Dynamic Induction of Lattice Gauge Theories on a Quantum Computer

Quantum Simulations of Two-Dimensional Non-Abelian Adjoint String Breaking

Quantum computers offer the potential to directly probe the dynamics of strongly coupled quantum field theories. As a step towards reaching this potential, local Krylov-based truncations of a pure SU(2) lattice gauge theory on a triangular lattice are constructed. Adjoint strings connected to dynamical gluons are constructed in this truncated theory, and the resonances dominating the long-term dynamics at a large value of the gauge coupling are determined. Local operators are constructed to identify string oscillations and breakings. This is used to perform a quantum simulation of adjoint string breaking on an $8\times8$ and $16\times8$-site lattice with ibm_boston using all 156 qubits. Quantitative agreement with tensor network simulations is obtained for circuits with 7,634 CZ gates with a two-qubit gate depth of 218. In this simulation, the rates of oscillations and glueball production are identified with a distinctly non-Abelian signature of the underlying gauge group.

Measurement-based simulation of lattice gauge theory dynamics with adaptive quantum circuits on a trapped-ion processor

Measurement-based quantum simulation (MBQS)---a recently proposed architecture for simulating lattice gauge theories---implements Hamiltonian dynamics by consuming a model-specific entangled resource state with adaptive mid-circuit measurements, rather than by a gate-based circuit. The local constraints in lattice gauge theories are mirrored by the higher-form symmetries of the resource state. Here we report, to our knowledge, the first experimental realization of MBQS of real-time dynamics in the $(2+1)$-dimensional $\mathbb{Z}_2$ gauge theory using the Quantinuum System Model H2 trapped-ion processor. We observe coherent evolution of gauge-invariant observables on $2\times2$ and $3\times3$ spatial lattices, consuming virtual three-dimensional cluster states of 200 and 288 resource-state qubits that are generated from instantaneous blocks of 48 and 54 qubits within the 56-qubit register by measurement, reset, and re-entanglement. The measurement record that drives the evolution simultaneously provides one-form-symmetry syndromes at no additional cost, enabling postselection that strongly suppresses observed Gauss-law violations and improves aggregate agreement with ideal Trotterized dynamics. Our results demonstrate that MBQS is a viable, symmetry-aware architecture for simulating lattice field theories on present-day hardware.

Efficient Quantum Simulations of Yang-Mills theory with Maximal-tree Gauge

The results provide a rigorous complexity-theoretic demonstration that non-Abelian Yang--Mills theories can be simulated efficiently on quantum computers, paving the way toward first-principles quantum simulations of non-perturbative QCD dynamics.

Nonplanar qubit with tunable gauge symmetry

Circuit quantum electrodynamics embeds Josephson junction qubits within superconducting cavities, and has emerged as a leading approach to quantum computing and quantum simulation. Despite the many permutations of circuit geometry that have been explored, Josephson connectivities have so far been planar, making them effectively low-dimensional. Here we show that a non-planar qubit -- a $3\times3$ crossbar Josephson array -- gives rise to flux-tunable $\mathbb{Z}_3$ combinatorial gauge symmetry (CGS), potentially enabling spin-liquid behavior when networked into a lattice. The observed excitation spectrum shows excellent agreement with predictions from a neural network trained to generate variational quantum states, demonstrating that we have predictive power over our high-dimensional quantum system. Fine-structure splittings near the CGS point are compatible with weak tunneling or symmetry breaking due to experimental imperfections. We additionally use the superconducting cavity to externally induce symmetry breaking, observing a restoration of symmetry at the CGS point where ground states differ only by a $\mathbb{Z}_3$ phase. This work initiates a general program exploring lattice gauge theories using the toolbox of circuit quantum electrodynamics. More broadly, introducing non-planar Josephson connectivities opens a vast space for experimental and theoretical exploration of structures in almost any imaginable dimensionality and geometry.

A gauge-invariant theory of small Markovian errors in quantum gate sets

Noisy logic operations on a quantum computational register -- e.g., one or more qubits -- can be described by transfer matrices (a.k.a. CPTP maps or superoperators) that act linearly on the density matrix representing the register's quantum state. Collectively, these operations form a gate set. Gate sets have a gauge freedom; many gate sets that appear different actually predict the same experimental outcomes. A property of a gate set can be observable (and thus physically relevant) only if it is gauge-invariant. Unfortunately, no good gauge-invariant parameterizations of gate sets are known. We introduce the next best thing, a perturbative gauge-invariant parameterization of small Markovian errors in gate sets. We construct vector spaces of properties that are first-order gauge-invariant (FOGI). We show how to construct and understand FOGI properties, how to use them as coordinates to parameterize gate sets without gauge freedom, and how to extract approximately gauge-invariant error metrics.

Toward the real-time evolution of gauge-invariant Z 2 and U ð 1 Þ quantum link models on noisy intermediate-scale quantum hardware with error mitigation