arXiv subjects

Patrick Emonts

Publications and source records attributed to Patrick Emonts.

At least 19 recordsLinked to original sources

arXiv2026

Exploring topological signatures of quantum Fisher information scaling in graph states

Graph states are a versatile resource for quantum metrology, and their quantum Fisher information (QFI) has a closed-form expression in terms of the underlying graph: it counts pairs of vertices with identical neighborhoods. It remains unclear, however, which global structural properties of a graph determine whether its QFI exceeds the standard quantum limit (SQL). Here we ask whether topological invariants, namely the Betti numbers of the graph's clique complex, capture this behavior, and we address the question numerically with two complementary approaches. First, we randomly add or delete edges in balanced complete multipartite graphs, which combine a QFI beyond the SQL with a single nonvanishing higher Betti number. Edge addition eventually destroys both the metrological advantage and the nontrivial topology. Under edge deletion, by contrast, higher Betti numbers persist well after the QFI has dropped to the SQL. Second, we start from Erdős--Rényi random graphs, whose QFI does not typically exceed the SQL, and maximize a chosen Betti number with a Monte Carlo search. The search drives the graphs toward near-extremal multipartite structures whose QFI lies well beyond the SQL. Our results show that topological optimization offers a route to metrologically useful graph states, but also that Betti numbers alone do not determine the QFI.

quant-ph↗

arXiv2026

Two-Sided Bounds on Ground State Properties in Lattice Gauge Theories

Gauge theories describe fundamental interactions in the standard model of particle physics and build effective theories in condensed matter physics. Being notoriously hard to simulate, these theories are commonly regularized as lattice gauge theories which can be evaluated with high precision through Monte Carlo algorithms or variational methods. However, Monte Carlo algorithms are not applicable in all regimes due to the sign problem; while variational methods, quantum and classical alike, only give upper-bounds on the ground-state energy. Their precision crucially depends on the chosen ansatz. Here, we present a framework based on a hierarchy of semidefinite programs to yield increasingly good lower-bounds on the ground-state energy and propagate these bounds to extended observables like Wilson loops and mesonic strings. We demonstrate the numerical capabilities by applying the algorithm to a (1+1)-dimensional $\mathbb{Z}_2$ theory with dynamic fermionic matter and its pure-gauge version in (2+1)-dimensions. In both cases, we obtain certified intervals for the ground-state energy. For a one-dimensional system with 129 sites, the certified interval has a relative spread of $0.04\%$. For a two-dimensional system with 97 sites (corresponding to a $7 \times 8$ lattice), the relative spread is $2.08\%$. Beyond energy estimates, the proposed method provides rigorous bounds on both short- and long-range observables such as Wilson loops over multiple plaquettes and the magnitude of the mesonic string. The method can be both used as a computational microscope into many-body physics and a way to certify results of quantum simulators.

quant-ph↗

arXiv2026

ggpeps: A package for Gauged Gaussian PEPS

Lattice gauge theories are a low-energy regularization of quantum field theories. They are the basis for the development of numerical algorithms that provide insight into the non-perturbative regime of quantum field theories which is difficult to achieve through other methods. We present a python package, ggpeps, implementing gauged Gaussian projected entangled pair states (GGPEPS), specialized to study lattice gauge theories. We give a an overview of the considered systems, describe the GGPEPS ansatz and provide a usage guide for the ggpeps package.

hep-lat↗

arXiv2026

Neural quantum states for non-Abelian lattice gauge theories with dynamical fermions

Determining the ground state of non-Abelian lattice gauge theories coupled to dynamical fermions is key to understanding confinement and the phase structure of gauge--matter systems. We present a variational Monte Carlo framework for the ground state of the untruncated fully-continuous SU$(2)$ lattice gauge theory coupled to dynamical staggered fermions on an $L\times L$ square lattice. We work in the magnetic basis with a neural-network representation of the gauge wavefunction. The fermions are described by a gauge-covariant Gaussian fermionic correction built on a fixed Néel reference state where, for each sampled gauge configuration $\mathbf{U}$, the correction is generated by a Hermitian operator. This operator is constructed from short Wilson lines and the eigenvectors of the mass--hopping Hamiltonian, with number of variational parameters polynomial in the system size. This Gaussian structure also gives analytical expressions for all fermionic contributions to the energy and related observables in terms of the fermion occupation matrix. The results are validated against strong-coupling perturbation theory, where they recover the expected effective antiferromagnetic spin Hamiltonian. Using this framework, we map a coarse ground state phase diagram in the plane of independent electric and magnetic couplings $(g^2, λ)$ and show that a hysteresis analysis can identify the existence of phase transitions. Restoring the physical relation $λ=4/g^2$, we characterize how increasing the system size and changing the electric coupling $g^2$ move the state away from the reference Néel state, for lattice sizes $L=4,6,8$. More broadly, the method offers a sign-problem-free variational framework for continuous non-Abelian gauge groups with dynamical matter that should extend to other matter content and higher-dimensional lattices.

hep-lat↗

arXiv2026

Quantum Phase Diagram of the $2+1$D Untruncated SU$(2)$ Lattice Gauge Theory with Dynamical Fermions

Non-Abelian gauge theories with dynamical matter govern the strong interaction and a broad class of strongly correlated quantum systems, yet their ground-state properties remain difficult to obtain from first principles. Using a continuous-group variational Monte Carlo approach that retains the full SU$(2)$ gauge field without truncation, we determine the ground-state behavior of the SU$(2)$ lattice gauge theory with staggered fermions on an $L\times L$ square lattice. Treating the magnetic and electric couplings $λ$ and $g^2$ independently, we find a magnetic-flux transition at $λ^\ast=-0.040\pm 0.005$, with no resolvable drift of the transition point as the electric coupling is varied. Along the physical coupling line $λ=4/g^2$, for $L=4,6,8$, we uncover a gauge-matter delocalization crossover from a flux-disordered regime at strong electric coupling to an ordered unity-flux regime at weak coupling. The chiral condensate, a gauge-invariant Wilson-line meson correlator, and the local color density consistently reveal the emergence of coherent gauge-assisted matter dynamics. Together, these results provide a unified physical picture of how magnetic-flux ordering and fermionic coherence develop in an untruncated non-Abelian lattice gauge theory.

hep-lat↗

arXiv2026

Algorithmic Aspects of Gauged Gaussian Fermionic PEPS: Gauge Fixing and Translation Invariance

Lattice gauge theories (LGTs) provide a powerful framework for studying non-perturbative phenomena in gauge theories. However, conventional approaches such as Monte Carlo (MC) simulations in imaginary time are limited, as they do not allow real time evolution and suffer from a sign problem in many important cases. Using Gauged Gaussian fermionic projected entangled pair states (GGFPEPS) as a variational ground state ansatz offers an alternative for studying LGTs through a sign-problem-free variational MC. As this method is extended to larger and more complex systems, understanding its numerical behavior becomes essential. While conventional action based MC has been extensively studied, the performance and characteristics of non-action-based MC within the GGFPEPS framework are far less explored. In this work, we investigate these algorithmic aspects, identifying an optimal update size for GGFPEPS-based MC simulations for $\mathbb{Z}_2$ in $2+1$ dimensions. We show that gauge fixing generally slows convergence, and demonstrate that not exploiting the translation-invariance can, in some cases, improve the computational time scaling of error convergence. We expect that these improvements will allow advancing the simulation to larger and more complex systems.

hep-lat↗

arXiv2026

Exact noise characterization of entanglement distribution in star networks

Multipartite entanglement forms the core of many networking applications. In the near-term future, it is expected that multipartite distribution will be achieved first through star topologies, making it important to understand the noise incurred during the distribution process. In such networks, elementary links are created stochastically and successful links must be stored while waiting for the remaining links, causing memory decoherence that depends on the random waiting times. We derive analytical expressions for both the average noise and its distribution, when distributing GHZ states under memory dephasing in star networks. We study and compare two distribution protocols: the factory and piecemaker protocol. Furthermore, we find expressions for the case of a global cut-off (allowing fast optimization of the cut-off without requiring Monte Carlo simulations) and extend the analysis for the factory protocol to depolarizing noise for arbitrary states.

quant-ph↗

arXiv2026

Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions

Lattice gauge theory is an important framework for studying gauge theories that arise in the Standard Model and condensed matter physics. Yet many systems (or regimes of those systems) are difficult to study using conventional techniques, such as action-based Monte Carlo sampling. In this paper, we demonstrate the use of gauged Gaussian projected entangled pair states as an ansatz for a lattice gauge theory involving dynamical physical matter. We study a $\mathbb{Z}_2$ gauge theory on a two dimensional lattice with a single flavor of fermionic matter on each lattice site. For small systems, our results show agreement with results computed by exactly diagonalizing the Hamiltonian, and demonstrate that the approach is computationally feasible for larger system sizes where exact results are unavailable. This is a further step on the road to studying higher dimensions and other gauge groups with manageable computational costs while avoiding the sign problem.

hep-lat↗

arXiv2026

A Hierarchy of Spectral Gap Certificates for Frustration-Free Spin Systems

Estimating spectral gaps of quantum many-body Hamiltonians is a highly challenging computational task, even under assumptions of locality and translation-invariance. Yet, the quest for rigorous gap certificates is motivated by their broad applicability, ranging from many-body physics to quantum computing and classical sampling techniques. Here we present a general method for obtaining lower bounds on the spectral gap of frustration-free quantum Hamiltonians in the thermodynamic limit. We formulate the gap certification problem as a hierarchy of optimization problems (semidefinite programs) in which the certificate -- a proof of a lower bound on the gap -- is improved with increasing levels. Our approach encompasses existing finite-size methods, such as Knabe's bound and its subsequent improvements, as those appear as particular possible solutions in our optimization, which is thus guaranteed to either match or surpass them. We demonstrate the power of the method on one-dimensional spin-chain models where we observe an improvement by several orders of magnitude over existing finite size criteria in both the accuracy of the lower bound on the gap, as well as the range of parameters in which a gap is detected.

quant-ph↗

arXiv2025

Tailoring Bell inequalities to the qudit toric code and self testing

Bell nonlocality provides a robust scalable route to the efficient certification of quantum states. Here, we introduce a general framework for constructing Bell inequalities tailored to the $\mathbb{Z}_d$ toric code for odd prime local dimensions. Selecting a suitable subset of stabilizer operators and mapping them to generalized measurement observables, we compute multipartite Bell expressions whose quantum maxima admit a sum-of-squares decomposition. We show that these inequalities are maximally violated by all states in the ground-state manifold of the $\mathbb{Z}_d$ toric code, and determine their classical (local) bounds through a combination of combinatorial tiling arguments and explicit optimization. As a concrete application, we analyze the case of $d=3$ and demonstrate that the maximal violation self-tests the full qutrit toric-code subspace, up to local isometries and complex conjugation. This constitutes, to our knowledge, the first-ever example of self-testing a qutrit subspace. Extending these constructions, we further present schemes to enhance the ratio of classical--quantum bounds and thus improve robustness to experimental imperfections. Our results establish a pathway toward device-independent certification of highly entangled topological quantum matter and provide new tools for validating qudit states in error-correcting codes and quantum simulation platforms.

quant-ph↗

arXiv2025

Boosting thermalization of classical and quantum many-body systems

Understanding and optimizing the relaxation dynamics of many-body systems is essential both for foundational studies in quantum thermodynamics and for applications such as quantum simulation and quantum computing. Efficient preparation of thermal states of a many-body Hamiltonian is governed by the spectral properties of the associated Lindbladian, in particular its spectral gap, which determines the slowest relaxation rate. In this work, we develop a systematic framework for constructing Lindbladians that prepare thermal states. Our approach reveals a simple relation between the relaxation dynamics at finite and infinite temperatures. The framework is scalable to larger system sizes when implemented using tensor-network methods. We find that efficient thermalization requires that the relaxation dynamics respect the symmetries of the thermal state, which reduces the number of free parameters. By applying gradient-based optimization to the Lindbladians, we enhance the spectral gap and thereby boost thermalization. When applied to both classical and quantum spin models, our method demonstrates a substantial enhancement of the spectral gap. For larger system sizes, our approach provides a variational upper bound and enables a certified lower bound on the minimum relaxation rate.

quant-ph↗

arXiv2025

Characterizing Translation-Invariant Bell Inequalities using Tropical Algebra and Graph Polytopes

Nonlocality is one of the key features of quantum physics, which is revealed through the violation of a Bell inequality. In large multipartite systems, nonlocality characterization quickly becomes a challenging task. A common practice is to make use of symmetries, low-order correlators, or exploiting local geometries, to restrict the class of inequalities. In this paper, we characterize translation-invariant (TI) Bell inequalities with finite-range correlators in one-dimensional geometries. We introduce a novel methodology based on tropical algebra tensor networks and highlight its connection to graph theory. Surprisingly, we find that the TI Bell polytope has a number of extremal points that can be uniformly upper-bounded with respect to the system size. We give an efficient method to list all vertices of the polytope for a particular system size, and characterize the tightness of a given TI Bell inequality. The connections highlighted in our work allow us to re-interpret concepts developed in the fields of tropical algebra and graph theory in the context of Bell nonlocality, and vice-versa. This work extends a parallel article [M. Hu \textit{et al.}, arXiv: 2208.02798 (2022)] on the same subject.

quant-ph↗

arXiv2025

Learning Pole Structures of Hadronic States using Predictive Uncertainty Estimation

Matching theoretical predictions to experimental data remains a central challenge in hadron spectroscopy. In particular, the identification of new hadronic states is difficult, as exotic signals near threshold can arise from a variety of physical mechanisms. A key diagnostic in this context is the pole structure of the scattering amplitude, but different configurations can produce similar signatures. The mapping between pole configurations and line shapes is especially ambiguous near the mass threshold, where analytic control is limited. In this work, we introduce an uncertainty-aware machine learning approach for classifying pole structures in $S$-matrix elements. Our method is based on an ensemble of classifier chains that provide both epistemic and aleatoric uncertainty estimates. We apply a rejection criterion based on predictive uncertainty, achieving a validation accuracy of nearly $95\%$ while discarding only a small fraction of high-uncertainty predictions. Trained on synthetic data with known pole structures, the model generalizes to previously unseen experimental data, including enhancements associated with the $P_{c\bar{c}}(4312)^+$ state observed by LHCb. In this, we infer a four-pole structure, representing the presence of a genuine compact pentaquark in the presence of a higher channel virtual state pole with non-vanishing width. While evaluated on this particular state, our framework is broadly applicable to other candidate hadronic states and offers a scalable tool for pole structure inference in scattering amplitudes.

hep-ph↗

arXiv2025

Multiple-basis representation of quantum states

Classical simulation of quantum physics is a central approach to investigating physical phenomena. Quantum computers enhance computational capabilities beyond those of classical resources, but it remains unclear to what extent existing limited quantum computers can contribute to this enhancement. In this work, we explore a new hybrid, efficient quantum-classical representation of quantum states, the multiple-basis representation. This representation consists of a linear combination of states that are sparse in some given and different bases, specified by quantum circuits. Such representation is particularly appealing when considering depth-limited quantum circuits within reach of current hardware. We analyze the expressivity of multiple-basis representation states depending on the classical simulability of their quantum circuits. In particular, we show that multiple-basis representation states include, but are not restricted to, both matrix-product states and stabilizer states. Furthermore, we find cases in which this representation can be used, namely approximation of ground states, simulation of deeper computations by specifying bases with shallow circuits, and a tomographical protocol to describe states as multiple-basis representations. We envision this work to open the path of simultaneous use of several hardware-friendly bases, a natural description of hybrid computational methods accessible for near-term hardware.

quant-ph↗

arXiv2024

Optimising entanglement distribution policies under classical communication constraints assisted by reinforcement learning

Quantum repeaters play a crucial role in the effective distribution of entanglement over long distances. The nearest-future type of quantum repeater requires two operations: entanglement generation across neighbouring repeaters and entanglement swapping to promote short-range entanglement to long-range. For many hardware setups, these actions are probabilistic, leading to longer distribution times and incurred errors. Significant efforts have been vested in finding the optimal entanglement-distribution policy, i.e. the protocol specifying when a network node needs to generate or swap entanglement, such that the expected time to distribute long-distance entanglement is minimal. This problem is even more intricate in more realistic scenarios, especially when classical communication delays are taken into account. In this work, we formulate our problem as a Markov decision problem and use reinforcement learning (RL) to optimise over centralised strategies, where one designated node instructs other nodes which actions to perform. Contrary to most RL models, ours can be readily interpreted. Additionally, we introduce and evaluate a fixed local policy, the `predictive swap-asap' policy, where nodes only coordinate with nearest neighbours. Compared to the straightforward generalization of the common swap-asap policy to the scenario with classical communication effects, the `wait-for-broadcast swap-asap' policy, both of the aforementioned entanglement-delivery policies are faster at high success probabilities. Our work showcases the merit of considering policies acting with incomplete information in the realistic case when classical communication effects are significant.

quant-ph↗

arXiv2024

Gauged Gaussian PEPS -- A High Dimensional Tensor Network Formulation for Lattice Gauge Theories

Gauge theories form the basis of our understanding of modern physics - ranging from the description of quarks and gluons to effective models in condensed matter physics. In the non-perturbative regime, gauge theories are conventionally treated discretely as lattice gauge theories. The resulting systems are evaluated with path-integral based Monte Carlo methods. These methods, however, can suffer from the sign problem and do not allow for a direct evaluation of real-time dynamics. In this work, we present a unified and comprehensive framework for gauged Gaussian Projected Entangled Pair States (PEPS), a variational ansatz based on tensor networks. We review the construction of Hamiltonian lattice gauge theories, explain their similarities with PEPS, and detail the construction of the state. The estimation of ground states is based on a variational Monte Carlo procedure with the PEPS as an ansatz state. This sign-problem-free ansatz can be efficiently evaluated in any dimension with arbitrary gauge groups, and can include dynamical fermionic matter, suggesting new options for the simulation of non-perturbative regimes of gauge theories, including QCD.

hep-lat↗

arXiv2024

Spectral Gap Optimization for Enhanced Adiabatic State Preparation

The preparation of non-trivial states is crucial to the study of quantum many-body physics. Such states can be prepared with adiabatic quantum algorithms, which are restricted by the minimum spectral gap along the path. In this letter, we propose an efficient method to adiabatically prepare tensor networks states (TNSs). We maximize the spectral gap leveraging degrees of freedom in the parent Hamiltonian construction. We demonstrate this efficient adiabatic algorithm for preparing TNS, through examples of random TNS in one dimension, AKLT, and GHZ states. The Hamiltonian optimization applies to both injective and non-injective tensors, in the latter case by exploiting symmetries present in the tensors.

quant-ph↗

arXiv2024

Improved Nonlocality Certification via Bouncing between Bell Operators and Inequalities

Bell nonlocality is an intrinsic feature of quantum mechanics, which can be certified via the violation of Bell inequalities. It is therefore a fundamental question to certify Bell nonlocality from experimental data. Here, we present an optimization scheme to improve nonlocality certification by exploring flexible mappings between Bell inequalities and Hamiltonians corresponding to the Bell operators. We show that several Hamiltonian models can be mapped to new inequalities with improved classical bounds than the original one, enabling a more robust detection of nonlocality. From the other direction, we investigate the mapping from fixed Bell inequalities to Hamiltonians, aiming to maximize quantum violations while considering experimental imperfections. As a practical demonstration, we apply this method to an XXZ-like honeycomb-lattice model utilizing over 70 superconducting qubits. The successful application of this technique, as well as combining the two directions to form an optimization loop, may open new avenues for developing more practical and noise-resilient nonlocality certification techniques and enable broader experimental explorations.

quant-ph↗