Classical Reversible Computation by Quantum Coherence

Abstract

Rising energy demand from data-center and AI applications has renewed interest in reversible computation, where logic need not dissipate heat at every step if information is uncomputed. Implementations have so far been classical: adiabatic CMOS recovers part of the switching energy but still moves thousands of $k_{B}T$ per logic node at room temperature. Here we propose classical reversible logic implemented by coherent spin dynamics in a spin quantum-dot array, with inputs and outputs in classical basis states and no algorithmic use of superposition. The same spin stores, transports, and computes, with unitary rotation replacing irreversible switching. The universal building block is an iToffoli gate driven by DC voltage pulses and exchange between hole spins in Ge/SiGe quantum dots. Simulations with realistic model parameters reproduce the Toffoli truth table and yield a testable error landscape. Because shuttling transports the bit without measurement, logic and data movement remain unitary until readout. Millivolt pulses on femtofarad gates with superconducting lines dissipate only dielectric loss and have no thermodynamic floor. With the loss parameters assumed for a demonstrated device the gate energy is $\sim 10^2{k}_{B}T\ln 2$ at 4 K; at a design point within reach of existing devices it can fall below the Landauer scale $k_{B}T\ln 2$, five to seven orders of magnitude less than a CMOS Toffoli. The same semiconductor hardware therefore serves both purposes, supporting quantum algorithms when superposition is used and classical reversible logic otherwise.

59-page Supplementary Information attached as ancillary file. v4: corrects an error in the energy calibration of v3; the sub-Landauer gate energy is now a design point with stated conditions