Analytical treatments of far-from-equilibrium quantum dynamics are few, even in well-thermalizing systems. The celebrated eigenstate thermalization hypothesis (ETH) provides a post hoc ansatz for the matrix elements of observables in the eigenbasis of a thermalizing Hamiltonian, given various response functions of those observables as input. However, the ETH cannot predict these response functions. We introduce a procedure, dubbed the statistical Jacobi approximation (SJA), to update the ETH ansatz after a perturbation to the Hamiltonian and predict perturbed response functions. The Jacobi algorithm diagonalizes the perturbation through a sequence of two-level rotations. The SJA implements these rotations statistically assuming the ETH throughout the diagonalization procedure and generates integrodifferential flow equations for various form factors in the ETH ansatz. We approximately solve these flow equations using statistical information about Jacobi rotations as input and predict both quench dynamics and autocorrelators in the thermal state of the perturbed Hamiltonian. The predicted dynamics agree with exact numerics in both random matrix models and spin chains, outperforming second-order time-dependent perturbation theory.

Stable operation of laser wakefield acceleration (LWFA) is essential for future applications of compact radiation sources and advanced accelerators. In this work, we investigate stabilization of LWFA electron beams through control of laser angular chirp and wavefront stability. We show that angular chirp strongly affects beam pointing stability and identify an instability-transfer chain that links laser-pointing fluctuations to group-delay dispersion, pulse-front tilt, and electron beam pointing jitter. Stabilization of the laser transport environment, including vacuum beam transport and thermal control, reduces wavefront fluctuations and improves beam stability in energy, charge, and pointing by factors of 2–4, enabling improved control of beam quality.

Unitary and dissipative models of quantum dynamics are linear maps on the space of states or density matrices. This linearity encodes the superposition principle, a key feature of quantum theory. However, this principle can break down in effective non-Hermitian dynamics arising from postselected quantum evolution. We theoretically characterize and experimentally investigate this breakdown in a dissipative superconducting transmon circuit. Within the circuit's three-level manifold, no-jump postselection generates an effective non-Hermitian Hamiltonian governing the excited two-level subspace and an anti-Hermitian nonlinearity. We prepare different initial states and use quantum state tomography to track their evolution under this effective, nonlinear Hamiltonian. By comparing the evolution of a superposition state to a superposition of individually evolved basis states, we test linearity and observe clear violations, which we quantify across the exceptional-point degeneracy of the non-Hermitian Hamiltonian. We extend the analysis to density matrices, revealing a breakdown in linearity for the two-level subspace while demonstrating that linearity is preserved in the full three-level system. These results provide an operational demonstration of postselection-induced nonlinearity in a controlled superconducting platform. The observed nonlinearity, organized by the exceptional-point degeneracy of the non-Hermitian Hamiltonian, is absent in classical non-Hermitian systems, where norm change reflects real exchange with an environment rather than renormalization.

Learning from imperfect data is a central theme in machine learning, connecting practical questions of robustness to fundamental questions of learnability. Here, we examine attribute noise: learning from corrupted inputs while keeping the labels intact, a setting that has received considerably less analytical attention than its label-noise counterpart. We consider two types of corruption models: additive noise and replacement noise. Through experiments with multilayer perceptrons (MLPs) on corrupted classification datasets, we find that neural networks remain robust, maintaining well-above-chance accuracy even when inputs are $>90\%$ corrupted—far beyond human recognition. To understand this robustness, we analyze infinite-width networks in the heavy-corruption regime using a mean-field-inspired approach and derive a leading-order decision rule for the classification outcome: The network implements a prototype rule, the nearest-class-mean, assigning each test point to the class whose training-set average it most closely resembles. This leading-order decision rule is universal across a broad range of MLP architectures, holding for any depth, as well as a wide class of activation functions and noise distributions. The same centroid mechanism closely matches finite-width network behavior in our experiments and provides an interpretable and analytically tractable account of why learning can succeed even when individual training examples carry almost no signal.

We use coupled-channel calculations to explore the nature of near-threshold bound states in a simplified model of $\mathrm{Rb}+\mathrm{KRb}$. This is a prototype for systems with very strong coupling at short range and chaotic behavior for the short-range states. We find that there are states with strong long-range character that exist close to threshold and probably persist to depths at least 100 GHz below each threshold. These states are only weakly coupled to the short-range states and do not form part of the chaotic manifold. Since they spend little time at short range, they are relatively insensitive to destruction by laser light. They can thus have long lifetimes that are unrelated to the density of states and can cause narrow Feshbach resonances when the states are shifted across thresholds by external fields.

Many well theoretically motivated models of ultralight dark matter are expected to give rise to feeble oscillatory forces on macroscopic objects. Optically trapped sensors have high force sensitivities but have remained relatively unexplored in this context. In this work, we propose a tunable, optically trapped sensor specifically designed to detect such forces. Our design features a high-mass ($\sim \mathrm{mg}$) plate whose high aspect ratio allows its weight to be supported by a vertical beam without excessive heating. We present the first systematic analysis and optimization of quantum noises in optically trapped systems and show that our setup has the potential to operate at the standard quantum limit with current off-the-shelf technologies. We demonstrate that our sensor could offer unique access to large regions of uncharted parameter space of vector baryon minus lepton dark matter, with projected sensitivities that could advance existing limits by several orders of magnitude over a broad range of frequencies.

The discovery of the ferroelectric nematic phase has brought with it a plethora of new polar liquid crystalline (LC) phases. One in particular is the antiferroelectric smectic A $\left({\mathrm{SmA}}_{\mathrm{AF}}\right)$ phase. In this article, we show via observation and analysis of satellite peaks in the x-ray scattering pattern that the structure of the ${\mathrm{SmA}}_{\mathrm{AF}}$ phase involves a one-dimensional density modulation of $\approx 10–20$ nm lateral to the smectic layer normal. Further, we demonstrate a previously undiscovered phase where the antiferroelectric order is maintained into a tilted smectic phase demonstrating the robustness of the underlying frustration that leads to the modulated structure. We suggest that the modulations are only in a single dimension and appear parallel to the tilt plane. This new phase also shows a significantly different and complex response to an electric field from other discovered polar LC phases due to the ability to modulate both tilt and polarization direction.

Finding the ground state of geometrically frustrated spin systems is a challenging problem with broad implications. Many hard optimization problems, including NP-complete problems, can be mapped, for instance, to frustrated Ising models, where competing interactions produce rugged, spin-glass-like energy landscapes. The difficulty is particularly pronounced in the weak-field regime, where geometrical frustration dominates, and the spectral gap becomes exponentially small, making it hard to identify the true ground state. In this work, we consider planar frustrated lattices constructed from the triangular motif, the minimal unit of geometrical frustration. We present a graph-based approach that allows for accurate state initialization of a frustrated triangular spin lattice with up to 20 sites while avoiding barren plateaus. To optimize circuit efficiency and trainability, we employ a clustering strategy that organizes qubits into distinct groups based on the maximum cut technique, which divides the lattice into two maximally disconnected subsets. We provide evidence that this Max-Cut-based lattice division offers a robust framework for optimizing circuit design and effectively modeling frustrated systems at polynomial cost. All simulations are performed within the variational quantum eigensolver formalism, the current paradigm for noisy intermediate-scale quantum devices, but can be extended beyond. Our results underscore the potential of hybrid quantum-classical methods in addressing complex optimization problems.

Unprecedented events intertwine with the repetition of the past in natural phenomena and human activities. Key statistical patterns, such as Heaps’ and Taylor’s laws and Zipf’s law, have been identified as characterizing the dynamical processes that govern the emergence of novelties and the abundance of repeated elements. Observing these statistical regularities has been pivotal in motivating the search for modeling schemes that can explain them and clarify key mechanisms underlying the appearance of new elements and their subsequent recurrence. In this study, we analyze sequences of novel and non-novel elements, referred to as avalanches, in real-world systems. We show that avalanche statistics provide a complementary characterization of innovation dynamics, extending beyond the three fundamental laws mentioned above. Although arising from collective dynamics, some systems behave as a single instance of a stochastic process. Others, such as natural language, exhibit features that we can only explain by a superposition of different dynamics. This distinction is not apparent when considering Heaps’ law alone, while it clearly emerges in the avalanche statistics. By interpreting these empirical observations, we also advance the theoretical understanding of urn-based models that successfully reproduce the observed behaviors associated with Heaps’, Zipf’s, and Taylor’s laws. We derive analytical expressions that accurately describe the probability distributions of avalanches and the Heaps law beyond its asymptotic regime. Building on these results, we derive a scaling relation that we show also holds in real-world systems, indicating a form of universality in the dynamics of novelty.

Discovering the microscopic composition of dark matter is one of the most important open problems in physics today. Axions are a leading candidate to be dark matter; however, a search of the full range of all likely axion masses is hampered by the standard quantum noise limit. This makes haloscope searches for axions with masses above $\sim 100\mu \mathrm{eV}$ unfeasible with current technologies. To overcome this limitation, we propose a photon counting technique designed to operate at 30–60 GHz for detecting axions with masses between 124 and $248\mu \mathrm{eV}$, based on a single electron in a Penning trap. The electron cyclotron mode absorbs microwave photons, and, via the continuous Stern-Gerlach effect, this absorption imparts a measurable phase shift onto the axial motion. In this paper, we comprehensively analyze this photon detection method. We introduce a type of fast, phase-sensitive axial detection technique, using axial-magnetron parametric amplification to overcome detector Johnson noise and cancel associated frequency shifts. This method may find other applications in precision Penning trap frequency measurements. We compare the efficiency of the electron single-photon counter with an ideal device and find that our proposed photon counter has sufficient performance to search for high-mass axions.

Angle-resolved photoemission spectroscopy (ARPES) provides the most direct experimental access to electronic band structures and many-body interactions in solids. Beyond energy and momentum, the measured intensity also carries detailed information about the initial-state wavefunction through the complex photoemission matrix element governing the transition to—and scattering character of—the photoelectron final state. Orbital tomography seeks to exploit this sensitivity to reconstruct electronic wavefunctions. However, its quantitative implementation has been hindered by the lack of direct information on the phase of the matrix element and by the nontrivial role of solid-state scattering. Here, we overcome these limitations by achieving an experimental reconstruction of the complex photoemission matrix element in quasi-freestanding monolayer graphene (QFMLG), including both amplitude and phase. By combining circular-dichroism ARPES with linearly polarized measurements within a controlled scattered-wave framework, we determine the full matrix element over a broad kinetic-energy range. The reconstructed amplitudes exhibit pronounced channel-selective resonances and Cooper minima, directly revealing substantial solid-state modifications beyond commonly used simplified models. Leveraging this quantitative reconstruction, we establish QFMLG as an easily available in situ intensity reference for ARPES. Its known complex matrix element enables direct normalization for the product of photon flux and detector response, allowing the determination of photoemission cross sections in other materials under identical experimental geometries. This advances orbital tomography by ARPES to a quantitatively normalized approach that separates the initial-state wavefunction from final-state scattering contributions, and more broadly may provide access to the associated quantum geometry.

This work investigates the nature of the ground state of the antiferromagnetic Heisenberg model on fundamental kagome cells, a triangle and a star, using the variational quantum eigensolver algorithm on real quantum hardware. We demonstrate that the ground-state preparation is achievable using a shallow hardware-efficient quantum circuit with a naturally Euclidean parameter space. Our custom ansatz is capable of accurately recovering meaningful properties of the ground state such as the spin-spin correlation terms and static structure factor without explicit error mitigation. These features are found to be resilient to noise. We exploited the Fubini-Study metric in constructing the ansatz, ensuring a singularity-free parameter space. With this ansatz design, the adaptive gradient descent optimizer achieves a faster convergence in terms of the number of iterations compared to simultaneous perturbation stochastic approximation. We further apply error mitigation techniques, including zero-noise extrapolation (ZNE) and qubitwise readout-error mitigation (REM). While ZNE does not obey the Rayleigh-Ritz variational principle, the conditions under which REM preserves it are discussed.

We connect the structure theorem for quasiprobability representations to quantum error correction. For a code space invariant under a subgroup of an extended Weyl-Heisenberg group, the Brif-Mann construction gives a semifunctorial representation whenever its kernel satisfies the Stratonovich-Weyl axioms and composes on channels covering full error-correction cycles. With phase-space parity available, a kernel other than the ordinary Wigner one exists iff the code space is invariant under a lattice of displacements: Among compact-phase-space bosonic codes, this is only the ideal Gottesman-Kitaev-Preskill family; in finite dimension, this is every qudit stabilizer code, whose negative volume for odd prime dimension is the syndrome-averaged logical magic. For rotation-symmetric, one-photon, non-Pauli qudit and spin codes, only the ordinary kernel remains, its negativity reflecting the physical carrier, not logical content; a sector-graded representation built from recovery isometries restores a resource reading. We add a channel atlas, a closed-form magic lifetime under displacement noise, a Kirkwood-Dirac layer, and finite-energy corrections.

Through a comprehensive free energy analysis, we demonstrate that finite temperature can simultaneously weaken superconductivity and mitigate Zeeman-effect-induced depairing, leading to potential nonmonotonic temperature-dependent behaviors in superconductors subjected to large exchange fields. Remarkably, superconductivity can be counterintuitively enhanced by temperature when the Zeeman energy exceeds the superconducting order parameter, owing to the competition between thermal and magnetic effects. We propose that multiband effect offers one possible microscopic route for this temperature-induced enhancement and demonstrate it explicitly within a two-band superconducting model. A detailed parameter analysis identifies the conditions under which this phenomenon emerges, suggesting that temperature-enhanced superconductivity may be observable in materials such as ${\mathrm{MgB}}_2$ and $\mathrm{FeSe}$ through transport and tunneling measurements.

Erasing memory is a fundamental operational task in quantum information processing, governed by Landauer's principle, which links information loss to thermodynamic work. We introduce and analyze assisted quantum erasure, where correlations with a remote system reduce the energetic cost of resetting a memory. We identify exclusive control of erasure as the central operational requirement: Only a designated party should be able to achieve the minimal cost, whereas any adversary must fail. In the device-dependent regime, we show that entanglement of formation exactly characterizes exclusivity, establishing entanglement as the decisive thermodynamic resource. Moving to a one-sided device-independent scenario, in which only the memory holder's device is trusted, we develop an operational erasure protocol based on random dephasing and conditional operations. Finally, in a fully device-independent setting, we show how Bell nonlocality and self-testing translate observed violations into lower bounds on any adversary's erasure capability, yielding a device-independent notion of exclusive thermodynamic control. Taken together, these results elevate quantum erasure from a thermodynamic constraint to an operational primitive: The erasure work cost quantifies secure, exclusive control over quantum memory, ensuring that an unauthorized agent cannot fully erase information under a bounded work budget.

We study the sample complexity of the prototypical tasks quantum purity estimation and quantum inner product estimation. The former has been a key subroutine for experimental benchmarking and entropy estimation, while the latter is a core task for cross-platform validation that compares the unknown quantum states produced by different physical platforms. In purity estimation, we are to estimate $\mathrm{tr}\left({\rho }^2\right)$ of an unknown quantum state $\rho$ to additive error $\varepsilon$. Meanwhile, for quantum inner product estimation, Alice and Bob are to estimate $\mathrm{tr}\left(\rho \sigma \right)$ to additive error $\varepsilon$, given copies of the unknown quantum states $\rho$ and $\sigma$ using classical communication and restricted quantum communication. We propose a protocol that solves quantum inner product estimation with $k$-qubit one-way quantum communication and unentangled local measurements using $O\left(\mathrm{median}\{1/{\varepsilon }^2,2^{n/2}/\varepsilon ,2^{n-k}/{\varepsilon }^2\}\right)$ copies of $\rho$ and $\sigma$. Our protocol can be modified to estimate the purity of an unknown quantum state $\rho$ using $k$-qubit quantum memory with the same sample complexity. We also prove that arbitrary protocols with $k$-qubit quantum memory that estimate purity to error $\varepsilon$ require $\mathrm{\Omega }\left(\mathrm{median}\{1/{\varepsilon }^2,2^{n/2}/\sqrt{\varepsilon },2^{n-k}/{\varepsilon }^2\}\right)$ copies of $\rho$. This indicates the same sample complexity lower bound for quantum inner product estimation with one-way $k$-qubit quantum communication and classical communication, and unentangled local measurements. We further improve the sample complexity lower bound for any purity estimation protocols using an identical single-copy projection-valued measurement. Last, we investigate a decisional variant of quantum distributed inner product estimation without quantum communication for mixed states and provide a sample complexity lower bound.