We discuss the fundamental limits of computing using a new paradigm for quantum computation, cellular automata composed of arrays of Coulombically coupled quantum dot molecules, which we term quantum cellular automata (QCA). Any logical or arithmetic operation can be performed in this scheme. QCA’s provide a valuable concrete example of quantum computation in which a number of fundamental issue...

: Quantum-dot cellular automata are an interesting nanoscale computing paradigm. The introduction of the ternary quantum-dot cell enabled ternary computing, and with the recent development of a ternary functionally complete set of elementary logic primitives and the ternary memorizing cell design of complex processing structures is becoming feasible. The specific nature of the ternary quantum-d...

In this paper, a novel quantum-dot cellular automata (QCA) adder design is presented that reduces the number of QCA cells compared to previously reported designs. The proposed one-bit QCA adder structure is based on a new algorithm that requires only three majority gates and two inverters for the QCA addition. By connecting n one-bit QCA adders, we can obtain an n-bit carry look-ahead adder wit...

In this paper we have discussed various memory architectures for Quantum Dot Cellular automata. New architectures have been proposed and their comparison has been done on the basis of area and latency. A protocol for using the serial memory has been outlined. A hybrid memory has been proposed. It is shown that the hybrid memory can be used as a tradeoff between area advantage of serial memory a...

We define a class of dynamical maps on the quasi-local algebra of a quantum spin system, which are quantum analogues of probabilistic cellular automata. We develop criteria for such a system to be ergodic, i.e., to possess a unique invariant state. Intuitively, ergodicity obtains if the local transition operators exhibit sufficiently large disorder. The ergodicity criteria also imply bounds for...

The numbers of the figures are th e same as those in our origin al publi cation [1] . The read er is requested to consult the text of t hat publi cation together with the figures presented here. For reasons of clarity, we also poin t out that the matrix of equat ion (1.1) is a N X N square matrix with zeroes in the main diagon al. Thi s work was supported by the Bundesmini sterium fur Wissensch...

In this paper we present a systematic view of Quantum Cellular Automata (QCA), a mathematical formalism of quantum computation. First we give a general mathematical framework with which to study QCA models. Then we present four different QCA models, and compare them. One model we discuss is the traditional QCA, similar to those introduced by Shumacher and Werner, Watrous, and Van Dam. We discus...

A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, in this paper we begin an investigation of exactly unitary cellular automata. After proving that there can be no nontrivial, homogeneous, local, unitary, scalar cellular automaton in one dimension, we weaken the homogeneity condition and show that there are nontrivial...

Quantum-dot cellular automata (QCA) are a promising nanotechnology to implement digital circuits at the nanoscale. Devices based on QCA have the advantages of faster speed, lower power consumption, and greatly reduced sizes. In this paper, we are presented the circuits, which generate random numbers in QCA.  Random numbers have many uses in science, art, statistics, cryptography, gaming, gambli...