GKP-Stabilized Bosonic Encoding Maps Compact U(1) Gauge Fields Exactly onto Oscillator Hardware

The arXiv preprint constructs the encoding by solving Gauss's law then placing one rotor per remaining link on an oscillator. Trigonometric interactions are realized via GKP-stabilized phase gates; finite squeezing produces only small, analytically tractable shifts rather than leakage. In the one-plaquette compact QED3 test, real-time evolution plus controlled extrapolation recovered the exponentially small charge-sector splitting to within 1 percent of the exact rotor value. Syndrome extraction removes the dominant photon-loss displacement component while leaving higher-order noise bounded.

This approach directly addresses the hardware mismatch between angular lattice variables and continuous bosonic quadratures that has limited prior digital and analog gauge-theory simulations. By converting compactness into a correctable stabilizer code rather than an approximation, the scheme inherits GKP error-correction thresholds already demonstrated on superconducting and trapped-ion platforms. It therefore offers a concrete route to scaling beyond the small lattices currently accessible with qubit or qudit encodings.

The main limitation remains the squeezing depth required for target accuracy; the paper's error budget shows that 12 dB squeezing suffices for few-percent observables once extrapolation is applied, but current hardware typically reaches only 8-10 dB. Extending the construction to non-Abelian groups and higher-dimensional lattices will require additional multi-mode stabilizers whose overhead the authors have not yet quantified.

Next steps include experimental implementation on existing bosonic modules and benchmarking against qubit-based Trotter or variational methods on the same plaquette system to quantify gate-count and coherence advantages.