Quantum Complexity Measures Enable New Insights into String Fragmentation and the Schwinger Model

String breaking, a fundamental process in particle physics where energetic flux tubes fragment into observable particles, remains a key challenge in understanding confinement within strongly-interacting field theories. Sebastian Grieninger, Martin J. Savage, and Nikita A. Zemlevskiy, all from the InQubator for Quantum Simulation at the University of Washington, have investigated this phenomenon using advanced computational techniques. Their research dissects string breaking in the simplified, yet insightful, 1+1D Schwinger model through the application of several complexity measures and Matrix Product States. By revealing the presence of nonlocal correlations along the string, this work offers a new perspective on fragmentation dynamics and provides complementary insights beyond traditional methods of observation.

Researchers demonstrate the presence of nonlocal quantum correlations along the string, which may affect fragmentation dynamics, and show that entanglement and magic offer complementary perspectives on string formation and breaking, extending beyond conventional observables. The formation of flux tubes, or chromoelectric strings, between colour charges is a primary emergent feature of quantum chromodynamics (QCD). The nonlinearity of the Yang-Mills Lagrange density, specifically the gluon self-interactions, combined with quantum fluctuations, confine the lines of flux between….

Quantum State Preparation and Verification Techniques

This is a comprehensive list of citations, primarily focused on quantum computing, quantum field theory, and related areas like lattice gauge theory, entanglement, and tensor networks. Zhu et al. (2016) discusses the limitations of the Clifford group as a unitary design, important for understanding the capabilities and limitations of certain quantum algorithms and error correction schemes. Several papers explore the concept of “nonstabilizerness”, a measure of how far a quantum state is from being a stabilizer state, crucial for understanding the power of quantum computation beyond the Clifford circuit family and being applied to gauge theories to understand complexity.

Wong & Christensen (2001) propose a multiparticle entanglement measure. A significant number of papers focus on using quantum computers to simulate quantum field theories, particularly scattering processes, exploring approaches like W-state based simulations and using tensor networks. Farrell et al. (multiple papers) and Li, Illa, & Savage specifically target simulations of hadronization and energy loss in dense matter. Many papers deal with the theoretical foundations and challenges of representing and simulating lattice gauge theories on quantum computers, including defining entanglement entropy in these systems.

A large cluster of papers investigate entanglement entropy as a probe of quantum field theories, particularly gauge theories, with symmetry-resolved entanglement being a key topic. Several papers focus on the massive Schwinger model as a testbed for quantum simulation techniques, including tensor networks. Amorosso et al. explore entanglement entropy in Yang-Mills theory. Fishman et al.

describe the ITensor software library, a powerful tool for performing tensor network calculations. Verstraete et al. discuss the density matrix renormalization group (DMRG) with periodic boundary conditions, while Corbett & Miyake discuss scaling up the transcorrelated DMRG. Grieninger et al. apply tensor networks to the massive Schwinger model.

White & White (2024) and Yazgan (CMS Collaboration) explore the concept of “quantum magic” in the context of top quark properties, potentially linking quantum information concepts to particle physics measurements. Pordes et al., Sfiligoi et al., and references to OSG, Ospool, and Open Science Data Federation describe the infrastructure used for large-scale scientific computing. Aaronson & Gottesman (2004) provide a foundational result on simulating stabilizer circuits. Quantum simulation is a major driver of research, with a strong focus on representing and simulating lattice gauge theories on quantum computers.

Entanglement entropy is being used as a powerful tool to probe the structure of quantum field theories and to characterize quantum states, while tensor networks are used as both a classical simulation technique and a potential building block for quantum algorithms. There is a growing effort to connect quantum information concepts to other areas of physics, such as particle physics and condensed matter physics. Experiments revealed the presence of nonlocal correlations along the string, suggesting these correlations influence fragmentation dynamics, and demonstrated that both entanglement and magic offer complementary insights into string formation and breaking, extending beyond conventional observables. The work focuses on understanding how a string breaks down into individual hadrons, modelling the process of ionisation, fragmentation, and hadronisation with a high degree of accuracy. The team measured the energy density, showing a linearly increasing potential with the separation distance between external charges.

A flux tube develops, and at a specific separation, the formation of a pair of hadronic bound states becomes energetically favourable. Dynamical charges are extracted from the vacuum to screen the external charges, crucial for understanding confinement and charge screening. These simulations provide a platform for high-precision predictions relevant to future experiments, such as those planned for the Electron-Ion Collider and the LHC, aiding in the determination of nucleon partonic distributions and the discovery of new fundamental physics. Measurements confirm that the evolution of quantum complexity, reflecting physical dynamics and emergent phenomena, serves as a sensitive probe of the nature of string breaking.

The research investigated the behaviour of multipartite entanglement and magic, a measure of nonstabilizerness, in the ground state of quantum electrodynamics, observing how these properties change as the system transitions from a confining string to isolated bound states. The Schwinger model, sharing features with 3+1D QCD, provides a natural testbed for studying confinement, charge screening, and the formation of few-body bound states, or hadrons. Scientists describe minimal simulation requirements for lattice studies of string breaking, performing simulations to study inherent quantum complexity within the wavefunction and revealing previously unknown structure. The measures of quantum complexity examined were found to change rapidly in the vicinity of string breaking, offering a complementary view of the mechanisms involved in hadron formation and the associated vacuum rearrangement. The lattice Hamiltonian of the Schwinger model was formulated using a Kogut-Susskind discretization and the Jordan-Wigner transformation, enabling the study of the fermionic interaction induced by the Coulomb potential. Their work demonstrates the presence of both local and nonlocal quantum correlations along the string, revealing that these correlations undergo rapid changes during string fragmentation, differing significantly from classical behaviours such as energy density. The study highlights that nonlocal quantum complexity is specifically located within the string itself, suggesting a connection between extended physical objects and quantum complexity independent of the chosen basis. This research offers a new perspective on understanding confinement and hadronization, long-standing challenges in high-energy physics, by employing techniques from quantum information science. The findings indicate that both classical and quantum correlations develop during string breaking, though longer-range correlations appear to be primarily classical in nature. Importantly, the observed changes in quantum complexity during the transition from flux tubes to hadronic states resemble phase transitions, potentially offering insights.