Geometric scaling effects on energy–delay trade-offs in QCA devices: A quantum coherence perspective

Quantum cellular automata (QCA) present a promising low-power paradigm for beyond-CMOS computing, representing logic states through electron configurations in quantum-dot cells and enabling current-free signal propagation via Coulomb interactions. In this work, a quantum-coherent modeling framework is employed, combining a two-level Hamiltonian with the coherence-vector formalism, to investigate energy dissipation and quantum-limited switching delay bounds in geometrically scaled QCA devices. Upper-bound estimates of leakage energy and switching-related dissipation are obtained in closed analytical form, providing a physics-based understanding of how the electronic tunneling matrix element, Coulomb coupling, and temperature govern dissipation. Lower bounds on switching delay are then derived from the energy–time uncertainty principle. The framework is applied to four representative full adder architectures, spanning conventional large layouts and compact designs across 18 and 4 nm technology nodes under multiple electronic tunneling regimes. The results highlight contrasting scaling effects. Compact circuits achieve substantial delay reduction (sub-5 fs) at the cost of enhanced leakage due to stronger Coulomb coupling, whereas larger layouts exhibit reduced switching dissipation but more modest delay improvements. These findings provide a physics-grounded perspective on energy–delay trade-offs in nanoscale QCA logic, offering insight into how cell-level design parameters influence dissipation and delay.