Quantum cellular automata

Quantum Cellular Automata (QCA) refers to models of quantum computation, which have been devised in analogy to conventional models of cellular automata introduced by von Neumann. It may also refer to quantum dot cellular automata, which is a proposed physical implementation of "classical" cellular automata by exploiting quantum mechanical phenomena. Scaling of CMOS devices is being aggressively pursued by shrinking transistor dimensions,reducing power supply voltages and increasing operating frequencies.Such aggressive scaling adversely results in a series of non-ideal behaviors such as high leakage current and high power density levels. These issues will eventually become road blocks and slow down the scaling trend that exists for years. Quantum-dot Cellular Automata(QCA)is attracting a lot of attention due to its extremely small feature size(at the molecular even atom level)and ultra low power consumption.A quantum cell consists of four dots at the corners with two excess electrons that can tunnel between the dots. Due to Coulomb repulsion the two excess electrons always occupy diagonally opposite dots. The high inter-cell barrier suppresses the electrons in a cell from tunneling out of the cell. There are two configurations with energetically equivalent polarizations designated as +1 and −1. In a second type of QCA cells, the dots are located at the middle of the sides of cells. The basic logic element in QCA logic is a majority gate. ^[1]

Usage of the term

In the context of models of computation or of physical systems, quantum cellular automaton refers to the merger of elements of both (1) the study of cellular automata in conventional computer science and (2) the study of quantum information processing. In particular, the following are features of models of quantum cellular automata:

• The computation is considered to come about by parallel operation of multiple computing devices, or cells. The cells are usually taken to be identical, finite-dimensional quantum systems (e.g. each cell is a qubit);
• Each cell has a neighborhood of other cells. Altogether these form a network of cells, which is usually taken to be regular (e.g. the cells are arranged as a lattice with or without periodic boundary conditions);
• The evolution of all of the cells has a number of physics-like symmetries. Locality is one: the next state of a cell depends only on its current state and that of its neighbours. Homogeneity is another: the evolution acts the same everywhere, and is independent of time;
• The state space of the cells, and the operations performed on them, should be motivated by principles of quantum mechanics.

One feature that is often considered important for a model of quantum cellular automata is that it should be universal for quantum computation (i.e. that it can efficiently simulate quantum Turing machines,^[2][3] some arbitrary quantum circuit^[4] or simply all other quantum cellular automata^[5] .^[6] Models which have been proposed recently impose further conditions, e.g. that quantum cellular automata should be reversible and/or local unitary, and have an easily determined global transition function from the rule for updating individual cells.^[3] Recent results show that these properties can be derived axiomatically, from the symmetries of the global evolution.^[7][8][9]

Models of QCA

Early proposals

Richard Feynman suggested an initial approach to quantizing a model of cellular automata^[10] Gerhard Grössing and Anton Zeilinger introduced the term "quantum cellular automata" to refer to a model they defined in 1988:^[11] however, their model has very little in common with the concepts developed in quantum computation after David Deutsch's formal development of that subject from 1985,^[12] and so has not been developed significantly as a model of computation.

Models of universal quantum computation

The first formal model of quantum cellular automata to be researched in depth was that introduced by John Watrous.^[2] This model was developed further by Wim van Dam,^[13] as well as Christoph Dürr, Huong LêThanh, and Miklos Santha,^[14][15] Jozef Gruska.^[16] and Pablo Arrighi.^[17] However it was later realised that this definition was too loose, in the sense that some instances of it allow superluminal signalling.^[7][8] A second wave of models includes those of Susanne Richter and Reinhard Werner,^[18] of Benjamin Schumacher and Reinhard Werner,^[7] of Carlos Pérez-Delgado and Donny Cheung,^[3] and of Pablo Arrighi, Vincent Nesme and Reinhard Werner.^[8][9] These are all closely related, and do not suffer any such locality issue. In the end one can say that they all agree to picture quantum cellular automata as just some large quantum circuit, infinitely repeating across time and space.

Models of physical systems

Models of quantum cellular automata have been proposed by David Meyer,^[19][20] by Bruce Bogosian and Washington Taylor,^[21] and by Peter Love and Bruce Bogosian^[22] as a means of simulating quantum lattice gases, motivated by the use of "classical" cellular automata to model classical physical phenomena such as gas dispersion.^[23]

Quantum dot cellular automata

A proposal for implementing classical cellular automata by systems designed with quantum dots has been proposed under the name "quantum cellular automata" by Doug Tougaw and Craig Lent,^[24] as a replacement for classical computation using CMOS technology. In order to better differentiate between this proposal and models of cellular automata which perform quantum computation, many authors working on this subject now refer to this as a quantum dot cellular automaton.

References