We present an application of quantics tensor trains (QTTs) and tensor cross interpolation (TCI) to the solution of a full set of self-consistent equations for multivariate functions, the so-called parquet equations. We show that the steps needed to evaluate the equations (Bethe-Salpeter equations, parquet equation, and Schwinger-Dyson equation) can be decomposed into basic operations on the QTT-TCI compressed objects. The repeated application of these operations does not lead to a loss of accuracy beyond a specified tolerance and the iterative scheme converges even for numerically demanding parameters. As examples, we take the Hubbard model in the atomic limit and the single impurity Anderson model, where the basic objects in parquet equations, the two-particle vertices, depend on three frequencies, but not on momenta. The results show that this approach is able to overcome major computational bottlenecks of standard numerical methods. The applied methods allow for an exponential increase of the number of grid points included in the calculations, and a corresponding exponential reduction of the computational error, for a linear increase in computational cost.

We formulate code concatenation as the action of a unitary quantum circuit on an expanding tree geometry and find that for certain classes of gates, applied identically at each node, a binary tree circuit encodes a single logical qubit with code distance that grows exponentially in the depth of the tree. When there is noise in the bulk or at the end of this encoding circuit, the system undergoes a phase transition between a coding phase, where an optimal decoder can successfully recover logical information, and a noncoding phase. Leveraging the tree structure, we combine the formalism of “tensor enumerators” from quantum coding theory with standard recursive techniques for classical spin models on the Bethe lattice to explore these phases. In the presence of bulk errors, the coding phase is a type of spin glass, characterized by a distribution of failure probabilities. When the errors are heralded, the recursion relation is exactly solvable, giving us an analytic handle on the phase diagram.

The Berry curvature, resembling the magnetic field in reciprocal space, offers a captivating avenue for exploring unique electromagnetic phenomena devoid of real-space analogs. Here, we investigate the emergent electromagnetic induction by solenoidal Berry curvature with its field lines forming loops, links, and knots. In stark contrast to the conventional results predicted by Faraday's law, which dictates that alternating magnetic fields yield alternating electric fields with a net zero average, the alternating Berry curvature can engender directional electromagnetic induction. Such an effect is attributed to the presence of singularities in the Berry curvature, accompanied by a $2\pi$ jump in the Berry flux. Notably, this jump does not trigger a diamagnetic impulse, due to the gauge invariance of the Berry phase modulo $2\pi$. Consequently, the induced electric field maintains finite values under time averaging, manifesting itself as a directional pumping current. Our research sheds light on a different type of anomalous electromagnetic induction effect, thereby expanding our comprehension of exotic electromagnetic phenomena.

We study the transition probabilities of a two-point measurement on a quantum system, initially prepared in a thermal state. We find two independent constraints on the difference between transition probabilities when the system is prepared at different temperatures, which both turn out to be particularly restrictive when the measured quantum system is small. These bounds take the form of a thermodynamic and of an energetic constraint because they are associated with the dissipated heat and with the absorbed energy required to increase or to reduce the temperature of the system. The derived constraints apply to arbitrary system Hamiltonians, including interactions or nonlinear energy spectra. We show the relevance of these constraints for the special case where transitions are induced by energy or particle exchange in weakly coupled bipartite systems out of equilibrium. This example is of interest for a wide range of experimentally relevant systems, from molecular junctions to coupled cavities, and can be tested by, for instance, measuring the out-of-equilibrium tunneling current and its noise.

Motivated by a recent experiment reporting the fractional quantum spin Hall effect in twisted ${\mathrm{MoTe}}_2$, we investigate microscopically the prospects of realizing exotic topologically ordered states beyond conventional quantum Hall physics. We show that a non-Abelian spin Hall insulator, a state of two copies of the non-Abelian Moore-Read state, can be stabilized at half filling of time-reversal conjugate Chern bands. We elucidate that the existence of this phase relies on the reduction of opposite-spin interactions at short distances to overcome the Ising ferromagnetism. Moreover, we demonstrate that band mixing provides a generic mechanism for this reduction to be achieved. Quite remarkably, we find that a renormalization of opposite-spin interactions at short distances as small as 15% of the moiré period is sufficient for a direct transition to a completely spin-unpolarized phase which supports the non-Abelian spin Hall insulator. Furthermore, we show that the non-Abelian spin Hall insulator can either break time-reversal symmetry or preserve it depending on the underlying topological order.

A key challenge in observing measurement-induced phase transitions is the mitigation of the post-selection barrier, which causes the reproducibility of specific sequences of measurement readouts—the trajectory—to be exponentially small in system size. Recent studies suggest that some classes of monitored infinite-range systems alleviate this problem by exhibiting a fast saturation of entanglement, resulting in only a polynomial post-selection overhead. This paper answers whether this feature is inherent in infinite-range systems, due to their underlying semiclassical dynamics. We consider three experimentally relevant monitored models: a Tavis-Cummings model, a Superradiance model, and a Bose-Hubbard dimer, each exhibiting nontrivial monitored dynamics. We unveil the occurrence of entanglement phase transitions in these models, showing how the saturation time is strongly affected by bistability regions, which also prevent the mitigation of the post-selection barrier. Finally, we propose experimental realizations of these models, providing a discussion of post selection from an experimental perspective.

In pursuing a carbon-neutral society, inertial fusion energy is a pivotal technology, offering a sustainable and virtually limitless energy source. Enhancing plasma heating efficiency is crucial for inertial fusion energy, following the ignition success using the laser-indirect-drive central-ignition approach at the U.S. National Ignition Facility. Fast ignition is a potentially high-efficiency approach among inertial confinement fusion methods. However, it remains significantly challenging due to the large divergence angle of relativistic electron beams (REBs) produced by high-intensity laser pulses. Here, we demonstrate the spontaneous collimation of REBs facilitated by an ultrahigh contrast of the heating laser in conjunction with a cone-shaped target. This collimation doubles the plasma heating efficiency compared to that achieved with the lower-contrast laser, as conducted with LFEX laser at Osaka University. This finding enables the use of a larger spot laser under ignition conditions, which is crucial for achieving the heating efficiency required for fusion ignition by reducing laser intensity and the mean kinetic energy of REBs. This collimation method significantly advances the field of inertial confinement fusion, elevating fast ignition to a practical level.

We propose a protocol to prepare a high-fidelity magic state on a two-dimensional (2D) color code using a three-dimensional (3D) color code. Our method modifies the known code-switching protocol with (1) a recently discovered transversal gate between the 2D and the 3D code and (2) a judicious use of flag-based postselection. We numerically demonstrate that these modifications lead to a significant improvement in the fidelity of the magic state. For instance, subjected to a uniform circuit-level noise of ${10}^{-3}$ (excluding idling noise), our code-switching protocol yields a magic state encoded in the distance-3 2D color code with a logical infidelity of $4.6\times {10}^{-5}\pm 1.6\times {10}^{-5}$ (quantified by an error-corrected logical state tomography) with an $84\%$ of acceptance rate. Used in conjunction with a postselection approach, extrapolation from a polynomial fit suggests a fidelity improvement to $5.1\times {10}^{-7}$ for the same code. Our protocol is aimed for architectures that allow nonlocal connectivity and should be readily implementable in near-term devices. Finally, we also present a simulation technique akin to an extended stabilizer simulator which effectively incorporates the non-Clifford $T$ gate, that permits to simulate the protocol without resorting to a resource intensive state-vector simulation.

Higher-order topological phases (HOTPs) possess localized and symmetry-protected eigenmodes at corners and along hinges in two- and three-dimensional lattices. The numbers of these topological boundary modes will undergo quantized changes at the critical points between different HOTPs. In this work, we reveal unique higher-order topology induced by time-periodic driving at the critical points of topological phase transitions, which has no equilibrium counterparts and also goes beyond the description of gapped topological matter. Using an alternately coupled Creutz ladder and its Floquet-driven descendants as illustrative examples, we analytically characterize and numerically demonstrate the zero and $\pi$ corner modes that could emerge at the critical points between different Floquet HOTPs. Moreover, we propose a unified scheme of bulk-corner correspondence for both gapless and gapped Floquet HOTPs protected by chiral symmetry in two dimensions. Our work reveals the possibility of corner modes surviving topological transitions in Floquet systems and initializes the study of higher-order Floquet topology at quantum criticality.

In three-dimensional turbulence, information of turbulent fluctuations at large scales is propagated to small scales. Here, we investigate the relation between the information flow and turbulent fluctuations described by a shell model. We first establish a connection between the information flow and phase-space contraction rate. From this relation, we then prove an inequality between the information flow and turbulent fluctuations, which suggests that the information flow from large to small scales amplifies turbulent fluctuations at small scales. This inequality can also be interpreted as a quantification of Landau's objection to the universality of turbulent fluctuations. We also discuss differences between the information flow and the Kolmogorov-Sinai entropy.

A two-dimensional periodically driven (Floquet) system with zero winding number in the absence of time-reversal symmetry is usually considered topologically trivial. Here we study the dynamics of a Gaussian wave packet placed at the boundary of a two-dimensional driven system with zero winding numbers but multiple valley-protected edge states that can be realized in a square Raman lattice and investigate the unidirectionally propagating topological edge currents. By carefully tuning the initial parameters of the wave packet, including its spin polarization as well as the initial time of the periodic driving, we control the population of different edge states, where the speed of the resulting propagation establishes a direct correspondence with the target dispersions across different gaps and valleys. Interestingly, we find that the edge states at different valleys in the $\pi$ gap can hybridize and form bow-tie-shaped edge bands fully detached from the bulk. This phase not only presents a favorable regime with narrower bulk bands but also exhibits distinct edge dynamics where the majority of particles bounce back-and-forth confined to a boundary while a small portion can follow a chiral transport around the sample.

We present a quantum algorithm for simulating a family of Markovian master equations that can be realized through a probabilistic application of unitary channels and state preparation. Our approach employs a second-order product formula for the Lindblad master equation, achieved by decomposing the dynamics into dissipative and Hamiltonian components and replacing the dissipative segments with randomly compiled, easily implementable elements. The sampling approach eliminates the need for ancillary qubits to simulate the dissipation process and reduces the gate complexity in terms of the number of jump operators. We provide a rigorous performance analysis of the algorithm. We also extend the algorithm to time-dependent Lindblad equations, generalize the family of Markovian master equations it can be applied to, and explore applications beyond the Markovian noise model. A new error bound, in terms of the diamond norm, for second-order product formulas for time-dependent Liouvillians is provided that might be of independent interest.

The investigations of spin angular momentum (SAM) of light have demonstrated many interesting photonic-spin-dependent effects. However, it is still a great challenge to manipulate a photonic SAM state in a designable and dynamic way. Here we propose to electrically control the SAM of light through lithium niobate (LN) domain engineering. In our design, each unit cell consists of a pair of positive and negative domains, which introduces a spin-dependent geometric phase. One can feasibly tune such geometric phase by applying an electric field. After properly arranging LN domains, we have successfully achieved a designed geometric phase distribution for electrically controlled separation of photonic SAM states. Our work paves the way to dynamically manipulate the SAM of light for high-speed beam steering, switchable wave front shaping, and dynamic holography.

The ubiquitous effects of the environment on quantum-mechanical systems generally cause temporally correlated fluctuations. This particularly holds for systems of interest for quantum computation where such effects lead to correlated errors. The Markovian approximation neglects these correlations and thus fails to accurately describe open-system dynamics where these correlations become relevant. In driven open systems, yet another approximation is persistently used, often unknowingly, in which one describes the decay effects independently from the time-dependent controlling fields acting on the system, thereby ignoring further temporally correlated effects. To overcome these shortcomings, we develop a quantum master equation for driven systems weakly coupled to quantum environments that avoids the aforementioned field-independent approximation, as well as the Markovian approximation. Our method makes it possible to track all occurring decay channels and their time-dependent generalized rates which we illustrate in the example of a generally driven two-level system. We also demonstrate that correlated and field-dependent dissipative effects can lead to an increase in the performance of single-qubit gate operations.

We investigate the effect of the photoexcited carrier density on helical spin dynamics using time- and spatially resolved magneto-optical Kerr rotation measurements. The helical spin lifetime is extended by increasing the photoexcited electron spin density because the phase decoherence by spin precession is suppressed owing to a decrease in the spin diffusion coefficient. As a result of the quantitative estimation of the photoexcited carrier density dependence of the spin-orbit parameters, the effect of the decrease in the spin diffusion coefficient on the helical spin lifetime is larger than that due to the modulation of the deviation from the persistent spin helix by optical doping.

A noncollinear resonator with two beams circulating and intersecting in the focus allows resonator-assisted high-harmonic generation of high-power femtosecond pulses with efficient geometrical output coupling. However, the synchronization of the two pulses and alignment of the two beams is a challenge. We describe a resonator design employing wedge mirrors which avoids the need for separate mirrors for the two circulating beams, providing intrinsic synchronization and alignment. Transverse shifting of the wedge mirrors allows fine tuning the relative phase of the pulses, i.e., the interference pattern in the focus. We present the design of two noncollinear resonators at MPQ and at Fraunhofer ILT as well as the results of thorough characterization measurements on a noncollinear resonator with a low-power cw beam, demonstrating its versatility. We also include cylindrical mirrors into the resonator to adjust the ellipticity of the focus, which allows reducing cumulative plasma effects. Ellipticities $\varepsilon >3$ are reached without compromising the resonator enhancement of >50. The MPQ resonator has been designed for an EUV frequency comb at 60.8 nm to perform high-precision spectroscopy on the $1s\text{−}2s$ two-photon transition in $\mathrm{H}{\mathrm{e}}^{+}$ ions for a test of quantum electrodynamics. The ILT resonator has been designed in the framework of developing a VUV frequency comb at around 148 nm envisaged as driver for the low-lying isomeric nuclear transition in ${}^{229}\mathrm{Th}$ (the so-called thorium isomer) as the presently only candidate for an ultra-high-precision nuclear frequency standard (“nuclear clock”).