Spiral waves emitted by topological defects and their instabilities are a fundamental and ubiquitous process in nature. We study this phenomenon using data from recent experiments and different prototype models ranging from coupled oscillators, reaction-diffusion, and nonlinear optics. Statistically we show that, for all systems considered, the spectral density exhibits a power-law decay on spatial scales shorter than the intrinsic wavelength. This reflects a common type of self-organization through a stationary turbulentlike dynamics. The role of short-range interactions due to high defects density is discussed. Using a generalized Hilbert transform in two dimensions, we show that local phase and amplitude field present similar power-law decays in their spectral density.

Measurements profoundly impact quantum systems and can be used to create novel states of matter out of equilibrium. We investigate the multipartite entanglement structure that emerges in hybrid quantum circuits involving unitaries and measurements. We describe how a balance between measurements and unitary evolution can lead to multipartite entanglement spreading to distances far greater than what is found in nonmonitored systems, thus evading the usual fate of entanglement. We introduce a graphical representation based on spanning graphs that allows to infer the evolution of genuine multipartite entanglement for general subregions. We exemplify our findings on hybrid random Haar circuits that realize a 1D measurement-induced dynamical phase transition, where we find genuine three-party entanglement at all separations. At criticality, our data are consistent with power-law decay with a tripartite exponent strictly larger than the one of the bipartite logarithmic negativity. The four-party case is also explored. Finally, we discuss how our approach can provide fundamental insights regarding entanglement dynamics for a wide class of quantum circuits and architectures.

We demonstrate that the widely used plasma analogy is unreliable at predicting edge properties of quantum Hall states. This discrepancy arises from a fundamental difference between quantum Hall droplets and plasmas (Coulomb gases): The former are incompressible liquids subject to area-preserving deformations, while the latter are governed by electrostatics and thus involve conformal transformations. Consequently, the plasma analogy fails at the edge, except in fine-tuned geometries, as it does not account for the emergent local edge velocity. We quantitatively show how the analogy's failure affects physical quantities, such as fluctuations of local observables and absorption rates in microwave spectroscopy, measurable in both solid-state experiments and quantum simulators.

The framework of measurement operators plays a fundamental role in extracting information about quantum systems. Recently, techniques based on induced coherence have been developed to access the same information for undetected photons. However, there has been a lack of consistent reformulation of quantum operators for these techniques. In this work, we introduce a set of parameters that quantify the polarization of undetected photons based on measured visibilities. Given their similarity to classical counterparts, we refer to them as visibility Stokes parameters. We apply these parameters and the corresponding quantum operators to the problem of quantum state tomography, thoroughly analyzing the environment of undetected photons and its role in the reconstruction process. Because these parameters provide a more intuitive and consistent understanding of the measurement process, we believe that some established quantum information protocols could be adapted for undetected photons.

Exceptional points are special degeneracy points in parameter space that can arise in (effective) non-Hermitian Hamiltonians describing open quantum and wave systems. At an $n\mathrm{th}$-order exceptional point, $n$ eigenvalues and the corresponding eigenvectors simultaneously coalesce. These coalescing eigenvalues typically exhibit a strong response to small perturbations that can be useful for sensor applications. A so-called generic perturbation with strength $\epsilon$ changes the eigenvalues proportional to the $n\mathrm{th}$ root of $\epsilon$. A different eigenvalue behavior under perturbation is called nongeneric. An understanding of the behavior of the eigenvalues for various types of perturbations is desirable and also crucial for applications. We advocate a graph-theoretical perspective that contributes to the understanding of perturbative effects on the eigenvalue spectrum of higher-order exceptional points, i.e., $n>2$. Our approach is mathematically derived and the intuitive consequences elucidated. To highlight the relevance of nongeneric perturbations and to give a physical interpretation for their occurrence, we consider an illustrative example, a system of microrings coupled by a semi-infinite waveguide with an end mirror. Furthermore, the saturation effect occurring for cavity-selective sensing in such a system is naturally explained within the graph-theoretical picture.

Quantum matter phases may coexist microscopically even when they display competing tendencies. A fundamental question is whether such a competition can be avoided through the elimination of one phase while the other one condenses into the ground state. Here, we present a high-resolution neutron spectroscopy study of the low-energy spin excitations in the high-temperature superconductor ${\mathrm{La}}_{1.855}{\mathrm{Sr}}_{0.145}{\mathrm{CuO}}_4$. In the normal state, we find low-energy magnetic fluctuations at incommensurate reciprocal lattice positions where spin-density-wave order emerges at lower Sr concentration or at high magnetic fields. While these spin excitations are largely suppressed by the emergence of the superconducting spin gap, some low-energy magnetic fluctuations persist deep inside the superconducting state. We interpret this result in terms of a dynamic competition between superconductivity and magnetism, where superconductivity impedes the condensation of low-energy magnetic fluctuations through the formation of magnetically mediated Cooper pairs.

Two-dimensional electronic spectroscopy (2DES) is a powerful tool for exploring quantum effects in energy transport within photosynthetic systems and investigating novel material properties. However, simulating the dynamics of these experiments poses significant challenges for classical computers due to the large system sizes, long timescales, and numerous experiment repetitions involved. This paper introduces the probe qubit protocol (PQP)-for quantum simulation of 2DES on quantum devices-addressing these challenges. The PQP offers several enhancements over standard methods, notably reducing computational resources, by requiring only a single-qubit measurement per circuit run and achieving Heisenberg scaling in detection frequency resolution, without the need to apply expensive controlled evolution operators in the quantum circuit. The implementation of the PQP protocol requires only one additional ancilla qubit, the probe qubit, with one-to-all connectivity and two-qubit interactions between each system and probe qubits. We evaluate the computational resources necessary for this protocol in detail, demonstrating its function as a dynamic frequency-filtering method through numerical simulations. We find that simulations of the PQP on classical and quantum computers enable a reduction on the number of measurements, i.e., simulation runtime, and memory savings of several orders of magnitude relative to standard quantum simulation protocols of 2DES. The paper discusses the applicability of the PQP on near-term quantum devices and highlights potential applications where this spectroscopy simulation protocol could provide significant speedups over standard approaches such as the quantum simulation of 2DES applied to the Fenna-Matthews-Olson (FMO) complex in green sulfur bacteria.

In the $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A =$ K, Rb, Cs) kagome materials, superconductivity coexists with a charge density wave (CDW), constituting a new platform to study the interplay of these two orders. Despite extensive research, the symmetry of the superconducting order parameter remains disputed, with experiments seemingly supporting different conclusions. As key aspects of the physics might lie in the intertwining of electronic orders, a better understanding of the impact of the CDW on superconductivity is crucial. In this paper, we develop a phenomenological framework to study the interplay of superconductivity and CDW order. In particular, we derive a Ginzburg-Landau free energy for both superconducting and CDW order parameters. Given the unclear nature of the superconducting state, we discuss general pairing symmetries with a focus on $s$-wave, $d$-wave, and pair-density-wave order parameters. Motivated by experiments, we consider the additional breaking of time-reversal or point-group symmetries of the CDW and determine in detail the consequences for the superconducting state. Our results show how the superconducting state mimics the broken symmetries of the CDW and can guide future microscopic calculations, as well as the experimental identification of the superconducting state in the $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ compounds.

Aberrant oscillatory activity is a hallmark of several brain disorders including Parkinson's disease (PD). Specifically, interactions between neurons of the subthalamic nucleus (STN) and globus pallidus externus (GPe) may contribute to the emergence and maintenance of overly synchronized beta-band (15–30 Hz) oscillations and may be associated with the motor symptoms of PD. Excessive beta synchrony can be mitigated by pharmacological intervention and deep brain stimulation (DBS). Alternatively, brain stimulation strategies that aim to selectively modulate interpopulation connections may have therapeutic potential. Here, we tested computationally whether dual targeting of STN and GPe by time-shifted stimulation can modulate pathologically strong synapses through inhibitory spike-timing-dependent plasticity. More specifically, we examined how time-shifted paired stimuli delivered to the STN and GPe can lead to interpopulation synaptic rewiring. To that end, we first theoretically analyzed the optimal range of stimulation time shift and frequency for effective synaptic rewiring. Then, as a minimal model for generating oscillations in healthy and PD conditions, we considered a STN-GPe loop with biologically inspired model parameters. Time-shifted stimulation modified STN-GPe interactions by long-lasting synaptic rewiring. This ultimately caused desynchronizing aftereffects, resulting in a reduced coupling of the STN-GPe network and restoration of healthy dynamics. Our findings demonstrate the critical role of neuroplasticity in shaping long-lasting stimulation effects and contribute to the optimization of a variety of multisite stimulation paradigms aimed at reshaping dysfunctional brain networks by targeting inhibitory plasticity.

Systems driven by innovation, a pivotal force in human society, present various intriguing statistical regularities, from the Heaps' law to logarithmic scaling or somewhat different patterns for the innovation rates. The urn model with triggering (UMT) has been instrumental in modeling these innovation dynamics. Yet a generalization is needed to capture the richer empirical phenomenology. Here we introduce a time-dependent urn model with triggering (TUMT), a generalization of the UMT that crucially integrates time-dependent parameters for reinforcement and triggering to offer a broader framework for modeling innovation in nonstationary systems. Through analytical computation and numerical simulations, we show that the TUMT reconciles various behaviors observed in a broad spectrum of systems from patenting activity to the analysis of gene mutations. We highlight how the TUMT features a “critical” region where both Heaps' and Zipf's laws coexist, for which we compute the exponents.

Recently, many experiments have been conducted with the goal of demonstrating a quantum advantage over classical computation. One popular framework for these experiments is Gaussian boson sampling, where quadratic photonic input states are interfered via a linear optical unitary and subsequently measured in the Fock basis. In this paper, we study the modal entanglement of the output states in this framework just before the measurement stage. Specifically, we compute Page curves as measured by various Rényi-$\alpha$ entropies, where the Page curve describes the entanglement between two partitioned groups of output modes averaged over all linear optical unitaries. We derive these formulas for $\alpha =1$ (i.e., the von Neumann entropy) and, more generally, for all positive integer $\alpha$, in the asymptotic limit of infinite number of modes and for input states that are composed of single-mode-squeezed-vacuum state with equal squeezing strength. We then analyze the limiting behaviors when the squeezing is small and large. Having determined the averages, we then explicitly calculate the Rényi-$\alpha$ variance for integers $\alpha >1$ and are able to show that these entropies are weakly typical.

Quantum noise reduction below the shot-noise limit is a signature of light-matter quantum interaction. A limited amount of squeezing can be obtained along the transient evolution of a two-level system resonantly interacting with a harmonic mode. We propose the use of optimal quantum control over the two-level system to enhance the transient noise reduction in the bosonic mode in a system described by the Jaynes-Cummings model. Specifically, we propose the use of a sequence of Gaussian pulses in a time window where the dissipative effects are negligible. We find that the correct choice of pulse times can reduce the noise in the quadrature field mode well below the shot noise, reaching reductions of over 80%. As the Jaynes-Cummings model describes a pivotal light-matter quantum system, our approach for noise reduction provides an experimentally feasible protocol to produce a nontrivial amount of squeezing with current technology.

Estimating the expectation value of a Hamiltonian and performing a Hamiltonian simulation are two fundamental tasks in quantum computation, with their efficiency heavily dependent on the Pauli norm of the Hamiltonian, which sums the absolute values of its Pauli coefficients. In this work, we propose a variational quantum algorithm called variational quantum Hamiltonian engineering (VQHE) to minimize the Pauli norm of a Hamiltonian, thereby reducing the overhead for expectation value estimation and Hamiltonian simulation. We first develop a theoretical framework that transforms the Pauli norm minimization problem into a vector $l_1$-norm minimization problem. We then design an appropriate cost function and employ parametrized quantum circuits to variationally minimize this cost function. Numerical experiments demonstrate the effectiveness of VQHE in reducing the Pauli norm for both the Ising Hamiltonian and molecular Hamiltonians. Furthermore, we show that VQHE is compatible with grouping strategies, enabling further reductions in measurement complexity for expectation value estimation. Our results highlight the potential of VQHE to enhance the efficiency of quantum algorithms in near-term quantum devices, offering a promising approach for practical quantum computing applications.

Adherent cells have long been known to display two modes during migration: a faster mode that is persistent in direction and a slower one where they turn. Compared to the persistent mode, the turns are less studied. Here we develop a simple yet effective protocol to isolate the turns quantitatively. With the protocol, we study different adherent cells in different morphological states and find that, during turns, the cells behave as rotors with constant turning rates but random turning directions. To perform tactic motion, the cells bias the sign of turning towards the stimuli. Our results clarify the bimodal kinematics of adherent cell migration. Compared to the rotational-diffusion-based turning dynamics, which has been widely implemented, our data reveal a distinct picture, where turns are governed by a deterministic angular velocity.

We study subsystem entropies in 2d CFTs for subsystems constituting a finite fraction of the full system. We focus on the extensive contribution, which scales linearly with the subsystem size in the thermodynamic limit. We employ the so-called diagonal approximation to evaluate subsystem entropy for chaotic CFTs in the thermal state (canonical ensemble), the microcanonical ensemble, and in a primary state, matching previously known results. We then proceed to find analytic expressions for the subsystem entropy at leading order in $c$, when the global CFT state is the KdV-generalized Gibbs ensemble or the KdV-microcanonical ensemble. Previous studies of primary eigenstates have shown that, akin to the fixed-area states in AdS/CFT, the corresponding subsystem entanglement spectrum is flat. This behavior is seemingly in sharp contradiction with that of the thermal (microcanonical) state, and thus in apparent contradiction with the subsystem eigenstate thermalization hypothesis (ETH). In this paper, we resolve this issue by comparing the primary state with the KdV-(micro)canonical ensemble. We show that the results are consistent with the KdV-generalized version of the subsystem ETH, in which local properties of quantum eigenstates are governed by their values of conserved KdV charges. Our paper solidifies evidence for the KdV-generalized ETH in 2d CFTs and emphasizes Rényi entropy as a sensitive probe of the reduced-density matrix.