Quantum Abacus: A Strain-Engineered Platform for Passive, Reversible Fermionic Computation

The scalability of active, gate-based quantum computers is fundamentally challenged by the “Thermodynamic Wall,” where the heat from control electronics becomes prohibitive. This study computationally investigates the “Quantum Abacus,” a passive quantum computing architecture that circumvents this limit by using static strain engineering to control fermionic transport. We introduce a theoretical framework that unifies the Signal-Worker ontology with the physics of strain-induced gauge fields and “Tensor Locking.” Using a 1D tight-binding model parameterized for the Weyl semimetal TaAs, we demonstrate that achievable strain gradients (0-5%) can form isolated quantum registers and modulate fermionic hopping integrals. Crucially, simulations utilizing optimized control pulses demonstrate coherent adiabatic transfer with fidelities exceeding 99.9%, resolving previous concerns regarding operation quality. Furthermore, thermodynamic analysis confirms that these strain-mediated operations operate near the Landauer limit, offering an energy efficiency advantage of orders of magnitude over active microwave gating. This work establishes the physical principles and quantifies the thermodynamic advantages of a passive, material-based computational paradigm, offering a rigorous blueprint for a new class of “Green Quantum” technologies.