Consequences of Many-Cell Correlations in Clocked Quantum-Dot Cellular Automata

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. The ICHA was originally proposed as a solution to the problem of exponential scaling in the computational cost of fully quantum mechanical treatments. However, in some cases, the ICHA predicted errors in QCA operation, and quantum correlations were required for circuits to operate correctly. While quantum correlations can remedy certain problems that present themselves in ICHA calculations, here we present simulations that show that quantum correlations may in fact be problematic in other situations, such as clocked QCA. Small groups of QCA cells are modelled with a Hamiltonian analogous to a quantum mechanical Ising-like spin chain in a transverse field, including the effects of intercellular entanglement completely. When energy relaxation is included in the model, we find that intercellular entanglement changes the qualitative behavior of the system, and new features appear. In clocked QCA, isolated groups of active cells have a tendency to oscillate between polarization states as information propagates. Additionally, energy relaxation tends to bring groups of cells to an unpolarized steady state. This contrasts with the results of previous simulations, which employed the ICHA. The ICHA may in fact be a good 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 intercellular correlations pose a problem for memory, and clocking depends upon implementation-specific details of the interaction of the system with its environment, as well as the system's internal dynamics.