Papers

In this paper, we study the ferromagnetic nearest-neighbor Ising model on rooted spherically symmetric trees with one or \(q\) children per vertex, according to a prescribed sequence of branching levels. Unbounded runs of one-child levels force uniqueness at every nonzero homogeneous field and every finite inverse temperature. We quantify this effect through the locations of sufficiently long nonbranching stretches. Conversely, uniqueness need not entail any uniform rate: for each prescribed vanishing sequence, we construct a density-one tree whose finite-volume boundary influence decays more slowly along a subsequence. The tree retains branching number \(q\), although its nonzero-field coexistence region disappears. For eventually bounded gaps, we prove an optimal uniform comparison with the periodic tree having the largest allowed gap and obtain an explicit interval of coexistence fields. Thus bounded gaps are equivalent, within this family, to coexistence at some finite temperature and nonzero field. For eventually periodic gaps, Gibbs uniqueness is equivalent to fixed-point uniqueness of the full-period return map. A negative Schwarzian derivative yields a complete classification: in the supercritical regime the map has three fixed points inside a closed coexistence interval, two at its endpoints, and one outside. The nonzero endpoints are automatically nondegenerate folds, with square-root splitting of the merging branches.

We study a dynamical model of repulsive needles with centers fixed on a square lattice. Needles that overlap are active and receive a repulsive rotation $ \theta \in [0,\epsilon)$; needles with no overlap do not move. This model exhibits an absorbing state transition. Nematic order was observed for long needles. For a range of needle lengths and $\epsilon$, the system self-organizes into a state with checkerboard symmetry. As $\epsilon$ is increased, this phase melts and becomes disordered. Remarkably, we find that this phase boundary exhibits critical exponents identical to those of the equilibrium 2D Ising model.

The sign problem remains a major obstacle to extending the success of Monte Carlo methods to generic quantum many-body systems. A powerful alternative relies on cluster expansions, which provide convergent representations of free energies and related quantities, with applications ranging from tensor network contractions to quantum dynamics and circuits. Within their convergence regime, these expansions often yield deterministic polynomial-time algorithms. However, such methods require exhaustive enumeration of connected clusters, leading to a computational overhead of $(N\varepsilon^{-1})^{\mathcal{O}(\log\Delta)}$, where $N$ is the system size, $\varepsilon$ the desired precision, and $\Delta$ the interaction-graph degree. This becomes particularly severe in long-range systems, where $\Delta\equiv N$, resulting in quasi-polynomial runtimes. Here, we introduce a Markov chain algorithm that samples cluster expansions directly in the space of connected clusters, replacing deterministic enumeration by Monte Carlo sampling. Because sampling occurs in an abstract cluster space rather than a physical configuration space, the conventional exponential sign problem is absent within the convergence regime. For general polymer models, we establish an FPRAS with runtime $\tilde{\mathcal{O}}(N^4\varepsilon^{-3})$. For quantum partition functions at temperatures $\beta\leq\beta_{\mathrm{sampling}}\equiv\mathcal{O}(1)$, this improves to $\tilde{\mathcal{O}}(N^{3+1/D}\varepsilon^{-3})$, where $D$ is the lattice dimension. The framework directly applies to long-range quantum systems with interactions $\propto1/r^\alpha$, including $2$-local models with $\alpha>2D$.

When the two largest eigenvalues of an entanglement or negativity spectrum meet, the gap of the corresponding entanglement or negativity Hamiltonian closes while entropies stay smooth, an event we call a temporal criticality. We ask when such criticalities occur in open fermionic systems, in which order, and whether they precede the geometric decoherence time, at which the negativity starts to fall. We compare loss and gain, which respect fermion parity only on average (weak symmetry) and keep the state Gaussian, with density dephasing, which respects it in every jump (strong symmetry) and makes the state non-Gaussian. We find that Gaussianity, rather than the symmetry, fixes the criterion for a criticality. In a Gaussian state the entanglement gap of a subsystem closes exactly when its two parity sectors carry equal weight, and the negativity gap closes exactly when this happens for the subsystem or its complement, so the negativity criticality never comes after the entanglement one. Uniform balanced loss and gain only shrink the two parities and leave both criticalities in place at every rate, for any quadratic Hamiltonian. In an open Kitaev chain, weak imbalanced loss and gain shift the criticalities by amounts set by the occupations at the cut, and at strong rates they allow a closing near the relaxation time only when an odd number of neighboring sites pass half filling. For dephasing we solve the non-Gaussian dynamics exactly at the point where the bond terms of the chain commute. Weak dephasing delays both criticalities and, away from the chain ends, moves them ahead of the parity balance, where the parity rules of Gaussian states would place them. As the dephasing rate approaches critical damping, both criticalities recede to infinite time, and at strong dephasing the negativity starts to fall long before either gap begins to shrink.

Krylov subspace methods provide an efficient tool for modeling any quantum initial value problem as a one dimensional chain. A time ordered path formulation, in which the dynamical generator successively splits probability between paths, yields a speed limit within such dynamical subspaces. For power law growing Lanczos coefficients $b_n \sim n^\delta$ we find super ballistic lightcones, with an exponentially spreading lightcone for maximal growth $\delta = 1$. Causality in the Krylov chain constrains the Lanczos coefficients to grow at most linearly. We illustrate the validity of the above in the $SL(2, R)$ and Heisenberg Weyl algebras, and in a many body skew field Ising model. Moreover, we extend the above bound to the family of $Q$ complexities. Lastly, mapping to a spin chain gives a Lieb Robinson bound analogue and opens the problem to standard condensed matter methods.

Correlation functions are central to understanding the behavior of quantum systems, with their spectra giving direct access to quasiparticle and collective excitations. However, the long-time evolution required for sufficient spectral resolution is challenging to reach for both classical and quantum simulations. In this work, we introduce a principled approach for extending time series of quantum correlation functions and reconstructing their spectral densities, based on their connection with covariance sequences of stationary stochastic processes. This connection enables us to apply Burg's maximum-entropy principle to find the least-committal extension compatible with the measured values of the correlation function, which corresponds to an all-pole autoregressive model whose coefficients solve a set of Yule–Walker equations. The resulting extension is positive semi-definite by construction, guaranteeing the positivity of the spectrum and the automatic satisfaction of its total spectral weight sum rule. The approach applies to both scalar and matrix-valued correlation functions, including those with highly structured or continuous spectra. The generalization to the matrix case makes it possible to trade simulation time for additional measured correlation functions, enabling accurate time-series extension and spectral reconstruction from short-time data, even in the presence of noise.

In fault-tolerant block encodings of structured Hamiltonians, the support geometry can set how the non-Clifford cost of SELECT scales with the system size, however many operators act on each support. We construct permute-act-unpermute circuits: a CSWAP network fixed by this geometry brings a selected support to a fixed target register, a shared local circuit acts there, and the permutation is undone. The operators add only an $XZ$ mask on this register, at a cost independent of the system size, and one query can mix several support geometries. For two-site supports, we establish and attain the minimum CSWAP count within address-controlled networks of site transpositions. Compiled for Pauli terms, these circuits use $8\mathrm{S}N+o(N)$ $T$ gates with $O(\log N)$ permutation work qubits, where $N$ is the number of system qubits and $\mathrm{S}$ is determined by the support geometry, with $\mathrm{S}=1$ for nearest-neighbour interactions and $\mathrm{S}=3/2$ for all-to-all pairs; in both cases the correction is $O(\log N)$. We also introduce a bridged CSWAP, which remembers the logical value of its temporary AND across the target action and repairs it from the prepared labels, so that the inverse CSWAP undoes the exchange without recomputing the value. When the repair is Clifford, it halves the $T$ count of a matched forward-inverse CSWAP pair at the cost of one retained work qubit. For a Heisenberg ring, the complete block-encoding query reduces the $T$ count by a factor approaching $3$ as the system size grows, relative to flat and product-wise Pauli walks. For a five-orbital Anderson impurity model, which combines nearest-neighbour and all-to-all support geometries, the reduction is about $1.7$ at large bath sizes, relative to the cheapest of three comparators, each built from the methods of the references it follows.

Given a finite-range, non-commuting Hamiltonian on a 1D chain of finite spins, we prove a modified logarithmic Sobolev inequality with constant $\Omega(1/\log n)$ for the heat-bath dynamics, a quasi-local Gibbs sampler, and for the regularised heat-bath dynamics. This implies rapid mixing of both samplers towards the Gibbs state in relative entropy and trace norm, with mixing times of order $\mathcal{O}(\log n\cdot \log(n/\epsilon))$. The interactions may be spatially inhomogeneous. The proof combines weak quasi-factorisation of relative entropy, decay-of-correlation estimates, a uniform conditional local gap, and a buffered comparison between conditional entropy and quadratic energy. The resulting bounded entropy defect is removed using the global gap. To the best of our knowledge, this is the first proof of MLSI in the non-commuting regime.

Fermionic non-Gaussianity is a key resource for universal quantum computation, and its behavior in quantum many-body systems has attracted growing interest. Recently, a convolution-based measure, which we call the magic Rényi entropy (MRE), has been proposed as a resource measure of non-Gaussianity, but its evaluation is limited to small systems due to the computational cost growing exponentially with system size. In this work, we develop a perfect-sampling method to calculate the second-order MRE from matrix product states (MPSs). Our method uses a bounded estimator to control sampling fluctuations and a recursive sweep to draw the samples directly from the input MPS, which allows us to generate each sample with $\mathcal O(nD^3)$ time, where $n$ and $D$ denote the number of modes and MPS bond dimension, respectively. We benchmark our method on the XXZ chain with up to $128$ sites, demonstrating that the MRE captures intricate higher-order correlations at large scales, which are inaccessible to covariance-based measures. These results provide a computational tool that quantitatively evaluates many-body fermionic non-Gaussianity by accounting for higher-order correlations.

For any physical process, varying the initial distribution over its states will change the resulting expected entropy production (EP). An initial distribution that minimizes the EP of a particular process is called the prior of that process. Varying the microphysical details of the process will change its prior. We consider the following question: if an engineer wants to design a system to implement a given map, what prior should they design into the system to minimize the EP for the worst-case actual distribution? We refer to the resulting optimal worst-case value as the minimax EP, and investigate how it depends only on the dynamics of the process. We derive the closed-form solution to this minimax problem when the map is deterministic. We also show that for stochastic maps, a worst-case actual distribution can always be chosen to be a point mass on a single state, and that the associated minimax prior resembles a Boltzmann-Gibbs equation and can be found by a globally convergent numerical algorithm. We further show that the minimax EP is the maximum uncertainty about the input that remains after observing the output. Finally, we extend the analysis to the continuous-time regime, showing that the minimax instantaneous EP diverges, while the corresponding finite-time minimax EP has a universal short-time scaling set by the largest escape rate of the dynamics.

Renormalization group (RG) flows for systems subject to an external field can be derived either by fixing the field or by fixing the conjugate order parameter. We show how to implement these boundary conditions within the functional renormalization group approach. We derive and compare the corresponding flow equations for $\phi^4$ theory and show that some scaling variables and scaling exponents associated with the linearized flow of the relevant three-point vertex in the vicinity of the Ising fixed point depend on the boundary conditions. We also discuss the effect of elasticity on Ising criticality. In this case two of the fixed points (namely the renormalized Ising fixed point and the spherical fixed point) obtained for constant strain are shifted to physically inaccessible regimes of parameter space when we perform the RG at constant stress.

Climate oscillations are intrinsically out-of-equilibrium phenomena, yet the connection between their predictability and nonequilibrium thermodynamic properties remains unexplored. We develop a coarse-grained stochastic thermodynamic framework for Ornstein-Uhlenbeck (OU) processes and apply this framework to climate data via linear inverse models (LIMs), linking predictability, entropy production, dynamical activity, and path action. Climate oscillations are often studied in a 2d phase space of climate indices, which are even under time-reversal, motivating our focus on 2d OU dynamics with even variables. We find that coordinate-invariant properties of 2d OU processes can be reduced to a minimal three-parameter description: two diffusivities and a phase-space rotation. We show that these quantities fundamentally characterize distinct aspects of the dynamics. We find that higher irreversibility and dynamical activity do not necessarily imply reduced predictability. Rather, it is the path action which is most closely connected to a commonly used measure of predictability, the anomaly correlation coefficient (ACC). As an illustrative example, we apply this framework to the Madden-Julian Oscillation (MJO) over the twentieth century. We find that the MJO has become simultaneously more predictable, as seen previously, while at the same time becoming more irreversible and more active. Predictability is driven predominantly by the reduced mean diffusion. Entropy production reflects the combined evolution of all three parameters. These results suggest that stochastic thermodynamics provides a powerful lens for studying nonequilibrium climate phenomena.

We study the full counting statistics of the integrated current in a one-dimensional hard-rod gas in equilibrium, employing two recently proposed fluctuating hydrodynamic frameworks: (i) Ballistic Macroscopic Fluctuation Theory (BMFT) and (ii) diffusive fluctuating hydrodynamic theory based on correlated Brownian motion approximation of hard-rod quasiparticles (CBFHD). We investigate how the predictions of these two approaches compare with each other and with the underlying microscopic dynamics. We show within BMFT that the current distribution admits a large-deviation form under ballistic scaling, and we derive an explicit expression for the large-deviation function, valid for an arbitrary inhomogeneous initial state factorized in point-particle coordinates. The corresponding current cumulants are also obtained. We subsequently analyze the current statistics within the CBFHD framework, which explicitly incorporates stochastic noise and dissipative terms, and demonstrate that the current distribution likewise obeys a large-deviation principle in this approach. We find that, while BMFT predictions for the first few cumulants and the rate function are in excellent agreement with direct numerical simulations of the microscopic hard-rod dynamics, CBFHD prediction is not. We further verify the predictions of the CBFHD independently using a collection of correlated Brownian motions, which provides an approximate description of the dynamics of hard-rod quasiparticles. Our findings indicate that CBFHD does not accurately capture large-scale current fluctuations in the hard-rod gas, whereas BMFT yields predictions in quantitative agreement with the microscopic dynamics, at least in the context of full counting statistics.

We consider the $\phi^4$ theory with $\phi(x)\in\mathbb{R}$ in three Euclidean dimensions. For a variety of self-couplings $\hat{\lambda}$, the critical (bare) parameter $\hat{\mu}_{0\mathrm{c}}^2(\hat{\lambda})$ is determined where the lattice-regulated system changes from the symmetric phase to the broken phase. Next, we send the box volume to infinity and switch to a universal scheme; this yields $\hat{\mu}_\mathrm{c}^2(\hat{\lambda})$ for each simulated $\hat{\lambda}$. Finally, a continuum extrapolation gives $f_\mathrm{c}=\lim_{\hat{\lambda}\to0} \hat{\lambda}^2/\hat{\mu}_\mathrm{c}^2(\hat{\lambda})$, and we find $f_\mathrm{c} = 18.808(64)_{\mathrm{stat}}(45)_{\mathrm{sys}} = 18.808(78)_{\mathrm{tot}}$. In addition, $\Delta\langle\phi^2\rangle_\mathrm{c}/\lambda = -0.00303(12)_{\mathrm{stat}}(12)_{\mathrm{sys}} = -0.00303(17)_{\mathrm{tot}}$ is determined in the combined continuum and infinite-volume limit.

In a world fraught with uncertainty, it behooves us to consider the most disastrous possible outcomes, in order that we can best mitigate against them. Often these are extreme risk events – of high consequence, but low probability. Yet, the rarity of such events limits our ability to study them; there is a paucity of past occurrences to draw upon, and sampling such rare events from models is typically costly in time. Here, we introduce an approach for rare-event sampling based on quantum stochastic models. This integrates the memory advantages of quantum stochastic modelling – and its associated efficient means of preparing quantum sample states – with the `speed-ups' of quantum amplitude amplification, to yield simultaneous reductions in spatial and temporal computational complexity compared to classical Monte Carlo-based approaches.

We investigate the relationship between long-range degree correlations and fractality in scale-free random networks. By analyzing degree correlations in scale-free random networks at the percolation threshold, at which a giant component emerges, we derive the ball volume $\tilde{\nu}_k(l)$, defined as the average number of nodes within distance $l$ from a root node with degree $k$. The resulting expression predicts a degree-dependent structural crossover. For $l\ll k^{1/(\df-1)}$, the ball volume grows as $\tilde{\nu}_k(l)\sim kl$, whereas for $l\gg k^{1/(\df-1)}$, it crosses over to the global fractal scaling $\tilde{\nu}_k(l)\sim l^{\df}$. Here, $\df$ is the fractal dimension of critical scale-free random networks. We further show that the structural crossover can be naturally understood in terms of critical branching processes and is also observed in empirical fractal networks.

We study an equilibrium system, where linear molecules with a rigid charge distribution interact via the mean-field generated by the Coulomb coupling. We focus on the nonlinear regime, which is valid close to external charges immersed in the system. The finite molecular size in this regime leads to a nonlocal response at short distances. First, we show that the mean-field potential is non-monotonic, i.e., like charges can attract each other. Second, we show that the polarization induced by an external charge (and hence its solvation structure) depends on the sign of this charge, violating the effective C-symmetry of the macroscopic electrodynamics. We identify several scenarios of this effect, characterize it with the free energy and entropy differences, and compare it with analogous effects in asymmetric electrolytes described by nonlinear Poisson-Boltzmann equations.

Disordered stealthy hyperuniform (SHU) systems are emerging as platforms for controlling classical and quantum transport due to vanishing single-scattering contributions in the stealthy regime. Here, to our knowledge, we present the first perturbation theory of one-dimensional quantum transport through a continuum of identical point scatterers with SHU positional disorder. Our perturbation theory indicates the exact cancellation of all the lower-order terms due to the Fourier-space stealthy condition $S(q)=0$, and the further suppression of the lowest non-vanishing fourth order in the Lyapunov exponent $\lambda(k)$ due to the real-space hyperuniform constraint $\lim\limits_{D\to\infty}\sigma_D^2=c<\infty$. Our findings presents universal implications of the general wave-propagation phenomena in disordered SHU systems.

Selective advantage leads to the proliferation of a species into an ecosystem. On the other hand, self-propulsion can lead to dynamic clustering of individuals. To analyze the intricate effects produced by such competing processes, we introduce a minimal model for a proliferating active population, where run-and-tumble migration is combined with a stochastic birth-death process. Beginning with the microscopic dynamics of the particles, we derive the corresponding hydrodynamic equations and validate them through numerical simulations. We demonstrate that the inclusion of activity leads to the emergence of novel morphological patterns, which are sensitive to the specific rules governing migration. Furthermore, we show that activity significantly alters the characteristics of invasion waves, increasing their propagation speed. However, beyond a threshold, excessive activity disrupts the wave-like nature of the invasion process. We also extend our study to two dimensions and analyze the instabilities that lead to pattern formation in such systems.

Counterdiabatic driving provides a universal route to fast quantum control, but its standard formulation presupposes a Hamiltonian generator. We develop a Hamiltonian-free theory of the adiabatic gauge potential (AGP) for parameter-dependent unitary operators $U_\lambda$. Exact and regularized versions of the AGP follow from a Hermitian, banded linear system at a cost comparable to the Lanczos construction in the Hermitian case, requiring neither diagonalization nor a matrix logarithm. We demonstrate rapid convergence of the truncated Krylov approximation for the kicked top and for an integrable brickwork circuit built from unitary $\check{R}$ matrices, a setting in which no local effective Hamiltonian is available. Our results extend shortcuts to adiabaticity, and AGP-based diagnostics of chaos, to Floquet systems and quantum circuits.

Random projective measurements are an effective tool to model the interlinked phenomenology of monitoring, inferring, and decoding highly entangled states such as quantum error-correcting codes. At the same time, the study of such monitored dynamics has opened a new arena for critical phenomena, renewing longstanding questions in disordered statistical mechanics, including percolation, random-bond models, and Nishimori physics. Here we investigate the robustness of stabilizer quantum error-correcting codes under a single round of independently sampled single-qubit Pauli measurements and demonstrate that their threshold behavior falls into two broad categories - geometric and homological percolation transitions, with the toric code and color code being the principal examples for each class. We establish the distinct character of these two threshold theories by analyzing the logical-support criteria of these codes and by providing numerical estimates of their respective critical exponents obtained from optimized stabilizer simulations of large-scale systems with over one million qubits. Our framework extends to non-CSS, subsystem, higher-dimensional, and Floquet stabilizer codes and allows us to determine their respective threshold phase diagrams. We exemplify how the latter provide quantitative and qualitative guidance for the computationally more demanding problems of tunable learning and maximum-likelihood decoding. As a practical application of our framework, we discuss the robustness of the gross code.

We conjecture that the universal logarithmic coefficient for capacity of entanglement $c_{\mathrm{cap}}$ is bounded below by the corresponding entropy coefficient $c_{\mathrm{eff}}$ at conformal interfaces. We prove the bound in free boson and fermion CFTs and in holographic models with interface branes, and establish it using defect perturbation theory. Numerical calculations at interacting interfaces between the tricritical Ising and Ising CFTs further support the bound. Despite this constraint, capacity provides independent interface data. We construct interfaces with identical entropy and energy transmission coefficients but different capacity coefficients, and show that capacity can even increase as entropy decreases.

Nearest-neighbor (NN) tight-binding models (TBMs) on plaquette-centered $\{ 10,3\}$ (Schläfli symbol), $\{ 8,3\}$, and $\{ 8,4\}$ hyperbolic lattices on a Poincaré disk with open boundary conditions display a vanishing, a finite, and a diverging density of states (DOS) near zero energy (band center), respectively, yielding a Dirac liquid, a Fermi liquid, and a flat band. Emergent bipartite nature of these lattices within the framework of NN-TBMs, allows us to scrutinize the impact of mass disorder on the electronic states and DOS therein. From extensive numerical calculations of the average and typical DOS using the kernel polynomial method, we show that hyperbolic Dirac liquid remains stable against weak mass disorder, undergoing a semimetal-to-metal quantum phase transition at moderate disorder, followed by an Anderson metal-to-insulator transition at even stronger disorder. The remaining two systems display only the latter transition. Critical exponents near all these transitions are found to be close to the ones mediated by on-site potential disorder.

Porter-Thomas statistics are a characteristic feature of the output distribution of random quantum states and, more broadly, chaotic quantum many-body systems. Convergence to Porter-Thomas plays a central role in random circuit sampling and experimental demonstrations of quantum advantage, where the output statistics of low-depth random quantum circuits are expected to be approximately Porter-Thomas, despite the absence of a rigorous proof of convergence. We show that the output distribution of polynomial-depth brickwork random circuits converges inverse-polynomially in total variation distance to the Porter-Thomas distribution. Specifically, consider the output probability distribution over a fixed bitstring of a local random quantum circuit, constructed from nearest-neighbor Haar random gates. Then, for any $m \geq 0$, the distribution corresponding to circuits of depth $O(n^{2m+1}\log(n))$ is at most $O(1/n^m)$ far in total variation distance from the Porter-Thomas distribution. Our proof uses moment bounds from approximate designs, analytic estimates for characteristic functions, and a local anticoncentration property for inverse moments.

Schur sampling is a fundamental primitive for extracting permutation-invariant information from many-body quantum systems and has broad applications in quantum information science. Circuit-based implementations typically rely on coherent representation-theoretic operations such as Clebsch-Gordan transforms, generalized phase estimation, or quantum Fourier transforms over the symmetric group. We show that unitary Schur sampling of arbitrary permutation-invariant mixed states on $n$ $d$-dimensional qudits can instead be implemented using only pairwise SWAP tests, namely, two-qudit projective measurements onto the symmetric and antisymmetric subspaces. Our protocol achieves error $\epsilon$ in diamond distance using $O(n\min\{n,d\}^{3}\log^2(n/\epsilon))$ random SWAP tests. The central idea is to repeatedly identify and extract the largest antisymmetric subsystem. This turns unitary Schur sampling into a search for antisymmetry and gives the algorithm a natural interpretation as a stochastic traversal of a Young diagram. The protocol preserves the $\mathrm{SU}(d)$-irrep state while preparing a canonical pure state in the multiplicity subsystem. As an application, we consider quantum purity amplification (QPA), in which multiple noisy copies of a pure quantum state are combined to produce a state of higher purity. We show that the optimal purified state can be obtained by retaining a single designated output qudit and discarding the rest.

Tensor networks are powerful tools for simulating quantum many-body systems, but the growth of spatial entanglement severely limits the direct evolution of pure states under chaotic unitary circuits. Here we consider a more targeted task: the approximate strong simulation of a specified output probability of a 1D chaotic brick-wall circuit at finite relative precision. Given input and output bit strings $\by$ and $\bx$, we evaluate $p(\bx|\by)=|\bra{\bx}U(T)\ket{\by}|^2$ using the Sweeping RTM algorithm, a transverse tensor-network contraction based on reduced transition matrices (RTMs). The algorithm compresses the left and right temporal boundary states jointly, seeking an output probability that converges across spatial cuts and as the bond dimension is increased. For chaotic one-dimensional brick-wall circuits at a fixed relative target precision, we find numerical evidence that the bond dimension required to obtain stable estimates grows subexponentially over the accessible time window. Our findings open a direct route to classical probability queries for chaotic quantum circuits, with potential applications to benchmarking and learning tasks.

Fermionic non-Gaussianity is a resource for universal quantum computation that can be generated by interactions in quantum many-body systems. Using the magic Rényi entropy (MRE) as a measure of non-Gaussianity, we derive its universal upper bound and Haar mean, proving that typical Haar-random states attain the maximal MRE density of $\ln(4/3)$ per Majorana in the large-system limit. We also show that the MRE can differ extensively between states with identical covariance matrices. To investigate how non-Gaussianity grows toward this maximal density, we evolve a Gaussian state in imaginary and real time under the Sachdev-Ye-Kitaev Hamiltonian. By varying the imaginary- and real-time durations, we identify a first-order transition marked by a kink in the MRE density and spontaneous breaking of the permutation symmetry among the four copies used to evaluate the MRE. This transition represents a qualitative change in the non-Gaussianity of the state that is not reflected in the thermal free energy.

We show that a two-dimensional chiral fluid supports an antisymmetric contribution to the pressure, and determine its microscopic expression. Its origin lies outside the standard kinetic and collisional channels of the normal pressure tensor, stemming instead from the average of a parity-breaking pseudo-scalar. This chiral pressure is set by the rotational (vortex) viscosity of micropolar hydrodynamics, whose kinetic value for rough disks we compute here, to Gaussian order. Crucially, both the chiral pressure and the rotational viscosity survive at zeroth order in the gradients, meaning they persist even in the fully homogeneous fluid – which we show is not only well defined but steady (the Quiescent Chiral State, QCS). Since this averaged pseudo-scalar does not vanish in a chiral fluid, any expansion of its distribution function must contain terms in this pseudo-scalar variable.

We present an analysis of pulsar spin noise based on physically-motivated two-component models of spin wandering. We focus on two models, distinguished by their total angular momentum dynamics: a singular, nonstationary model with a diffusive total angular momentum, and a minimal, stationary model anchored on a conserved total angular momentum. We develop scalable Gaussian process methods and, using mock data, show that the two models are fully testable and distinguishable with full-state observations, i.e., simultaneous independent data on the crust and the superfluid rotational states. This paves a path to testing stationarity in pulsar spin noise, potentially achievable with joint continuous gravitational wave observations and radio timing of pulsars. However, robust inferences and predictions are harder to achieve, and depend on the priors and data quality, when only one component is observationally accessible.

We study coherent release from a finite serial Krylov sector into an exact conformal tail with asymptotically linear Lanczos coefficients. We derive the cumulative occupation up to a cut that moves to greater Krylov depth with time, tracking the probability accumulated behind the propagating front. This quantity separates the release dynamics of the finite sector from subsequent propagation through the tail. The tail sets the logarithmic transit scale, while the finite sector shapes the resulting distribution. The early edge records the number of serial steps before emission, while the late edge reflects slow resonances and interference and can also exhibit logarithmic enhancements. Thus, one- and two-site sectors can share the same leading resonance in their continued-fraction descriptions yet produce distinct cumulative occupation patterns. We illustrate this framework in thermal AdS$_2$, where a dressed oscillator yields, in the weak-coupling limit, a two-site shallow sector coupled to the conformal tail.