Consequences of Many-cell Correlations in Treating Clocked Quantum-dot Cellular Automata Circuits

TL;DR

This paper investigates how intercellular entanglement affects the behavior of clocked quantum-dot cellular automata, revealing significant differences from traditional approximations and highlighting implications for molecular and atomic implementations.

Contribution

It introduces a Hamiltonian-based simulation including entanglement effects in QCA, contrasting with the commonly used ICHA approximation, and analyzes the impact of energy relaxation on system dynamics.

Findings

Entanglement alters the qualitative behavior of QCA systems.

Energy relaxation leads to unpolarized ground states in active cell groups.

Oscillations in polarization states occur during information propagation.

Abstract

Quantum-dot Cellular Automata (QCA) provides a basis for classical computation without transistors. Many simulations of QCA rely upon the so-called Intercellular Hartree Approximation (ICHA), which neglects the possibility of entanglement between cells. Here, we present computational results that treat small groups of QCA cells with a Hamiltonian analogous to a quantum mechanical Ising-like spin chain in a transverse field, including the effects of intercellular entanglement. When energy relaxation is included in the model, we find that intercellular entanglement changes the qualitative behaviour of the system, and new features appear. In clocked QCA, isolated groups of active cells experience oscillations in their polarization states as information propagates. Additionally, energy relaxation tends to bring groups of cells to an unpolarized ground state. This contrasts with the results of previous simulations which employed the ICHA. The ICHA is a valid approximation in the limit of very low tunneling rates, which can be realized in lithographically defined quantum-dots. However, in molecular and atomic implementations of QCA, entanglement will play a greater role. The degree to which entanglement poses a problem for memory and clocking depends upon the interaction of the system with its environment, as well as the system's internal dynamics.