We simulate the thermalization dynamics for minimally truncated SU(2) pure gauge theory on linear plaquette chains with up to 151 plaquettes using IBM quantum computers. We study the time dependence of the entanglement spectrum, Renyi-2 entropy and anti-flatness on small subsystems. The quantum hardware results obtained after error mitigation agree with extrapolated classical simulator results for chains consisting of up to 101 plaquettes. Our results demonstrate the feasibility of local thermalization studies for chaotic quantum systems, such as non-Abelian lattice gauge theories, on current noisy quantum computing platforms.

A scattering event in a quantum field theory is a coherent superposition of all processes consistent with its symmetries and kinematics. While real-time simulations have progressed toward resolving individual channels, existing approaches rely on knowledge of the asymptotic particle wavefunctions. This work introduces an experimentally inspired method to isolate scattering channels in Matrix Product State simulations based on the entanglement structure of the late-time wavefunction. Schmidt decompositions at spatial bipartitions of the post-scattering state identify elastic and inelastic contributions, enabling deterministic detection of outgoing particles of specific species. This method may be used in settings beyond scattering and is applied to detect heavy particles produced in a collision in the one-dimensional Ising field theory. Natural extensions to quantum simulations of other systems and higher-order processes are discussed.

String breaking is at the core of hadronization models of relevance to particle colliders. Yet, studies of string-breaking dynamics rooted in quantum chromodynamics remain fundamentally challenging. Tensor networks enable sign-problem-free studies of static and dynamical properties of lattice gauge theories (LGTs). In this work, we develop and apply a tensor-network toolkit based on the loop-string-hadron (LSH) formulation of an SU(2) LGT in 1+1 dimensions with dynamical quarks. We apply this toolkit to study static and dynamical aspects of strings and their breaking in this theory. The simple, gauge-invariant, and local structure of the LSH states and constraints removes the need to impose non-Abelian constraints in the algorithm, and allows for a systematic computation of observables at increasingly large bosonic cutoffs, and toward the infinite-volume and continuum limits. Our study of static strings yields a determination of the string tension in the continuum and thermodynamic limits. Our study of dynamical string breaking illuminates underlying processes at play during the quench dynamics of a string. The loop, string, and hadron description offers a systematic and intuitive way to diagnose these processes, including string expansion and contraction, endpoint splitting and particle shower, chain scattering events, and inelastic processes resulting from string dissociation and recombination, and particle production. We relate these processes to several features of the dynamics, such as energy transport, entanglement-entropy production, and correlation spreading. This work opens the way to future tensor-network studies of string breaking and particle production in increasingly complex LGTs.

Three-dimensional Weyl materials provide a controlled setting for exploring Floquet dynamics in open quantum systems, including nonequilibrium steady states (NESS). Motivated by the desire for a strongly-coupled description, we employ holography to analyze the formation and stability of a NESS in a Weyl semi-metal induced by an external circularly polarized electric field. A time-periodic steady-state solution is constructed and its stability is determined from the spectrum of out-of-equilibrium quasinormal modes (Floquet exponents). A stable region in the drive parameter space is identified; beyond a critical curve, the Floquet exponents enter the upper half of the complex plane, leading to a superharmonic response. At sufficiently strong driving, chaotic time evolution emerges in the fully nonlinear initial-boundary value problem. The anomaly-induced response of the NESS to an external magnetic field is also computed, and the resulting behavior is related to the previously proposed chiral pumping effect.

String breaking, the process by which flux tubes fragment into hadronic states, is a hallmark of confinement in strongly-interacting quantum field theories. We examine a suite of quantum complexity measures using Matrix Product States to dissect the string breaking process in the 1+1D Schwinger model. We demonstrate the presence of nonlocal quantum correlations along the string that may affect fragmentation dynamics, and show that entanglement and magic offer complementary perspectives on string formation and hadronization beyond conventional observables.

We would like to thank Roland Farrell, Henry Froland, Tobias Haug, Dima Kharzeev, Eliana Marroquin and
Caroline Robin for helpful discussions. This work was supported, in part, by U.S. Department of Energy, Office of Science, Office of Nuclear Physics, InQubator for Quantum Simulation (IQuS) under Award Number DOE (NP) Award DE-SC0020970 via the program on Quantum Horizons: QIS Research and Innovation for Nuclear Science. Sebastian was supported in part by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, Grants No. DE-FG02-97ER-41014 and in part by a Feodor Lynen Research fellowship of the Alexander von Humboldt foundation. This work was also supported, in part, by the Department of Physics and the College of Arts and Sciences at the University of Washington. This work was enabled, in part, by the use of advanced computational, storage and networking infrastructure provided by the Hyak supercomputer system at the University of Washington. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a Department of Energy Office of Science User Facility using NERSC award NP-ERCAP0032083. This research was done using services provided by the OSG Consortium, which is supported by the National Science Foundation awards #2030508 and #1836650. We have made use of the ITensor library for tensor network computations.

We study SU(3) gauge theory on small lattices in the minimal (qutrit) electric field truncation retaining only the 1, 3, 3bar representations for the link variables. Explicit expressions are given for the Kogut-Susskind Hamiltonian for the square plaquette chain and the two-dimensional honeycomb lattice. Our formalism can be easily extended to the minimally truncated general SU(Nc) gauge theory. The addition of (static) quarks is discussed. We present results for the energy spectrum of the gauge field on these lattices by exact diagonalization of the Hamiltonian and analyze its statistical properties. We also compute the SU(3) string tension and discuss how it is modified by vacuum fluctuations. Finally, we calculate the potential energies of a static quark-antiquark pair and three static quarks and study their screening at finite temperature.

Quantum simulations of many-body systems offer novel methods for probing the dynamics of the Standard Model and its constituent gauge theories. Extracting low-energy predictions from such simulations rely on formulating systematically-improvable representations of lattice gauge theory Hamiltonians that are efficient at all values of the gauge coupling. One such candidate representation for SU(2) is the fully gauge-fixed Hamiltonian defined in the mixed basis. This work focuses on the quantum simulation of the smallest non-trivial system: two plaquettes with open boundary conditions. A mapping of the continuous gauge field degrees of freedom to qubit-based representations is developed. It is found that as few as three qubits per plaquette is sufficient to reach percent-level precision on predictions for observables. Two distinct algorithms for implementing time evolution in the mixed basis are developed and analyzed in terms of quantum resource estimates. One algorithm has favorable scaling in circuit depth for large numbers of qubits, while the other is more practical when qubit count is limited. The second algorithm is used in the measurement of a real-time observable on IBM’s Heron superconducting quantum processor, ibm_fez. The quantum results match classical predictions at the per-mille level. This work lays out the path forward for two- and three-dimensional simulations of larger systems, as well as demonstrating the viability of mixed-basis formulations for studying the properties of SU(2) gauge theories at all values of the gauge coupling.

This work is the second installment of a series on the Loop-String-Hadron (LSH) approach to SU(3) lattice Yang-Mills theory. Here, we present the infinite-dimensional matrix representation for arbitrary gauge-invariant operators at a trivalent vertex, which results in a standalone framework for computations that supersedes the underlying Schwinger-boson framework. To that end, we evaluate in closed form the result of applying any gauge-invariant operators on the LSH basis states introduced in Part I. Classical calculations in the LSH basis run significantly faster than equivalent calculations performed using Schwinger bosons. A companion code script is provided, which implements the derived formulas and aims to facilitate rapid progress towards Hamiltonian-based calculations of quantum chromodynamics.

 Simulations of energy loss and hadronization are essential for understanding a range of phenomena in non-equilibrium strongly-interacting matter. We establish a framework for performing such simulations on a quantum computer and apply it to a heavy quark moving across a modest-sized 1+1D SU(2) lattice of light quarks. Conceptual advances with regard to simulations of non-Abelian versus Abelian theories are developed, allowing for the evolution of the energy in light quarks, of their local non-Abelian charge densities, and of their multi-partite entanglement to be computed. The non-trivial action of non-Abelian charge operators on arbitrary states suggests mapping the heavy quarks to qubits alongside the light quarks, and limits the heavy-quark motion to discrete steps among spatial lattice sites. Further, the color entanglement among the heavy quarks and light quarks is most simply implemented using hadronic operators, and Domain Decomposition is shown to be effective in quantum state preparation. Scalable quantum circuits that account for the heterogeneity of non-Abelian charge sectors across the lattice are used to prepare the interacting ground-state wavefunction in the presence of heavy quarks. The discrete motion of heavy quarks between adjacent spatial sites is implemented using fermionic SWAP operations. Quantum simulations of the dynamics of a system on L=3 spatial sites are performed using IBM’s ibm_pittsburgh quantum computer using 18 qubits, for which the circuits for state preparation, motion, and one second-order Trotter step of time evolution have a two-qubit depth of 398 after transpilation. A suite of error mitigation techniques are used to extract the observables from the simulations, providing results that are in good agreement with classical simulations. The framework presented here generalizes straightforwardly to other non-Abelian groups, including SU(3) for quantum chromodynamics.

We would like to thank Roland Farrell, Henry Froland and Nikita Zemlevskiy for helpful discussions. This work was supported, in part, by U.S. Department of Energy, Office of Science, Office of Nuclear Physics, InQubator for Quantum Simulation (IQuS) under Award Number DOE (NP) Award DE-SC0020970 via the program on Quantum Horizons: QIS Research and Innovation for Nuclear Science, by the Quantum Science Center (QSC) which is a National Quantum Information Science Research Center of the U.S Department of Energy, and by PNNL’s Quantum Algorithms and Architecture for Domain Science (QuAADS) Laboratory Directed Research and Development (LDRD) Initiative. The Pacific Northwest National Laboratory is operated by Battelle for the U.S. Department of Energy under Contract DE-AC05 76RL01830. It was also supported, in part, by the Department of Physics and the College of Arts and Sciences at the University of Washington. This research used resources of the Oak Ridge Leadership Computing Facility (OLCF), which is a DOE Office of Science User Facility supported under Contract DE AC05-00OR22725. We acknowledge the use of IBM Quantum services for this work. The views expressed are those of the authors, and do not reflect the official policy or position of IBM or the IBM Quantum team. This work was enabled, in part, by the use of advanced computational, storage and networking infrastructure provided by the Hyak supercomputer system at the University of Washington. We have made extensive use of Wolfram Mathematica, python, julia, jupyter notebooks in the Conda environment, and IBM’s quantum programming environment qiskit. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a Department of Energy Office of Science User Facility using NERSC award NP-ERCAP0032083.

We construct two quantum error correction codes for pure SU(2) lattice gauge theory in the electric basis truncated at the electric flux $j_{\rm max}=1/2$, which are applicable on quasi-1D plaquette chains, 2D honeycomb and 3D triamond and hyperhoneycomb lattices. The first code converts Gauss’s law at each vertex into a stabilizer while the second only uses half vertices and is locally the carbon code. Both codes are able to correct single-qubit errors. The electric and magnetic terms in the SU(2) Hamiltonian are expressed in terms of logical gates in both codes. The logical-gate Hamiltonian in the first code exactly matches the spin Hamiltonian for gauge singlet states found in previous work.