilute gas of spin-1/2 particles interacting via an $s$-wave interaction tuned to infinite scattering length. The calculation is based on kinetic theory and the Chapman-Enskog method at second order in the Knudsen expansion. We take into account the exact two-body collision integral. We extend previous results on second-order coefficients related to shear stress by including terms related to heat flow and gradients of the fugacity. We confirm that the thermal relaxation time is given by the simple estimate ${\tau }_{\kappa }=\kappa m/\left(c_{P}T\right)$ even if the full collision kernel is taken into account. Here, $\kappa$ is the thermal conductivity, $m$ is the mass of the particles, $c_P$ is the specific heat at constant pressure, and $T$ is the temperature.

Vortex mass is a key concept in the study of superfluid dynamics, referring to the inertia of vortices in a superfluid, which affects their motion and behavior. Despite being an important quantity, the vortex mass has never been observed experimentally, and remains an unresolved issue in this field. As of now, a large body of research assumes that the vortex mass is a local parameter. In contrast, we present a calculation that suggests a logarithmic dependence on the system size, agreeing with some earlier predictions in the context of Bose gases. We analyze the problem using an effective field theory that describes ultracold atomic Fermi gases over the BEC-BCS crossover at both zero and nonzero temperatures. Our study reveals a strong dependence of the vortex mass on the scattering length; in particular, the vortex mass grows rapidly when moving toward the BCS side. Furthermore, we find that the system-size dependence of the vortex mass results in values an order of magnitude larger than those predicted by other models for realistic system sizes. This implies that the vortex mass could be observable in a wider parameter range than was previously expected. This is particularly relevant considering recent advances in experimental techniques that place the observation of vortex mass in superfluid Fermi gases within reach.

Due to its peculiar superfluid-crystal duality feature, the supersolid has received great research interest. Recently, researchers have paid much attention to its elastic response properties; however, the inelastic deformation has barely been explored. In this work, we study the transition from elastic to inelastic deformation of a dipolar supersolid Bose-Einstein condensate trapped in a box potential (i.e., a dipolar supersolid with finite size). We obtain the stationary supersolid states (both ground and excited) of the system and examine the relation between the supersolid size and the number of unit cells it can accommodate, which can essentially help us to understand the dynamical responses of the supersolid during a dilation or compression process. We found that within a certain dilation or compression extent, the supersolid can retain its original crystal structure, that is, it endures an elastic deformation; however, when the extent exceeds a critical threshold, the original crystal structure of the supersolid will be disrupted, which signifies an inelastic deformation. Furthermore, we both analytically and numerically determine the critical point of the transition from elastic to inelastic deformation and map out a phase diagram. These results open up new territory in the research of supersolid mechanical properties and may find applications in quantum material science and quantum-based technologies.

We report the formation of the chiral quantum droplet in a spin-orbit-coupled Bose gas, where the system turns to a self-bound droplet when moving towards a particular direction and remains gaseous otherwise. The chirality arises from the breaking of Galilean invariance by spin-orbit coupling, which enables the system to dynamically adjust its condensation momentum and spin polarization in response to its velocity. As a result, only towards a specific moving direction and beyond a critical velocity, the acquired spin polarization can trigger collective interactions sufficient for self-binding and drive a first-order transition from gas to droplet. We map out a phase diagram of the droplet, gas, and their coexistence for realistic spin-orbit-coupled ${}^{39}\mathrm{K}$ mixtures with tunable moving velocity and magnetic detuning. Our results reveal the emergence of chirality in spin-orbit-coupled quantum gases, which shed light on general chiral phenomena in moving systems with broken Galilean invariance.