Quantum many-body scars are eigenstates in non-integrable isolated quantum systems that defy typical thermalization paradigms, violating the eigenstate thermalization hypothesis and quantum ergodicity. We identify exact analytic scar solutions in a 2+1 dimensional lattice gauge theory in a quasi-1d limit as zero-magic stabilizer states. We propose a protocol for their experimental preparation, presenting an opportunity to demonstrate a quantum over classical advantage via simulating the non-equilibrium dynamics of a strongly coupled system. Our results also highlight the importance of magic for gauge theory thermalization, revealing a connection between computational complexity and quantum ergodicity.

This work is supported by the DOE, Office of Science, Office of Nuclear Physics, IQuS, via the program on Quantum Horizons: QIS Research and Innovation for Nuclear Science under Award DE-SC0020970, and by the National Science Foundation, NSF DMR-2300172.

We review recent and present new results on thermalization of nonabelian gauge theory obtained by exact numerical simulation of the real-time dynamics of two-dimensional SU(2) lattice gauge theory. We discuss: (1) tests confirming the Eigenstate Thermalization Hypothesis; (2) the entanglement entropy of sublattices, including the Page curve, the transition from area to volume scaling with increasing energy of the eigenstate and its time evolution that shows thermalization of localized regions to be a two-step process; (3) the absence of quantum many-body scars for j(max)>1/2; (4) the spectral form factor, which exhibits the expected slope-ramp-plateau structure for late times; (5) the entanglement Hamiltonian for SU(2), which has properties in accordance with the Bisognano-Wichmann theorem; and (6) a measure for non-stabilizerness or “magic” that is found to reach its maximum during thermalization. We conclude that the thermalization of nonabelian gauge theories is a promising process to establish quantum advantage.

We consider the quantum magic in systems of dense neutrinos undergoing coherent flavor transformations, relevant for supernova and neutron-star binary mergers. Mapping the three flavor-neutrino system to qutrits, the evolution of quantum magic is explored in the single scattering angle limit for a selection of initial tensor-product pure states for N< 8 neutrinos. For initial states of electron-type neutrinos, the magic, as measured by the M(2) stabilizer Renyi entropy, is found to decrease with radial distance from the neutrino sphere, reaching a value that lies below the maximum for tensor-product qutrit states. Further, the asymptotic magic per neutrino, M(2)/N, decreases with increasing N. In contrast, the magic evolving from states containing all three flavors reaches values only possible with entanglement, with the asymptotic M(2)/N increasing with N. These results highlight the connection between the complexity in simulating quantum physical systems and the parameters of the Standard Model.

Simulations of collisions of fundamental particles on a quantum computer are expected to have an exponential advantage over classical methods and promise to enhance searches for new physics. Furthermore, scattering in scalar field theory has been shown to be BQP-complete, making it a representative problem for which quantum computation is efficient. As a step toward large-scale quantum simulations of collision processes, scattering of wavepackets in one-dimensional scalar field theory is simulated using 120 qubits of IBM’s Heron superconducting quantum computer ibm_fez. Variational circuits compressing vacuum preparation, wavepacket initialization, and time evolution are determined using classical resources. By leveraging physical properties of states in the theory, such as symmetries and locality, the variational quantum algorithm constructs scalable circuits that can be used to simulate arbitrarily-large system sizes. A new strategy is introduced to mitigate errors in quantum simulations, which enables the extraction of meaningful results from circuits with up to 4924 two-qubit gates and two-qubit gate depths of 103. The effect of interactions is clearly seen, and is found to be in agreement with classical Matrix Product State simulations. The developments that will be necessary to simulate high-energy inelastic collisions on a quantum computer are discussed.

We study a quantum algorithm to calculate energy correlators for quantum field theories, which consists of ground state preparation, applying source, sink, energy flux and real-time evolution operators and Hadamard test. We discuss how to take the asymptotic detector limit in the Hamiltonian lattice approach. We then calculate the energy correlators for the SU(2) pure gauge theory in 2+1 dimensions on 3 x 3 and 5 x 5 honeycomb lattices with j_max=1/2 at fixed couplings, by using both classical methods and the quantum algorithm studied. The results obtained from the quantum algorithm and the IBM emulator are consistent with the classical methods’ results. We lay out the path forward for calculations in the physical limit.

Motivated by the Gottesman-Knill theorem, we present a detailed study of the quantum complexity of p-shell and sd-shell nuclei. Valence-space nuclear shell-model wavefunctions generated by the BIGSTICK code are mapped to qubit registers using the Jordan-Wigner mapping (12 qubits for the p-shell and 24 qubits for the sd-shell), from which measures of the many-body entanglement (n-tangles) and magic (non-stabilizerness) are determined. While exact evaluations of these measures are possible for nuclei with a modest number of active nucleons, Monte Carlo simulations are required for the more complex nuclei. The broadly applicable Pauli-String I Z exact (PSIZe-) MCMC technique is introduced to accelerate the evaluation of measures of magic in deformed nuclei (with hierarchical wavefunctions), by factors of ∼ 8 for some nuclei. Significant multi-nucleon entanglement is found in the sd-shell, dominated by proton-neutron configurations, along with significant measures of magic. This is evident not only for the deformed states, but also for nuclei on the path to instability via regions of shape coexistence and level inversion. These results indicate that quantum-computing resources will accelerate precision simulations of such nuclei and beyond. [IQuS@UW-21-088]

We demonstrate how to construct a fully gauge-fixed lattice Hamiltonian for a pure SU(2)  gauge theory. Our work extends upon previous work, where a formulation of an SU(2) lattice gauge theory was developed that is efficient to simulate at all values of the gauge coupling. That formulation utilized maximal-tree gauge, where all local gauge symmetries are fixed and a residual global gauge symmetry remains. By using the geometric picture of an SU(2) lattice gauge theory as a system of rotating rods, we demonstrate how to fix the remaining global gauge symmetry. In particular, the quantum numbers associated with total charge can be isolated by rotating between the lab and body frames using the three Euler angles. The Hilbert space in this new “sequestered” basis partitions cleanly into sectors with differing total angular momentum, which makes gauge-fixing to a particular total charge sector trivial, particularly for the charge-zero sector. In addition to this sequestered basis inheriting the property of being efficient at all values of the coupling, we show that, despite the global nature of the final gauge-fixing procedure, this Hamiltonian can be simulated using quantum resources scaling only polynomially with the lattice volume.