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This article is from Nanoscale Research Letters , volume 7 . Abstract : 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-dot cell makes wire crossings one of the most problematic areas of ternary quantum-dot cellular automata circuit design. We hereby present a two-layer wire crossing that uses a specific clocking scheme, which ensures the crossed wires have the same effective delay.

Rapid progress in the field of nanotechnology includes using quantum dotcellular automata (QCA) as a replacement for conventional transistor-based complementary metal oxide semiconductor (CMOS) circuits in the construction of nano-circuits. Due to ultra low thermal dissipation, rapid clocking, and extremely high density, the QCA is a rapidly growing field in the nanotechnological field to inhibit the field effect transistor (FET)-based circuit. This paper discusses and evaluates two multiplexer (MUX) architectures: an innovative and effective 4×1 MUX structure and an 8×1 MUX structures using QCA technology. The suggested architectural designs are constructed using the Fredkin and controlled-NOT (CNOT) gates. These constructions were designed to simulate using tool QCA designer 2.0.3. The 591 and 1,615 cells would be used by the 4×1 and 8×1 QCA MUX architectures, respectively. The simulation results demonstrate that, when compared to the previous QCA MUX structures, the suggested QCA MUX designs have the best clock latency performance and use of different gate types.

A novel algorithm for working out the Kink energy of quantum-dot cellular automata (QCA) circuits and their fault tolerability is introduced. In this algorithm at first with determining the input values on a specified design, the calculation between cells makes use of Kink physical relations will be managed. Therefore, the polarization of any cell and consequently output cell will be set. Then by determining missed cell(s) on the discussed circuit, the polarization of output cell will be obtained and by comparing it with safe state or software simulation, its fault tolerability will be proved. The proposed algorithm was implemented on a novel and advance fault tolerance full adder whose performance has been demonstrated. This algorithm could be implemented on any QCA circuit. Noticeably higher speed of the algorithm than simulation and traditional manual methods, expandability of this algorithm for variable circuits, beyond of four-dot square of QCA circuits, and the investigation of several damaged cells instead just one and special cell are the advantages of algorithmic action.

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We consider Clifford Quantum Cellular Automata (CQCAs) and their time evolution. CQCAs are an especially simple type of Quantum Cellular Automata, yet they show complex asymptotics and can even be a basic ingredient for universal quantum computation. In this work we study the time evolution of different classes of CQCAs. We distinguish between periodic CQCAs, fractal CQCAs and CQCAs with gliders. We then identify invariant states and study convergence properties of classes of states, like quasifree and stabilizer states. Finally we consider the generation of entanglement analytically and numerically for stabilizer and quasifree states.

We consider Clifford Quantum Cellular Automata (CQCAs) and their time evolution. CQCAs are an especially simple type of Quantum Cellular Automata, yet they show complex asymptotics and can even be a basic ingredient for universal quantum computation. In this work we study the time evolution of different classes of CQCAs. We distinguish between periodic CQCAs, fractal CQCAs and CQCAs with gliders. We then identify invariant states and study convergence properties of classes of states, like quasifree and stabilizer states. Finally we consider the generation of entanglement analytically and numerically for stabilizer and quasifree states.

Molecular quantum-dot cellular automata (QCA) is an emerging nanocomputing paradigm, which operates on electrostatic repulsion phenomena between two electrons to keep those apart at the maximum distance to a rest position for obtaining the highest finding probability. In the field of Quantum-dot Cellular Automata, the digital logic gate approaches nearly about to nanometer in scale. In QCA quantum gates operate by the tunnelling effect of electrons from one quantum dot to another dot through revealing its wave nature. The operating speed of the device gains the speed of light because the quantum tunnelling occurs at the light speed. This paper compares two methodologies of quantum logic gate designing, those are universal T gate designing and conventional gate designing practice. One 22 cells 2x1 MUX is proposed which is designed by a conventional method, that provides 20.35% optimization in area occupancy compared to the best-reported designs. Furthermore, one 11 cells 2:1 MUX layout is proposed which achieves 33.33% area reduction compared to the best ever multiplexer designed in QCA technology.

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 exponential decay of correlations in the unique invariant state. The main technical tool is a quantum version of oscillation norms, defined in the classical case as the sum over all sites of the variations of an observable with respect to local spin-flips.

In this paper, in order to investigate natural transformations from discrete CA to QCA, we introduce a new formulation of finite cyclic QCA and generalized notion of partitioned QCA. According to the formulations, we demonstrate the condition of local transition functions, which induce a global transition of well-formed QCA. Following the results, extending a natural correspondence of classical cells and quantum cells to the correspondence of classical CA and QCA, we have the condition of classical CA such that CA generated by quantumization of its cells is well-formed QCA. Finally we report some results of computer simulations of quantumization of classical CA.

Quantum computation based on quantum cellular automata (QCA) can greatly reduce the control and precision necessary for experimental implementations of quantum information processing. A QCA system consists of a few species of qubits in which all qubits of a species evolve in parallel. We show that, in spite of its inherent constraints, a QCA system can be used to study complex quantum dynamics. To this aim, we demonstrate scalable operations on a QCA system that fulfill statistical criteria of randomness and explore which criteria of randomness can be fulfilled by operators from various QCA architectures. Other means of realizing random operators with only a few independent operators are also discussed.

Motivated by the recent work of Patel et al., this paper clarifies a connection between coined quantum walks and quantum cellular automata in a general setting. As a consequence, their result is naturally derived from the connection.

Motivated by the recent work of Patel et al., this paper clarifies a connection between coined quantum walks and quantum cellular automata in a general setting. As a consequence, their result is naturally derived from the connection.

In recent work [quant-ph/0405174] by Schumacher and Werner was discussed an abstract algebraic approach to a model of reversible quantum cellular automata (CA) on a lattice. It was used special model of CA based on partitioning scheme and so there is a question about quantum CA derived from more general, standard model of classical CA. In present work is considered an approach to definition of a scheme with "history", valid for quantization both irreversible and reversible classical CA directly using local transition rules. It is used language of vectors in Hilbert spaces instead of C*-algebras, but results may be compared in some cases. Finally, the quantum lattice gases, quantum walk and "bots" are also discussed briefly.

We give a one-dimensional quantum cellular automaton (QCA) capable of simulating all others. By this we mean that the initial configuration and the local transition rule of any one-dimensional QCA can be encoded within the initial configuration of the universal QCA. Several steps of the universal QCA will then correspond to one step of the simulated QCA. The simulation preserves the topology in the sense that each cell of the simulated QCA is encoded as a group of adjacent cells in the universal QCA. The encoding is linear and hence does not carry any of the cost of the computation. We do this in two flavours: a weak one which requires an infinite but periodic initial configuration and a strong one which needs only a finite initial configuration. KEYWORDS: Quantum cellular automata, Intrinsic universality, Quantum computation.

The present manuscript deals with the realization of Processing In-memory (PIM) computing architecture using Quantum Dot Cellular Automata (QCA) and Akers array. The PIM computing architecture becomes popular due to its effective framework for storage and computation of data in a single unit. Here, we illustrate two input NAND and NOR gate with the help of QCA based Akers Array as a case study. The QCA flip-flop is used as a primitive cell to design PIM architecture. The results suggested that both the gate have minimum power dissipation. The polarization results of proposed architecture suggested that the signals are in good control. The foot print of the primitive cell equals to 0.04 micron^2, which is smaller than conventional CMOS primitive cell. The combination of QCA and Akers array provides many additional benefits over the conventional architecture like reduction in the power consumption and feature size, furthermore, it also improves the computational speed.

Cellular automata can show well known features of quantum mechanics, such as a linear rule according to which they evolve and which resembles a discretized version of the Schroedinger equation. This includes corresponding conservation laws. The class of "natural" Hamiltonian cellular automata is based exclusively on integer-valued variables and couplings and their dynamics derives from an Action Principle. They can be mapped reversibly to continuum models by applying Sampling Theory. Thus, "deformed" quantum mechanical models with a finite discreteness scale $l$ are obtained, which for $l\rightarrow 0$ reproduce familiar continuum results. We have recently demonstrated that such automata can form "multipartite" systems consistently with the tensor product structures of nonrelativistic many-body quantum mechanics, while interacting and maintaining the linear evolution. Consequently, the Superposition Principle fully applies for such primitive discrete deterministic automata and their composites and can produce the essential quantum effects of interference and entanglement.

Operation parameters of magnetic quantum cellular automata are evaluated for the purposes of reliable logic operation. The dynamics of the nanomagnets is simulated via the Landau-Lifshitz-Gilbert equations with a stochastic magnetic field corresponding to thermal fluctuations. It is found that in the macrospin approximation the switching speed does not change under scaling of both size and distances between nanomagnets. Thermal fluctuations put a limitation on the size of nanomagnets, since the gate error rate becomes excessive for nanomagnets smaller than 200nm at room temperature.

We investigate a connection between a property of the distribution and a conserved quantity for the reversible cellular automaton derived from a discrete-time quantum walk in one dimension. As a corollary, we give a detailed information of the quantum walk.

The purpose of the workshop was to bring together a select group of physicists and computer scientists to discuss methods of domesticating quantum dots for computational purposes. There are a variety of ways of constructing with modern lithography two-dimensional arrays of these quantum dots, in which the individual dots can range from simple quantum wells to sophisticated resonant tunneling devices. In each case, the arrays to date have been limited to two dimensions, or planar technology. Cellular automata provide a computing paradigm where uniform arrays with local interconnections can be made to yield general purpose computation in a reasonably compact way.

We present a scheme to perform universal quantum computation using global addressing techniques as applied to a physical system of endohedrally doped fullerenes. The system consists of an ABAB linear array of Group V endohedrally doped fullerenes. Each molecule spin site consists of a nuclear spin coupled via a Hyperfine interaction to an electron spin. The electron spin of each molecule is in a quartet ground state $S=3/2$. Neighboring molecular electron spins are coupled via a magnetic dipole interaction. We find that an all-electron construction of a quantum cellular automata is frustrated due to the degeneracy of the electronic transitions. However, we can construct a quantum celluar automata quantum computing architecture using these molecules by encoding the quantum information on the nuclear spins while using the electron spins as a local bus. We deduce the NMR and ESR pulses required to execute the basic cellular automata operation and obtain a rough figure of merit for the the number of gate operations per decoherence time. We find that this figure of merit compares well with other physical quantum computer proposals. We argue that the proposed architecture meets well the first four DiVincenzo criteria and we outline various routes towards meeting the fifth criteria: qubit readout.

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, exactly unitary, partitioning cellular automata. We find a one parameter family of evolution rules which are best interpreted as those for a one particle quantum automaton. This model is naturally reformulated as a two component cellular automaton which we demonstrate to limit to the Dirac equation. We describe two generalizations of this automaton, the second of which, to multiple interacting particles, is the correct definition of a quantum lattice gas.

Quantum cellular automata (QCA) are reviewed, including early and more recent proposals. QCA are a generalization of (classical) cellular automata (CA) and in particular of reversible CA. The latter are reviewed shortly. An overview is given over early attempts by various authors to define one-dimensional QCA. These turned out to have serious shortcomings which are discussed as well. Various proposals subsequently put forward by a number of authors for a general definition of one- and higher-dimensional QCA are reviewed and their properties such as universality and reversibility are discussed.

The use of buried dopants to construct quantum-dot cellular automata is investigated as an alternative to conventional electronic devices for information transport and elementary computation. This provides a limit in terms of miniaturisation for this type of system as each potential well is formed by a single dopant atom. As an example, phosphorous donors in silicon are found to have good energy level separation with incoherent switching times of the order of microseconds. However, we also illustrate the possibility of ultra-fast quantum coherent switching via adiabatic evolution. The switching speeds are numerically calculated and found to be 10's of picoseconds or less for a single cell. The effect of decoherence is also simulated in the form of a dephasing process and limits are estimated for operation with finite dephasing. The advantages and limitations of this scheme over the more conventional quantum-dot based scheme are discussed. The use of a buried donor cellular automata system is also discussed as an architecture for testing several aspects of buried donor based quantum computing schemes.

We discuss the action principle and resulting Hamiltonian equations of motion for a class of integer-valued cellular automata introduced recently [1]. Employing sampling theory, these deterministic finite-difference equations are mapped reversibly on continuum equations describing a set of bandwidth limited harmonic oscillators. They represent the Schroedinger equation. However, modifications reflecting the bandwidth limit are incorporated, i.e., the presence of a time (or length) scale. When this discreteness scale is taken to zero, the usual results are obtained. Thus, the linearity of quantum mechanics can be traced to the postulated action principle of such cellular automata and its conservation laws to discrete ones. The cellular automaton conservation laws are in one-to-one correspondence with those of the related quantum mechanical model, while admissible symmetries are not.

The goal of this study is to provide an exact unitary quantum cellular automata that, under discrete time steps, converges towards the Generalized Dirac Equation (GDE) in the continuum limit. The evolutionary rules for such a single particle walk are discussed in this paper, and it is shown that this quantum celluar automata will maintain similar properties to the GDE.

In a series of recent papers it has been shown how free quantum field theory can be derived without using mechanical primitives (including space-time, special relativity, quantization rules, etc.), but only considering the easiest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the simple principles of unitarity, homogeneity, locality, and isotropy. This has opened the route to extending the axiomatic information-theoretic derivation of the quantum theory of abstract systems to include quantum field theory. The inherent discrete nature of the informational axiomatization leads to an extension of quantum field theory to a quantum cellular automata theory, where the usual field theory is recovered in a regime where the discrete structure of the automata cannot be probed. A simple heuristic argument sets the scale of discreteness to the Planck scale, and the customary physical regime where discreteness is not visible is the relativistic one of small wavevectors. In this paper we provide a thorough derivation from principles that in the most general case the graph of the quantum cellular automaton is the Cayley graph of a finitely presented group, and showing how for the case corresponding to Euclidean emergent space (where the group resorts to an Abelian one) the automata leads to Weyl, Dirac and Maxwell field dynamics in the relativistic limit. We conclude with some perspectives towards the more general scenario of non-linear automata for interacting quantum field theory.

In this paper we present a quantization of Cellular Automata. Our formalism is based on a lattice of qudits, and an update rule consisting of local unitary operators that commute with their own lattice translations. One purpose of this model is to act as a theoretical model of quantum computation, similar to the quantum circuit model. It is also shown to be an appropriate abstraction for space-homogeneous quantum phenomena, such as quantum lattice gases, spin chains and others. Some results that show the benefits of basing the model on local unitary operators are shown: universality, strong connections to the circuit model, simple implementation on quantum hardware, and a wealth of applications.

Several proposed schemes for the physical realization of a quantum computer consist of qubits arranged in a cellular array. In the quantum circuit model of quantum computation, an often complex series of two-qubit gate operations is required between arbitrarily distant pairs of lattice qubits. An alternative model of quantum computation based on quantum cellular automata (QCA) requires only homogeneous local interactions that can be implemented in parallel. This would be a huge simplification in an actual experiment. We find some minimal physical requirements for the construction of unitary QCA in a 1 dimensional Ising spin chain and demonstrate optimal pulse sequences for information transport and entanglement distribution. We also introduce the theory of non-unitary QCA and show by example that non-unitary rules can generate environment assisted entanglement.

Clifford quantum cellular automata (CQCAs) are a special kind of quantum cellular automata (QCAs) that incorporate Clifford group operations for the time evolution. Despite being classically simulable, they can be used as basic building blocks for universal quantum computation. This is due to the connection to translation-invariant stabilizer states and their entanglement properties. We will give a self-contained introduction to CQCAs and investigate the generation of entanglement under CQCA action. Furthermore, we will discuss finite configurations and applications of CQCAs.

We investigate the possibility to have electron-pairs in dephasing-free subspace (DFS), by means of the quantum-dot cellular automata (QCA) and single-spin rotations, to carry out a high-fidelity and deterministic universal quantum computation. We show that our QCA device with electrons tunneling two dimensionally is very suitable for DFS encoding, and argue that our design favors a scalable quantum computation robust to collective dephasing errors.

We introduce a quantum cellular automaton that achieves approximate phase-covariant cloning of qubits. The automaton is optimized for 1-to-2N economical cloning. The use of the automaton for cloning allows us to exploit different foliations for improving the performance with given resources.

We consider discrete and integer-valued cellular automata (CA). A particular class of which comprises "Hamiltonian CA" with equations of motion that bear similarities to Hamilton's equations, while they present discrete updating rules. The dynamics is linear, quite similar to unitary evolution described by the Schroedinger equation. This has been essential in our construction of an invertible map between such CA and continuous quantum mechanical models, which incorporate a fundamental discreteness scale. Based on Shannon's sampling theory, it leads, for example, to a one-to-one relation between quantum mechanical and CA conservation laws. The important issue of linearity of the theory is examined here by incorporating higher-order nonlinearities into the underlying action. These produce inconsistent nonlocal (in time) effects when trying to describe continuously such nonlinear CA. Therefore, in the present framework, only linear CA and local quantum mechanical dynamics are compatible.

Information in a Quantum Cellular Automata architecture is encoded in the polarizazion state of a cell, i.e., in the occupation numbers of the quantum dots of which the cell is made up. Non-invasive charge detectors of single electrons in a quantum dot are therefore needed, and recent experiments have shown that a quantum constriction electrostatically coupled to the quantum dot may be a viable solution. We have performed a numerical simulation of a system made of a quantum dot and a nearby quantum point contact defined, by means of depleting metal gates, in a two-dimensional electron gas at a GaAs/AlGaAs heterointerface. We have computed the occupancy of each dot and the resistance of the quantum wire as a function of the voltage applied to the plunger gate, and have derived design criteria for achieving optimal sensitivity.

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.

If a one-dimensional quantum lattice system is subject to one step of a reversible discrete-time dynamics, it is intuitive that as much "quantum information" as moves into any given block of cells from the left, has to exit that block to the right. For two types of such systems - namely quantum walks and cellular automata - we make this intuition precise by defining an index, a quantity that measures the "net flow of quantum information" through the system. The index supplies a complete characterization of two properties of the discrete dynamics. First, two systems S_1, S_2 can be pieced together, in the sense that there is a system S which locally acts like S_1 in one region and like S_2 in some other region, if and only if S_1 and S_2 have the same index. Second, the index labels connected components of such systems: equality of the index is necessary and sufficient for the existence of a continuous deformation of S_1 into S_2. In the case of quantum walks, the index is integer-valued, whereas for cellular automata, it takes values in the group of positive rationals. In both cases, the map S -> ind S is a group homomorphism if composition of the discrete dynamics is taken as the group law of the quantum systems. Systems with trivial index are precisely those which can be realized by partitioned unitaries, and the prototypes of systems with non-trivial index are shifts.

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 discuss also Margolus QCA, also discussed by Schumacher and Werner. We introduce two new models, Coloured QCA, and Continuous-Time QCA. We also compare our models with the established models. We give proofs of computational equivalence for several of these models. We show the strengths of each model, and provide examples of how our models can be useful to come up with algorithms, and implement them in real-world physical devices.

It is shown that irreversible classical cellular automata can be performed by quantum algorithm using additional ancilla registers. The algorithm for cellular automata states analysis has been proposed. This algorithm is based on the elements of Grover's algorithm - the inversion of amplitude of searched states and unitary transform of inversion about the average. The inversion of searched states amplitudes can be performed by quantum Toffoli gate.

Quantum dot cellular autometa presents a promissing nanoscale technology for replacement of conventional cmos based circuits.In this paper we introduce qca logic gates such has qca inverter and qca majority gate.This paper design the sequential logic gates.such as D latch,SR latch,JK latch,T flipflop,D flipflop,2 bit counter,4 bit shift register.These designs are captured and simulated using a design calld QCA designer.

Quantum dot-cellular automata (QCA) technology has recently emerged as a potential candidate for the design of nanometer-scale computational circuits. In digital logic circuits, the comparator is the basic building block for comparing two binary values. This paper presents and implements two 1-bit QCA-based comparator designs. The proposed QCA implementations are compact, require only a single layer and are less complex compared to recently reported designs. The QCADesigner tool has been used to confirm the functional validity of the proposed QCA structures. The simulation results of the proposed comparators have shown considerable improvements compared to their existing counterparts in terms of the number of QCA cells and occupational area requirements in addition to cost and efficient complexity values. Furthermore, all of the proposed structures are dissipating extremely low energy values. Thus, the proposed QCA-based comparators can be viewed as viable options for low power digital applications. 

We discuss novel nanoelectronic architecture paradigms based on cells composed of coupled quantum dots. Boolean logic functions may be implemented in specific arrays of cells representing binary inlormation, the so-called Quantum Dot Cellular Automata (QCA). In addition, we discuss possible realizations of these structures in a variety of semiconductor system (including GaAs/AlGaAs, Si/SiGe, and Si/SiO2), rings of metallic tunnel junctions, and candidates for molecular implementations.

Quantum dot cellular automata (QCA) is a computing approach, in which binary information is represented as the charge configuration among the quantum dots. In nanoscale integrated circuit energy consumption and area utilization are a major concern, hence in recent years QCA has attracted a lot of attention as a result of its extremely small feature size and low power consumption. This technology is best suited for the semiconductor fabrication because of its less time consuming and less expensive methods . As per Moore’s law, number of transistors in an integrated circuit doubles for every two years, fabrication process faces some technical barriers. In context of this, QCA has emerged as the most promising technology, as an alternative to CMOS technology. In this paper efforts have been made to show the work carried out on QCA and focused on the science and technology applications of QCA due to its many interesting and important applications such as parity generator and checker.

Linear quantum cellular automata were introduced recently as one of the models of quantum computing. A basic postulate of quantum mechanics imposes a strong constraint on any quantum machine: it has to be unitary, that is its time evolution operator has to be a unitary transformation. In this paper we give an efficient algorithm to decide if a linear quantum cellular automaton is unitary. The complexity of the algorithm is O(n^((3r-1)/(r+1))) = O(n^3) in the algebraic computational model if the automaton has a continuous neighborhood of size r, where $n$ is the size of the input.

In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in an observation as the squared magnitude of its amplitude. We give an efficient algorithm which decides if a linear quantum cellular automaton is well-formed. The complexity of the algorithm is $O(n^2)$ in the algebraic model of computation if the input automaton has continuous neighborhood.

One-dimensional quantum cellular automata (QCA) consist in a line of identical, finite dimensional quantum systems. These evolve in discrete time steps according to a local, shift-invariant unitary evolution. By local we mean that no instantaneous long-range communication can occur. In order to define these over a Hilbert space we must restrict to a base of finite, yet unbounded configurations. We show that QCA always admit a two-layered block representation, and hence the inverse QCA is again a QCA. This is a striking result since the property does not hold for classical one-dimensional cellular automata as defined over such finite configurations. As an example we discuss a bijective cellular automata which becomes non-local as a QCA, in a rare case of reversible computation which does not admit a straightforward quantization. We argue that a whole class of bijective cellular automata should no longer be considered to be reversible in a physical sense. Note that the same two-layered block representation result applies also over infinite configurations, as was previously shown for one-dimensional systems in the more elaborate formalism of operators algebras [9]. Here the proof is made simpler and self-contained, moreover we discuss a counterexample QCA in higher dimensions.

The experimental demonstration of a basic cell of Quantum Dot Cellular Automata, a transistorless conmutation paradigm is presented. The device studied is a six-dot quantum dot cellular system consisting of a four-dot QCA cell and two electrometer dots. The system is fabricated using metal dots, connected by capacitors and tunnel junctions. The operation of a basic cell is confirmed by the externally detected change of the cell polarization controlled by the input signal. The cell exhibits a bistable response, with more than 80% charge polarization within a cell.

We define quantum cellular automata as infinite quantum lattice systems with discrete time dynamics, such that the time step commutes with lattice translations and has strictly finite propagation speed. In contrast to earlier definitions this allows us to give an explicit characterization of all local rules generating such automata. The same local rules also generate the global time step for automata with periodic boundary conditions. Our main structure theorem asserts that any quantum cellular automaton is structurally reversible, i.e., that it can be obtained by applying two blockwise unitary operations in a generalized Margolus partitioning scheme. This implies that, in contrast to the classical case, the inverse of a nearest neighbor quantum cellular automaton is again a nearest neighbor automaton. We present several construction methods for quantum cellular automata, based on unitaries commuting with their translates, on the quantization of (arbitrary) reversible classical cellular automata, on quantum circuits, and on Clifford transformations with respect to a description of the single cells by finite Weyl systems. Moreover, we indicate how quantum random walks can be considered as special cases of cellular automata, namely by restricting a quantum lattice gas automaton with local particle number conservation to the single particle sector.

We formalize a notion of discrete Lorentz transforms for Quantum Walks (QW) and Quantum Cellular Automata (QCA), in (1 + 1)-dimensional discrete spacetime. The theory admits a diagrammatic representation in terms of a few local, circuit equivalence rules. Within this framework, we show the first-order-only covariance of the Dirac QW. We then introduce the Clock QW and the Clock QCA, and prove that they are exactly discrete Lorentz covariant. The theory also allows for non-homogeneous Lorentz transforms, between non-inertial frames.

In quantum dot cellular automata emerge the electronic circuits. This technology takes more attention because of current silicon transistor technology faces many problems. The main advantages of QCA is fast speed and low power consumption. A quantum dot cell can be used to make gates (AND, OR and NAND) wires and memories also. The QCA has main benefits is faster speed reduced size digital circuits and minimum power consumption. In this paper QCA circuit design basic logic gate with the help of MV, Invertors and QCA wire. Jayshree Chouksey | Er. Deepak Pancholi"Review Paper on Quantum Dot Cellular Automata Using Nanoelectronics" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-5 , August 2018, URL: http://www.ijtsrd.com/papers/ijtsrd18214.pdf http://www.ijtsrd.com/engineering/electronics-and-communication-engineering/18214/review-paper-on-quantum-dot-cellular-automata-using-nanoelectronics/jayshree-chouksey

Quantum-dot Cellular Automata (QCA) is one of the most important computing technologies for the future and will be the alternative candidate for current CMOS technology. QCA is attracting a lot of researchers due to many features such as high speed, small size, and low power consumption. QCA has two main building blocks (majority gate and inverter) used for design any Boolean function. QCA also has an inherent capability that used to design many important gates such as XOR and Multiplexer in optimal form without following any Boolean function. This paper presents a novel design 2:1 QCA-Multiplexer in two forms. The proposed design is very simple, highly efficient and can be used to produce many logical functions. The proposed design output comes from the inherent capabilities of quantum technology. New 4:1 QCA-Multiplexer has been built using the proposed structure. The output waveforms showed the wonderful performance of the proposed design in terms of the number of cells, area, and latency.

As transistor geometries are reduced, quantum effects begin to dominate device performance. At some point, transistors cease to have the properties that make them useful computational components. New computing elements must be developed in order to keep pace with Moore s Law. Quantum dot cellular automata (QCA) represent an alternative paradigm to transistor-based logic. QCA architectures that are robust to manufacturing tolerances and defects must be developed. We are developing software that allows the exploration of fault tolerant QCA gate architectures by automating the specification, simulation, analysis and documentation processes.