QCA qubits and electrostatic limitations on single qubit operations

Andreas Weichselbaum, Sergio E. Ulloa

F. A. Calderon-Vargas, J. P. Kestner

Andreas Weichselbaum, Sergio E. Ulloa

We investigate the characteristics of purely electrostatic interactions with external gates in constructing full single-qubit manipulations. The quantum bit is naturally encoded in the spatial wave function of the electron system. Single-electron transistor arrays based on quantum dots or insulating interfaces typically allow for electrostatic controls where the interisland tunneling is considered constant, e.g., determined by the thickness of an insulating layer. A representative array of $3\ifmmode\times\else\texttimes\fi{}3$ quantum dots with two mobile electrons is analyzed using a Hubbard Hamiltonian and a capacitance matrix formalism. Our study shows that it is easy to realize the first quantum gate for single-qubit operations, but that a second quantum gate comes only at the cost of compromising the low-energy two-level system that encodes the qubit. We use perturbative arguments and the Feshbach formalism to show that this compromising of the two-level system is a rather general feature for electrostatically interacting qubits and is not just related to the specific details of the system chosen. We show further that full implementation requires tunable tunneling or external magnetic fields.

Kara Maller

S. Arash Sheikholeslam, Konrad Walus

In this work, we develop a method to use Quantum- Dot Cellular Automata (QCA) for universal quantum computing. This method is based conceptually on refocusing in NMR systems. We show how an array of QCA cells can be used for isolated single qubit, as well as multi-qubit operations, such as the CNOT, by dividing the cells into active and passive sets such that the active cells undergo the transform while passive cells hold their quantum states. The same technique is used for developing a multi-qubit quantum memory. The effect of imperfect control parameters is discussed and the total time for a typical quantum operation is given. Using this approach, different quantum gates are implemented using pulse sequences applied to the QCA cells via control fields and potentials, while the layout remains the same.

D. V. Averin