Statistical properties of a quantum cellular automaton

The density classification (DC) task, a computation which maps global density information to local density, is studied using one-dimensional non-unitary quantum cellular automata (QCAs). Two approaches are considered: one that preserves the number density and one that performs majority voting. For number-preserving DC, two QCAs are introduced that reach the fixed-point solution in a time scaling quadratically with the system size. One of the QCAs is based on a known classical probabilistic cellular automaton which has been studied in the context of DC. The second is a new quantum model that is designed to demonstrate additional quantum features and is restricted to only two-body interactions. Both can be generated by continuous-time Lindblad dynamics. A third QCA is a hybrid rule defined by both discrete-time and continuous-time three-body interactions that is shown to solve the majority voting problem within a time that scales linearly with the system size.

Quantum Cellular Automata (QCA) offers a new approach to building computer circuits. In the light of these global research led to the development are found. Since memory is one of the most applicable basic units in digital circuits, but Its smaller components, which are called by filip-flop is created. Although there are some QCA structures for a memory cell in the literature, however, QCA characteristics may be used in designing a more optimized memory cell than blindly modeling CMOS logics in QCA. It is trying to propose a new design of the D-ff be paid within QCA. It is designed to lower the number of cells used to build D-ff. Also, to prove the correctness of implementation in routine simulator (QCADesigner) is used and the result schema is also expressed.

Recently, P. Shor (1994) has shown that quantum computers (computers which can operate simultaneously on a quantum superposition of inputs) permit efficient (i.e. polynomial-time) solutions of problems for which no efficient classical-mechanical solution is known. This has led to renewed interest in the question of whether or not quantum computers can be physically realized. One kind of quantum computer, quantum cellular automata, can be described by relatively simple Hamiltonians that resemble the Hamiltonians of spin systems. In this paper, we report a quantum cellular automaton which, though not itself computation-universal, forms an essential part of any quantum cellular automaton which is synchronized using Feynman's technique. This quantum cellular automaton has as its Hamiltonian the one-dimensional XY Hamiltonian, which is exactly solvable. Furthermore, there is experimental evidence from low-temperature measurements of the heat capacity and electric susceptibility that the Hamiltonian of the quantum cellular automaton is realized in nature by the rare-earth compound praseodymium ethyl sulfate near 1 K. >

We construct a novel three-dimensional quantum cellular automaton (QCA) based on a system with short-range entangled bulk and chiral semion boundary topological order. We argue that either the QCA is nontrivial, i.e. not a finite-depth circuit of local quantum gates, or there exists a two-dimensional commuting projector Hamiltonian realizing the chiral semion topological order (characterized by $U(1)_2$ Chern-Simons theory). Our QCA is obtained by first constructing the Walker-Wang Hamiltonian of a certain premodular tensor category of order four, then condensing the deconfined bulk boson at the level of lattice operators. We show that the resulting Hamiltonian hosts chiral semion surface topological order in the presence of a boundary and can be realized as a non-Pauli stabilizer code on qubits, from which the QCA is defined. The construction is then generalized to a class of QCAs defined by non-Pauli stabilizer codes on ${2^n}$-dimensional qudits that feature surface anyons described by $U(1)_{2^n}$ Chern-Simons theory. Our results support the conjecture that the group of nontrivial three-dimensional QCAs is isomorphic to the Witt group of non-degenerate braided fusion categories.

Missing-cell defects in QCA wires: The ground and excited electronic states perspectives

Quantum Cellular Automata (QCA) represents an emerging technology at the nanotechnology level. The effects of space radiations in QCA inverter gate are investigated in this paper. Single Electron Fault (SEF) is a fault which may happen during operation of QCA circuits. A detailed simulation based logic level modelling of Single Electron Fault for QCA inverter gate is represented in this paper. It will be shown that the behaviour of single electron fault in QCA devices is not similar to either previously investigated faults or conventional CMOS logic

Quantum cellular automata (QCA) technology is a nanotechnology provides a very different computation platform than traditional CMOS, in which polarization of electrons indicates the digital information. This paper discusses about the quantum cellular automata complex gate structure consist of 3, 4 and 5 input majority gates. Multi input complex gates can be constructed with the single QCA structure that can be configured in to Boolean functions and logic gates. We have also constructed product of sum and sum of product representation and other different Boolean functions. QCA circuits are simulated using QCAdesinger tool and waveforms are presented. We also validate the constructed structure by building combination al circuits like comparators etc. A single fixed QCA structure is useful for building module in QCA FPGA and ASIC applications.

We present on the use of well-known stochastic methods for computing the steady-state polarizations of quantum cellular automata (QCA) circuits. Typically, a Boltzmann distribution, which requires the exploration of the complete configuration space of an $$N$$ N -cell QCA circuit, is used to compute the $$2^N$$ 2 N steady-states of the QCA circuit. However, the exponential growth in states as the circuit size grows makes computing the Boltzmann distribution infeasible for large circuits. Thus, we approximate the Boltzmann distribution of a QCA circuit by conducting a partial exploration of the complete configuration space by means of a Monte Carlo method, simulated annealing, and a genetic algorithm. The approximated Boltzmann distribution from each method was able to compute the steady-state polarizations with a very high degree of accuracy, with the simulated annealing algorithm producing the best results.

A QCA in 2 + 1 and 3 + 1 dimensions

In this paper, we propose an alternative heterostructure device geometry to realize a semiconductor quantum cellular automata (QCA) cell. This device, called a split current quantum cellular automata (SCQCA) cell, has some attractive features which may enable the fabrication and circuit realization of QCA systems with current fabrication technologies. We present the device model and simulation results by incorporating this model in QCADesigner, a design and simulation tool for QCA. The simulations consist of the two cell interaction, showing the nonlinear cell-cell response function, a short wire, as well as the majority gate created with a cross pattern of five QCA cells.

We present results to show the effects of device scaling on the relativeperformance of three device technologies, namely resonant tunnellingdiodes (RTD), electronic quantum cellular automata (QCA) andcomplementary metal-oxide-semiconductor (CMOS) transistortechnology. The minimumfeature size (MOSFET or HFET gate lengths λ) is scaled from 250 to50 nm, while QCA inter-dot separations of 20 to 2 nm are examined. Thecomparison is made using a standard digital circuit architecture, namely amemory-adder model. Our aim is to compare these device technologies on thesystem level rather than individual device level. The results show that theRTDs offer speed advantages over CMOS, but improvements in the circuit densityare limited. The electronic QCAs will suffer both from effectively low packingdensity and low operating speeds in comparison to CMOS if conventional designsand a 2D architecture are used.

We study integrable spin chains and quantum and classical cellular automata with interaction range ℓ≥3. This is a family of integrable models for which there was no general theory so far. We develop an algebraic framework for such models, generalizing known methods from nearest-neighbor interacting chains. This leads to a new integrability condition for medium-range Hamiltonians, which can be used to classify such models. A partial classification is performed in specific cases, including U(1)-symmetric three-site interacting models, and Hamiltonians that are relevant for interaction-round-a-face models. We find a number of models which appear to be new. As an application we consider quantum brickwork circuits of various types, including those that can accommodate the classical elementary cellular automata on light cone lattices. In this family we find that the so-called Rule150 and Rule105 models are Yang-Baxter integrable with three-site interactions. We present integrable quantum deformations of these models, and derive a set of local conserved charges for them. For the famous Rule54 model we find that it does not belong to the family of integrable three-site models, but we cannot exclude Yang-Baxter integrability with longer interaction ranges.

In the past few years, CMOS semiconductor has been a growing and evolving technology in VLSI. However, due to the scaling issue and some other constraints like heat generation, high power consumption QCA (quantum cellular automata) emerged as an alternate and enhanced solution that provides a new technique of computing than CMOS in recent years. QCA is highly effective in implementing both Irreversible and Reversible logic, which has been shown to be incredibly efficient in terms of power consumption. A novel technique to data encryption called as SCV (select, cross, and variation) is demonstrated in this paper, which is based on ASCII to binary conversion and uses reversible logic. The data security procedure is aided by implementing SCV logic in reversible logic. Using Fredkin gate, it is built in QCA. QCADesigner tool has been used here for design and verification purposes. Total 80 cell counts and 0.14 μm 2 area are required. The theoretical data and the simulation results are the same as the intended circuit. Comparison to previous QCA architectural features is featured.

In this review we shortly summarize in an accessible way the physical and nanoscale material science aspects of the promising field of molecular quantum cellular automata (QCA). QCA is a revolutionary paradigm in quantum electronics with promising application in the conceptually new computing scheme which can be referred to as “computing with molecules”. This scheme of devices have vitally important advantages compared with conventional schemes of quantum computing in which the binary information is stored in the eigenvectors of a two‐level quantum system and therefore their practical application is strongly limited by the requirement of coherence. Molecular QCA promise nanometer‐scale units with ultra‐high device densities, as well as room temperature operation with extremely small heat release. Molecular materials provide at the same time options to control the key properties of the active molecules by chemical means. Hereunder we summarize the background of the electronic and vibronic problems in QCA cells represented by the tetrameric mixed‐valence (MV) complexes and organic molecules proposed for implementation as four‐site molecular QCA. We discuss the basic model of the molecular cell that include the following ingredients: 1) intracell Coulomb repulsion energy of the electrons in different electronic distributions among the redox sites; 2) electron transfer between redox sites which changes electronic distributions; 3) interaction of the itinerant electrons with molecular vibrations which is referred to as the vibronic interactions; 4) intercell Coulomb interaction by mean of which the binary information is transmitted from cell to cell. On the basis of this model we will study the cell polarization, adiabatic picture of the switching cycle describing interaction between the “input” and “output” molecular cells, non‐linear cell‐cell response function whose shape describes the action of molecular logic gates. Along with developed and current problems, we discuss new challenging trends of research in this fascinating area.

Kolmogorov complexity and cellular automata classification