The quantum SearchRank algorithm is a promising tool for a future quantum search engine based on PageRank quantization. However, this algorithm loses its functionality when the $N/M$ ratio between the network size $N$ and the number of marked nodes $M$ is sufficiently large. We propose a modification of the algorithm, replacing the underlying Szegedy quantum walk with a semiclassical walk. To maintain the same time complexity as the quantum SearchRank algorithm we propose a simplification of the algorithm. This new algorithm is called randomized SearchRank, since it corresponds to a quantum walk over a randomized mixed state. The performance of the SearchRank algorithms is first analyzed on an example network and then statistically on a set of different networks of increasing size and different number of marked nodes. On the one hand, to test the search ability of the algorithms, it is computed how the probability of measuring the marked nodes decreases with $N/M$ for the quantum SearchRank, but remarkably it remains at a high value around 0.9 for our semiclassical algorithms, solving the quantum SearchRank problem. The time complexity of the algorithms is also analyzed, obtaining a quadratic speedup with respect to the classical ones. On the other hand, the ranking functionality of the algorithms has been investigated, obtaining a good agreement with the classical PageRank distribution. Finally, the dependence of these algorithms on the intrinsic PageRank damping parameter has been clarified. Our results suggest that this parameter should be below a threshold so that the execution time does not increase drastically.

Single topological defects and related structures have been experimentally created inside clouds of Bose-Einstein condensates. However, a practical protocol for creating multiple defects inside a single cloud—a prerequisite for studying defect interactions—has been lacking. Here we propose, and theoretically analyze, a practical protocol for the creation of configurations of topological monopoles, quantum knots, and skyrmions in Bose-Einstein condensates by employing fictitious magnetic fields induced by the interaction of the atomic cloud with coherent light fields. It is observed that a single coherent field is not enough for this purpose, but instead we find incoherent superpositions of several coherent fields that introduce topological point charges. We numerically estimate the experimentally achievable strengths and gradients of the induced fictitious magnetic fields and find them to be adjustable at will to several orders of magnitude greater than those of the physical magnetic fields employed in previous experimental studies. This property together with ultrafast control of the optical fields paves the way for advanced engineering of topological defects in quantum gases.

Many experimental techniques aim at determining the energy landscape of a system given and compare it to a model Hamiltonian. This landscape governs the system's evolution in the absence of dissipation. Here, we theoretically propose and experimentally demonstrate a method to measure the energy landscape of a system without knowing its functional form. A crucial ingredient for our method is the presence of dissipation, which enables sampling of the landscape over a large area of phase space through ringdown-type measurements, overcoming the main limitation of previous techniques. We apply the method to a driven-dissipative system–a parametric oscillator–observed in a rotating frame. We first measure the phase-space flow dynamics of the system via ringdown measurements, unveiling its attractors and separatrices. With these measurements, we reconstruct the (quasi-)energy landscape of the system. Furthermore, we demonstrate that our method provides direct experimental access to the so-called symplectic norm of the stationary states of the system, which is tied to the particle- or holelike nature of excitations of these states. In this way, we establish a method to identify qualitative differences between the fluctuations around stabilized minima and maxima of the nonlinear out-of-equilibrium stationary states. Our method constitutes a versatile approach to characterize a wide class of driven-dissipative systems.

For about two decades, ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ has remained an enigma in condensed matter physics and frustrated magnetism. This material evades long-range order down to temperature as low as 20 mK, and, as in spin ice, its ground state exhibits puzzling diffuse magnetic scattering. To shed light on this issue, we present spin dynamics measurements by inelastic neutron scattering, which we confront with random phase approximation calculations (RPA) to determine exchange couplings capable of reproducing the dispersion of the first excited crystal electric field level. These couplings suggest that ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ lives at the boundary between several phases, in particular the spin ice and planar antiferromagnetic ones.

Based on an accurate determination of the potential energy surfaces of ${\mathrm{Rb}}_3^{+}$ correlated to its first asymptotic limit ${\mathrm{Rb}}^{+}+\mathrm{Rb}\left(5s\right)+\mathrm{Rb}\left(5s\right)$, we identify the presence of intersections of a pair of singlet and triplet surfaces over all interparticle distances, leading to Jahn-Teller (JT) couplings. We elaborate scenarios for charge exchange between ultracold charged atom-dimer complex ($\mathrm{Rb}+{\mathrm{Rb}}_2^{+}$ or ${\mathrm{Rb}}^{+}+{\mathrm{Rb}}_2$), predicting a strong selectivity on the preparation of the initial state of the dimer. We also demonstrate that the JT couplings must drive the three-body recombination (TBR) of ${\mathrm{Rb}}^{+}$, Rb, and Rb at ultracold energies. Using the current analysis, we provide a consistent picture of the TBR experiments performed in ion-atom hybrid Rb samples. We also demonstrate the presence of JT coupling as a general phenomenon in the singly charged homonuclear alkali triatomic systems.

We investigate the phenomenon of electron-positron pair production from vacuum in the presence of a uniform time-dependent electric field of arbitrary polarization. Taking into account the interaction with the external classical background in a nonperturbative manner, we quantize the electron-positron field and derive a system of ten quantum kinetic equations (QKEs) showing that the previously-used QKEs are incorrect once the external field rotates in space. We employ then the Wigner-function formalism of the field quantization and establish a direct connection between the Dirac-Heisenberg-Wigner (DHW) approach to investigating the vacuum pair-production process and the QKEs. We provide a self-contained description of the two theoretical frameworks rigorously proving their equivalence and present an exact one-to-one correspondence between the kinetic functions involved within the two techniques. Special focus is placed on the analysis of the spin effects in the final particle distributions.

We introduce an quantum-classical hybrid algorithm, named automatic quantum circuit encoding (AQCE), that is designed to encode an arbitrary quantum state $|\mathrm{\Psi }\rangle$ onto an optimal quantum circuit $\widehat{C}$ composed of a finite set of single- and two-qubit quantum gates. The algorithm employs an objective function based on the absolute value of fidelity, $F=\langle 0\left|{\widehat{C}}^{†}\right|\mathrm{\Psi }\rangle$, which is iteratively maximized to construct an optimal quantum circuit $\widehat{C}$ with controlled accuracy. Here, $|0\rangle$ denotes a trivial product state in the computational basis of a quantum computer. The core of this algorithm lies in the sequential determination of an optimal set of two-qubit unitary operators, identified one by one through the singular value decomposition of the fidelity tensor. Once an optimal set of operators is determined, including the location of qubits on which each operator acts, elementary quantum gates are assigned algebraically to these two-qubit unitary operators. Importantly, these procedures are deterministic without assuming any quantum circuit ansatz and therefore eliminate the need for parameter optimization of parametrized quantum gates. Through noiseless numerical simulations, we demonstrate the effectiveness of the AQCE algorithm in encoding ground states of quantum many-body systems, including the spin-1/2 antiferromagnetic Heisenberg model and the spin-1/2 $XY$ model. We also compare these results with quantum circuit encoding employing predefined circuit structures such as Trotter-like and MERA-like circuit ansatze. Furthermore, our algorithm extends to classical data, for instance, classical images represented as quantum states using amplitude encoding. The adaptability enables us to adjust the quantum resource requirement, i.e., the number of qubits, by partitioning classical data into multiple distinct segments. This feature holds potential for near-term applications in quantum machine learning, such as a state preparation of classical data for an input quantum state to be processed. Finally, using a real quantum device provided by IBM Quantum, we experimentally validate that a quantum circuit generated by the AQCE algorithm can indeed reasonably represent the original quantum state.

Subsystem quantum error-correcting codes typically involve measuring a sequence of noncommuting parity check operators. They can sometimes exhibit greater fault tolerance than conventional subspace codes, which use commuting checks. However, unlike subspace codes, it is unclear if subsystem codes—in particular their advantages—can be understood in terms of ground-state properties of a physical Hamiltonian. In this paper, we address this question for the three-dimensional subsystem toric code (3D STC), as recently constructed by Kubica and Vasmer [Nat. Commun. 13, 6272 (2022)], which exhibits single-shot error correction. Motivated by a conjectured relation between single-shot properties and thermal stability, we study the zero- and finite-temperature phases of an associated noncommuting Hamiltonian. By mapping the Hamiltonian model to a pair of 3D ${\mathbb{Z}}_2$ gauge theories coupled by a kinetic constraint, we find various phases at zero temperature, all separated by first-order transitions: There are 3D toric code-like phases with deconfined point-like excitations in the bulk, and there are phases with a confined bulk supporting a 2D toric code on the surface when appropriate boundary conditions are chosen. The latter is similar to the surface topological order present in 3D STC. However, the similarities between the single-shot correction in 3D STC and the confined phases are only partial: they share the same sets of degrees of freedom, but they are governed by different dynamical rules. Instead, we argue that the process of single-shot error correction can more suitably be associated with a path (rather than a point) in the zero-temperature phase diagram, a perspective, which inspires alternative measurement sequences enabling single-shot error correction. Moreover, since none of the above-mentioned phases survives at nonzero temperature, the single-shot error-correction property of the code does not imply thermal stability of the associated Hamiltonian phase.

The rate at which individual bacterial cells grow depends on the concentrations of cellular components such as ribosomes and proteins. These concentrations continuously fluctuate over time and are inherited from mother to daughter cells, leading to correlations between the growth rates of cells across generations. Division sizes of cells are also stochastic and correlated across generations due to a phenomenon known as cell size regulation. Fluctuations and correlations from both growth and division processes affect the population dynamics of an exponentially growing culture. Here, we provide analytic solutions for the population dynamics of cells with continuously fluctuating growth rates coupled with a generic model of cell-size regulation. We show that in balanced growth, the effects of growth and division processes decouple; the population growth rate only depends on the single-cell growth rate process, and the population cell size distribution only depends on the model of division and cell size regulation. The population growth rate is always higher than the average single-cell growth rate and the difference increases with growth rate variability and its correlation time. This difference also sets the timescale for the population to reach its steady state. We provide analytical solutions for oscillations in population growth rate and traveling waves in size distribution during this approach to the steady state.

We develop and demonstrate a fully real-space perspective on high harmonic generation (HHG) in crystals. Due to the Wannier-Stark localization induced on subcycle timescales in the presence of a strong field, real-space descriptions are natural for strongly driven solids. Our approach allows us to address the origin of the extremely short dephasing times, which appear necessary for agreement between experimental HHG measurements and theoretical calculations generally performed in reciprocal space. We develop a physically transparent model of real-space dephasing which relates its rate to the distance between different sites in a laser-driven lattice. Our approach leads to well-structured high harmonic spectra at the microscopic level, reproduces the results of macroscopic propagation, and demonstrates that the requirement for ultrafast dephasing times stems from the need for suppressing recombination events with large electron-hole separations during radiative recombination.

Oblivious transfer between two untrusting parties is an important primitive in cryptography. There are different variants of oblivious transfer. In Rabin oblivious transfer, the sender Alice holds a bit, and the receiver Bob either obtains the bit, or obtains no information with probability $p_{?}$. Alice should not know whether or not Bob obtained the bit. We examine a quantum Rabin oblivious transfer (OT) protocol that uses two pure states. Investigating different cheating scenarios for the sender and for the receiver, we determine optimal cheating probabilities in each case. Comparing the quantum Rabin oblivious transfer protocol to classical Rabin oblivious transfer protocols, we show that the quantum protocol outperforms classical protocols, which do not use a third party, for some values of $p_{?}$. We find that quantum Rabin OT protocols that use mixed states can outperform quantum Rabin OT protocols that use pure states for some values of $p_{?}$.

Understanding whether a droplet adheres to or detaches from a flexible filament upon axial impact is of significant interest, particularly in the context of raindrop impact on natural surfaces. This process involves dynamic buckling followed by mode coarsening, dissipating the initial droplet kinetic energy and converting the remaining into elastic energy of the filament. To elucidate this phenomenon, we construct two phase diagrams, one while fixing the filament height and the other the droplet diameter. Notably, we observe that the energy conversion rate is inversely proportional to a Cauchy number, defining the transition between attached and detached droplet in the filament length–falling height diagram. This enables us to derive an expression for the critical falling height as a function of the filament parameters, accounting for the energy conversion rate, which emerges as a key factor for droplet detachment.

We experimentally investigate the evolution of spatial phase correlations in a rapidly quenched inhomogeneous Bose gas of rubidium using off-resonant matter-wave interferometry. We measure the phase coherence length $\ell$ of the sample and directly probe its increase during the early stage of condensate growth before vortices are formed. Once the vortices are formed stably in the quenched condensate, the measured value of $\ell$ is shown to be linearly proportional to the mean distance between the vortex. These results confirm the presence of phase coarsening prior to vortex formation, which is crucial for a quantitative understanding of the resultant defect density in samples undergoing critical phase transitions.

We propose a finite-time quantum Szilard engine (QSE) with a spin-1/2 quantum particle as the working substance (WS) to accelerate the operation of information engines. We introduce a Maxwell's demon (MD) to probe the spin state within a finite measurement time $t_{\mathrm{M}}$ to capture the which-way information of the particle, quantified by the mutual information $I\left(t_M\right)$ between WS and MD. We establish that the efficiency $\eta$ of QSE is bounded by $\eta \le 1-(1-{\eta }_C)\ln 2/I\left(t_{\mathrm{M}}\right)$, where $I\left(t_M\right)/\ln 2$ characterizes the ideality of quantum measurement, and approaches 1 for the Carnot efficiency reached under ideal measurement in quasistatic regime. We find that the output power of QSE scales as $P_{\mathrm{O}}\propto t_M^3$ in the short-time regime and as $P_{\mathrm{O}}\propto t_M^{-1}$ in the long-time regime. Additionally, considering the energy cost for erasing the MD's memory required by Landauer's principle, there exists a threshold time that guarantees QSE to output positive work.

We report feedback cooling of translational and librational degrees of freedom of a levitated m icromagnet cylinder, utilizing a piezoelectric actuator to apply linear feedback to high-Q mechanical modes. The normal modes are measured with a superconducting pick-up coil coupled to a dc SQUID, and phase information is fed back to the piezoelectric actuator to feedback cool a center-of-mass mode to $\sim 7\mathrm{K}$, and a librational mode to $830\pm 200\mathrm{mK}$. Q-factors of $1.0\times {10}^7$ are evaluated for the center-of-mass mode. We find that it is plausible to achieve ground state cooling of the center-of-mass mode by introducing vibration isolation, optimizing the geometry of the pick-up coil to focus on the specific mode of interest and utilizing a state-of-the-art SQUID for detection.