We introduce a fast and highly efficient physically realizable bit swap. Employing readily available and scalable Josephson junction microtechnology, the design implements the recently introduced paradigm of momentum computing. Its nanosecond speeds and sub-Landauer thermodynamic efficiency arise from dynamically storing memory in momentum degrees of freedom. As such, during the swap, the microstate distribution is never near equilibrium and the memory-state dynamics fall far outside of stochastic thermodynamics that assumes detailed-balanced Markovian dynamics. The device implements a bit-swap operation-a fundamental operation necessary to build reversible universal computing. Extensive, physically calibrated simulations demonstrate that device performance is robust and that momentum computing can support thermodynamically efficient, high-speed, large-scale general-purpose computing that circumvents Landauer's bound.