Circuit Knitting for Periodic Boundary Conditions

by Peter Vander Griend (Brookhaven National Laboratory)

Wednesday 4 Nov 2026, 15:30 → 17:00 US/Eastern

Large Seminar Room (BNL Building 510)

Extracting physical predictions from quantum simulations of lattice gauge theories requires treating finite-volume corrections. Periodic boundary conditions (PBC) reduce these corrections with respect to open boundary conditions (OBC) (exponentially vs. power law in lattice size L) at the price of routing overhead or increased hardware connectivity. Circuit knitting is the decomposition of a non-local gate into a quasi-probability distribution over local circuits (i.e., mid-circuit measurement, single-qubit insertions), the outputs of which are recombined by classical post processing. This allows for the implementation of PBC without low-fidelity SWAP gates or beyond-nearest-neighbor hardware connectivity. In this talk, I will present an introduction to Z2 lattice gauge theory in 1+1D: the simplest confining lattice gauge theory and, in essence, a transverse-field Ising chain coupled to dynamical matter. Simulating this theory, we find, for targeted observables, PBC converges to within 10^-3 of the infinite-volume limit already at 6 sites while OBC requires ~120 sites. We find additionally that implementation of PBC with circuit knitting provides a decrease in the number of entangling CNOT gates and comparable accuracy to PBC with SWAP gates at the price of a large resampling overhead. I will close with an outlook on relevance and implementation on larger lattices and in higher dimensions.