Researchers used IBM quantum computers to simulate how a simple SU(2) lattice gauge theory relaxes to local thermal equilibrium. They evolved chains of up to 151 plaquettes and tracked measures of quantum entanglement on small regions. After applying error mitigation, the hardware results matched extrapolated classical simulator results for chains up to 101 plaquettes. The work shows that current noisy quantum machines can study local thermalization in a chaotic, nonabelian quantum system.

The theory they simulate is a minimally truncated version of the Kogut–Susskind Hamiltonian for SU(2) pure gauge fields. “Minimally truncated” means the electric field on each link is limited to the two lowest representation values (j ≤ 1/2). With that truncation the lattice model can be mapped to a one-dimensional spin chain. The mapped Hamiltonian contains several types of spin interactions, labeled in the paper as HZZ, HZ, HX, HZX, HXZ and HZXZ, and the authors use open boundary conditions to simplify the circuit layout.

Time evolution was implemented by Trotterization, a standard way to break a continuous time step into a sequence of simpler unitary gates. The needed gates include single-qubit rotations (RZ, RX) and two-qubit gates (RZZ, RZX). A nonstandard three-qubit operator was built from Hadamard gates, single-qubit Z rotations and CNOT gates. The authors start from a simple product state called the strong-coupling vacuum (all spins down) because it is easy to prepare on hardware. To read out local thermal properties they perform subsystem tomography: they measure many Pauli operator combinations on a small block of spins, reconstruct the reduced density matrix, and from that compute the entanglement spectrum, the Rényi-2 entropy (a simple entanglement measure), and the “anti-flatness” of the entanglement spectrum, which signals how "quantum" the transient state is.