Quantum simulation of real-time bosonic dynamics with binary and unary position encodings on superconducting and trapped-ion processors

arXiv:2611.13079v1 Announce Type: new Abstract: Simulating a bosonic degree of freedom on qubit hardware requires discretizing its position space, and the qubit encoding of the resulting lattice determines the circuits that realize its real-time dynamics. We compare binary and unary encodings of a position lattice on superconducting (IBM) and trapped-ion (IonQ) processors. Binary encoding applies the kinetic term through the quantum Fourier transform; unary encoding uses one qubit per site, single-qubit rotations for the potential and excitation-conserving exchange gates for the kinetic term. For a single degree of freedom the unary dynamics is a free-fermion problem, and its product formula compresses exactly into a nearest-neighbor circuit of fixed size.