We present results from co-designed quantum simulations of the neutrinoless double-beta decay of a two-hadron nucleus in 1+1D quantum chromodynamics using IonQ’s Forte-generation trapped-ion quantum computers. Two flavors of dynamical quarks and leptons are distributed across two lattice sites and mapped to 32 qubits. An effective four-Fermi contact interaction is used to implement charged-current weak interactions between quarks and leptons, and lepton-number violation is induced by a neutrino Majorana mass. Statistically-significant signals for the neutrinoless decay of a two-hadron nucleus are measured during time evolution with a non-zero Majorana mass, making this the first quantum simulation to observe lepton-number violation in real time. This was made possible by co-designing the state preparation and time evolution quantum circuits to maximally utilize the all-to-all connectivity and native gate-set available on IonQ’s quantum computers. Quantum circuit compilation techniques and symmetry-aware error-mitigation methods, tailored to neutrinoless decays, allow accurate results to be extracted from quantum circuits with up to 470 two-qubit gates using Forte Enterprise. We present first benchmarks toward the real-time simulation of neutrinoless double-beta decay, and discuss the potential of future quantum simulations to provide yocto-second resolution of the reaction pathway for nuclear processes.

We would like to thank Saurabh Kadam 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 (MJS, IC, RCF), and by the Quantum Science Center (QSC) which is a National Quantum Information Science Research Center of the U.S. Department of Energy (MI, IC). This work is also supported, in part, through the Department of Physics and the College of Arts and Sciences at the University of Washington. RCF acknowledges support from the U.S. Department of Energy QuantISED program through the theory consortium “Intersections of QIS and Theoretical Particle Physics” at Fermilab, from the U.S. Department of Energy, Office of Science, Accelerated Research in Quantum Computing, Quantum Utility through Advanced Computational Quantum Algorithms (QUACQ), and from the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (PHY-2317110). RCF additionally acknowledges support from a Burke Institute prize fellowship. 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. AM, FT, MALR, AA, YDS, AB, CG, AK and MR are employees and equity holders of IonQ, Inc.

We present a digital quantum computation of two-hadron scattering in a Z2 lattice gauge theory in 1+1 dimensions. We prepare well-separated single-particle wave packets with desired momentum-space wavefunctions, and simulate their collision through digitized time evolution. Multiple hadronic wave packets can be produced using the systematically improvable algorithm of this work, achieving high fidelity with the target initial state, and demanding only polynomial resources in system size. Specifically, employing a trapped-ion quantum computer (IonQ Forte), we prepare up to three meson wave packets\ using 11 and 27 system qubits, and simulate collision dynamics of two meson wave packets for the smaller system. Despite noise effects, post-processing with a global-symmetry-based noise mitigation yields results consistent with numerical simulations, but decoherence limits evolution into long times. We demonstrate the critical role of high-fidelity initial states for precision measurements of state-sensitive observables, such as S-matrix elements and decay amplitudes. While we have not established quantum advantage by this early hardware demonstration, our algorithms are general, and our findings imply the potential of quantum computers in simulating scattering processes in strongly interacting gauge theories.

This is a theoretical overview of quarkonium production in relativistic heavy ion collisions given for the Hard Probe 2024 conference at Nagasaki. The talk focuses on the application of the open quantum system framework and the formulation of the chromoelectric correlator that uniquely encodes properties of the quark-gluon plasma relevant for quarkonium dynamics and thus can be extracted from theory-experiment comparison.

We identify a new element in quantum simulations of lattice gauge theories, arising from spacetime-dependent quantum corrections in the relation between the link variables defined on the lattice and their continuum counterparts.  While in Euclidean spacetime simulations, based on Monte Carlo sampling, the corresponding tadpole improvement leads to a constant rescaled value per gauge configuration, in Minkowski spacetime simulations it requires a state- and time dependent update of the coefficients of operators involving link variables in the Hamiltonian. To demonstrate this effect, we present the results of numerical simulations of the time evolution of truncated SU(2) plaquette chains and honeycomb lattices in 2+1D, starting from excited states with regions of high energy density, and with and without entanglement.

We would like to thank Randy Lewis for helpful discussions regarding the classical implementation of tadpole improvement. 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 (Martin, Xiaojun), and by the Quantum Science Center (QSC) which is a National Quantum Information Science Research Center of the U.S. Department of Energy (Marc). This work is also supported, in part, through the Department of Physics and the College of Arts and Sciences at the University of Washington. We have made extensive use of Wolfram Mathematica. 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.

A new quantum algorithm for preparing the initial state (wavepackets) of a quantum field theory scattering simulation is introduced. This method extends recent techniques for preparing W states using mid-circuit measurement and feedforward to efficiently create wavepackets. The required circuit depth is independent of wavepacket size, representing a superexponential improvement over previous methods. Explicit examples are provided for one-dimensional Ising field theory, scalar field theory, the Schwinger model, and two dimensional Ising field theory. The circuits that prepare wavepackets in one-dimensional Ising field theory are used to simulate scattering on 100 qubits of IBM’s quantum computer ibm_marrakesh. Quantum simulations are performed at a center of mass energy above inelastic threshold, and measurements of the energy density in the post-collision state reveal the production of new particles. A novel error mitigation strategy based on energy conservation enables accurate results to be extracted from circuits with up to 6,412 two-qubit gates. The prospects for a near-term quantum advantage in simulations of scattering are discussed.

Suppression of open heavy quarks and quarkonia in heavy-ion collisions are among the most informative probes of quark-gluon plasma (QGP). Interpreting the full wealth of data obtained from the collision events requires a precise theoretical understanding of the evolution of heavy quarks and quarkonia as they propagate through a strongly coupled plasma. Such calculations require the evaluation of a gauge-invariant correlator of chromoelectric fields. This chromoelectric correlator encodes all the characteristics of QGP that the dissociation and recombination dynamics of quarkonium are sensitive to, which is to say can in principle measure. We review its distinctive qualitative features at weak coupling in QCD up to next-to-leading order and at strong coupling in $\mathcal{N}=4$ SYM using the AdS/CFT correspondence, as well as its formulation in Euclidean QCD. Furthermore, we report on recent progress in applying our results to the calculation of the final quarkonium abundances after propagating through a cooling droplet of QGP, which illustrates how we may learn about QGP from quarkonium measurements. We devote special attention to how the presence of a strongly coupled plasma modifies the transport description of quarkonium, in comparison to approaches that rely on weak coupling approximations to describe quarkonium dissociation and recombination.

Simulating the dynamics of non-equilibrium matter under extreme conditions lies beyond the capabilities of classical computation alone. Remarkable advances in quantum information science and technology are profoundly changing how we understand and explore fundamental quantum many-body systems, and have brought us to the point of simulating essential aspects of these systems using quantum computers. I discuss highlights, opportunities and the challenges that lie ahead.

Improved Kogut-Susskind Hamiltonians for quantum simulations of non-Abelian Yang-Mills gauge theories are developed for honeycomb (2+1D) and hyper-honeycomb (3+1D) spatial tessellations. This is motivated by the desire to identify lattices for quantum simulations that involve only 3-link vertices among the gauge field group spaces in order to reduce the complexity in applications of the plaquette operator. For the honeycomb lattice, we derive a classically O(b²)-improved Hamiltonian, with b being the lattice spacing. Tadpole improvement via the mean-field value of the plaquette operator is used to provide the corresponding quantum improvements. We have identified the (non-chiral) hyper-honeycomb as a candidate spatial tessellation for 3+1D quantum simulations of gauge theories, and determined the associated O(b)-improved Hamiltonian.

This work was supported, in part, by the Quantum Science Center (QSC) which is a National Quantum Information Science Research Center of the U.S. Department of Energy (Marc), and 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 (Martin, Xiaojun).

Recent measurements of polarization phenomena in relativistic heavy ion collisions have aroused a great interest in understanding dynamical spin evolution of the QCD matter. In particular, the spin alignment signature of $J/\psi$ has been recently observed in Pb-Pb collisions at LHC, which may infer nontrivial spin transport of quarkonia in quark gluon plasmas. Motivated by this, we study the spin-dependent in-medium dynamics of quarkonia by using the potential nonrelativistic QCD (pNRQCD) and the open quantum system framework. By applying the Markovian approximation and Wigner transformation, we systematically derive the Boltzmann transport equation for vector quarkonia with polarization dependence in the quantum optical limit. As opposed to the previous study for the spin-independent case where the collision terms depend on chromoelectric correlators, the new kinetic equation incorporates gauge invariant correlators of chromomagnetic fields that determine the recombination and dissociation terms with polarization dependence at the order we are working in the multipole expansion. In the quantum Brownian motion limit, the Lindblad equation with new transport coefficients defined in terms of the chromomagnetic field correlators have also been derived. Our formalism is generic and valid for both weakly-coupled and strongly-coupled quark gluon plasmas. It may be further applied to study spin alignment of vector quarkonia in heavy ion collisions.

We search for emergent hydrodynamic modes in real-time Hamiltonian dynamics of $2+1$-dimensional SU(2) lattice gauge theory on a quasi one dimensional plaquette chain, by numerically computing symmetric correlation functions of energy densities on lattice sizes of about $20$ with the local Hilbert space truncated at $j_{\rm max}=\frac{1}{2}$. Due to the Umklapp processes, we only find a mode for energy diffusion. The symmetric correlator exhibits transport peak near zero frequency with a width proportional to momentum squared at small momentum, when the system is fully quantum ergodic, as indicated by the eigenenergy level statistics. This transport peak leads to a power-law $t^{-\frac{1}{2}}$ decay of the symmetric correlator at late time, also known as the long-time tail, as well as diffusion-like spreading in position space. We also introduce a quantum algorithm for computing the symmetric correlator on a quantum computer and find it gives results consistent with exact diagonalization when tested on the IBM emulator. Finally we discuss the future prospect of searching for the sound modes.