We propose a formally valid machine-learning-assisted global proposal mechanism for Monte Carlo sampling in lattice gauge theory. The construction is based on a coupling-flow update on the SU(2) lattice-link manifold, in which active links are transformed conditionally on a frozen-link background. For fixed frozen links, the proposal is explicitly invertible and preserves the product Haar measure, so it can be embedded into a Metropolis-Hastings correction without requiring an explicit model of the full proposal density. We implement the method in two-dimensional pure SU(2) lattice gauge theory and benchmark it against a baseline local Metropolis algorithm used as a controlled reference kernel. In the present testbed, the learned proposal reproduces the target ensemble within statistical resolution across the tested configurations. In matched local-step comparisons, the learned proposal reproduces the target ensemble at a quality comparable to the baseline, but does not outperform the pure local baseline in the conservative matched-step case examined with seed-level statistics within this proof-of-principle setup. At the same time, a favorable mixed-step hybrid configuration yields a modest improvement in effective sample size per unit runtime. Because the learned transformation remains in a near-identity regime, the present results should be interpreted as a proof-of-principle demonstration of formal correctness and limited, configuration-dependent efficiency gain within a controlled comparison, rather than as evidence of superiority over optimized conventional update schemes. This work provides a concrete foundation for extending machine-learned nonlocal updates to larger lattices and non-Abelian gauge theories relevant to lattice QCD.

Twist fields are a powerful formal tool to compute Rényi entropies in quantum many-body systems, but their conventional formulation in tensor network states involves operations acting on virtual degrees of freedom, which are not directly accessible in experiments. In this work, we construct explicit local operators acting on the physical Hilbert space whose expectation values reproduce the action of twist fields in matrix product states. Our construction is exact in the injectivity limit and when the tensor is chosen at the center of orthogonality, and provides a direct operational method to evaluate Rényi entropies without accessing auxiliary tensor indices. We test our formulation numerically in the transverse-field Ising model, demonstrating rapid convergence to the exact entanglement entropy as the injectivity scale is reached. Furthermore, we show that twist operators determined from relatively small reference systems can be reliably transferred to larger systems, once the reference size exceeds a characteristic scale set by the correlation length. Since the resulting operators admit a decomposition in terms of a finite number of local observables, our results provide a scalable and experimentally accessible framework to probe entanglement in quantum simulators.

Constrained symplectic quantization is a functional formulation of quantum field theory in which quantum fluctuations are sampled through a deterministic Hamiltonian flow in an auxiliary intrinsic time $\tau$. In this paper we extend the quantum-mechanical framework introduced in [1] to a relativistic scalar quantum field theory in Minkowski space-time. The construction is based on the analytic continuation of fields and action from $\mathbb{R}$ to $\mathbb{C}$ together with constraints that select stable intrinsic-time trajectories and, at the same time, define convergent integration cycles for the corresponding microcanonical functional. We show that, in the continuum limit, the microcanonical generating functional reproduces the Feynman generating functional. For the free scalar field in $1+1$ dimensions we derive the constrained equations of motion, implement the resulting dynamics numerically, and verify real-time two-point correlators, equal-time commutator relations, and Dyson--Schwinger equations including the expected contact terms.

Motivated by a recent conjecture of Misumi and Yumoto relating the number of zero modes of lattice Dirac operators to the sum of the Betti numbers of the underlying spacetime manifold, we study formal naive Dirac operators on a class of graphs admitting such in terms of their zero modes. Our main result is that for graphs on which translations commute, the conjecture of Misumi and Yumoto can be shown and indeed can be strengthened to obtain bounds on the individual Betti numbers rather than merely on their sum. Interpretations of the zero modes in terms of graph quotients and of the representation theory of abelian groups are given, and connections with a homology theory for such graphs are highlighted.

Confinement prohibits isolation of color charges, e.g., quarks, in nature via a process called string breaking: the separation of two charges results in an increase in the energy of a color flux, visualized as a string, connecting those charges. Eventually, creating additional charges is energetically favored, hence breaking the string. Such a phenomenon can be probed in simpler models, including quantum spin chains, enabling enhanced understanding of string-breaking dynamics. A challenging task is to understand how string breaking occurs as time elapses, in an out-of-equilibrium setting. This work establishes the phenomenology of dynamical string breaking induced by a gradual increase of string tension over time. It, thus, goes beyond instantaneous quench processes and enables tracking the real-time evolution of strings in a more controlled setting. We focus on domain-wall confinement in a family of quantum Ising chains. Our results indicate that, for sufficiently short strings and slow evolution, string breaking can be described by the transition dynamics of a two-state quantum system akin to a Landau-Zener process. For longer strings, a more intricate spatiotemporal pattern emerges: the string breaks by forming a superposition of bubbles (domains of flipped spins of varying sizes), which involve highly excited states. We finally demonstrate that string breaking driven only by quantum fluctuations can be realized in the presence of sufficiently long-ranged interactions. This work holds immediate relevance for studying string breaking in quantum-simulation experiments.

We develop new methods for approximating conformal blocks as positive functions times polynomials, with applications to the numerical bootstrap. We argue that to obtain accurate bootstrap bounds, conformal block approximations should minimize a certain error norm related to the asymptotics of dispersive functionals. This error norm can be made small using interpolation nodes with an appropriate optimal density. The optimal density turns out to satisfy a kind of force-balance equation for charges in one dimension, which can be solved using standard techniques from large-N matrix models. We also describe how to use optimal density interpolation nodes to improve condition numbers inside the semidefinite program solver SDPB. Altogether, our new approximation scheme and improvements to condition numbers lead to more accurate bootstrap bounds with fewer computational resources. They were crucial in the recent bootstrap study of stress tensors in the 3d Ising CFT.

Classical shadows provide a versatile framework for estimating many properties of quantum states from repeated, randomly chosen measurements without requiring full quantum state tomography. When prior information is available, such as knowledge of symmetries of states and operators, this knowledge can be exploited to significantly improve sample efficiency. In this work, we develop three classical shadow protocols for $\mathbb{Z}_2$ lattice gauge theory, where a dual formulation enables a rigorous analysis of resource requirements, including both circuit depth and sample complexity. Our approaches can offer exponential improvements in sample complexity over symmetry-agnostic methods, albeit at the cost of increased circuit complexity. While our analysis is restricted to $\mathbb{Z}_2$ lattice gauge theory, our approach offers a blueprint for similar protocols for more general lattice gauge theory models which are currently at the forefront of quantum simulation efforts.

Hadronic tensors encode the nonperturbative structure of hadrons probed in deep inelastic scattering (DIS), yet their direct evaluation requires real-time evolution that presents a challenge for traditional Euclidean lattice approaches. In this work, we present the first quantum simulation of real-time hadronic current-current correlators in a confining gauge theory, from which DIS-inspired structure functions are extracted as a proof-of-principle demonstration in the Schwinger model, i.e (1+1)-dimensional QED. Using two complementary quantum-simulation strategies -- quantum-circuit and tensor-network methods -- we compute the real-time current-current correlator directly on the lattice and validate our results against exact diagonalization where applicable. From this correlator, we compute the hadronic tensor and determine the longitudinal structure function, the sole nonvanishing DIS observable in two space-time dimensions. Our study demonstrates that quantum simulation offers a viable complementary pathway towards the evaluation of real-time observables relevant for hadronic structure. It also provides a foundation for extending the calculations from Schwinger model to other gauge theories.

Dynamical quantum phase transitions (DQPTs) are an exciting paradigm of out-of-equilibrium criticality in many-body systems manifested in nonanalytic behavior in the return rate to the initial state following a sudden quench. While previous work has tried to distinguish between distinct types of DQPTs, such as regular and anomalous, or manifold and branch, a comprehensive understanding of why each type appears in a given scenario is still lacking. In this work, we propose a unified framework addressing this gap in terms of the energy structure of different product state configurations. In particular, while manifold DQPTs are governed by resonances within the initial state manifold, branch DQPTs are governed by resonances with a transitional manifold of states dynamically connected to the initial manifold by low-order processes. We show that the (ir)regularity of branch DQPTs is related to the multiplicity of this transitional manifold, and we also observe exotic periods of extended degeneracy in the return rate (beyond the conventional level crossing of a DQPT) which are also conditioned on the structure of this transitional manifold. We demonstrate this by studying quenches of two different configurations in the 1 + 1D Z_2 LGT to various parameter regimes. Our findings provide a dynamical mechanism underlying branch DQPTs and frames DQPTs as probes of resonant connectivity in constrained Hilbert spaces, paving the way to a more complete understanding of the multifaceted nature of dynamical criticality.