Quantum cellular automata

Conventional CA are defined by assigning to each of the N linearly connected sites, a time-dependent variable Oi t) (i=0,l. N), belonging to a finite commutative ring TZk (usually represented by the integers modulo A , Zk). These site values, or colors, evolve iteratively according to a range-r mapping (j  

Although the two quantum models are defined somewhat dilferently, both QCA-I and QCA-II start with the same basic premise, endowing the classical system with two characteristically quantum features. They both (1) replace each site variable with a quantum state containing all fc classical site-color possibilities, and (2) introduce a quantum transition operator I , defining mixed color — mixed a)lor transitions. Only in QCA-II, however, is also unitary see discussion below. 

Focusing on strictly local (i.e. nearest neighbor) interactions. Grossing and Zeilinger [gross88a] consider the following unitary evolution operator U, approximated to first order by  

Using (5 = et/fi., the corresponding evolution operator and rule for QCA-I then become, respectively. 

The qualitative behavior of this system is most conveniently studied by looking at space-time mai)S of the normalized probability values Pj(t) = Tj(f), using grey shades to represent different probabilities. For simplicity, 6 is sot equal to (j(,(l -f i), and the effects of varying magnitudes of the off-diagonal terms is observed by varying S.  

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Quantum Cellular Automata (QCA) in order to address the possibly very fundamental role CA-like dynamics may play in the microphysical domain, some form of quantum dynamical generalization to the basic rule structure must be considered. One way to do this is to replace the usual time evolution of what may now be called classical site values ct, by unitary transitions between fe-component complex probability- amplitude states, ct > - defined in sncli a way as to permit superposition of states. As is standard in quantum mechanics, the absolute square of these amplitudes is then interpreted to give the probability of observing the corresponding classical value. Two indepcuidently defined models - both of which exhibit much of the typically quantum behavior observed in real systems are discussed in chapter 8.2,... 

Ient93] Lent, C.S., P.D.Tougaw and W.Porod, Bistable saturation in coupled quantum dots for quantum cellular automata, Appl. Phys. Lett. 62 (1993) 714-716. 

Quantitative XPS, 24 92-94 Quantum and molecular mechanical simulations, combined, 76 750-751 Quantum condition equation, 23 803 Quantum cellular automata (QCA),... 

Quantum dots (QDs, small conducting regions less than 1 pm in size that can contain from one to a few thousand electrons and have a variety of geometries and dimensions) are a component of the quantum cellular automata (QCA) approach to molecular computing64 while quantum islands (QIs) are wider versions of QDs that have similar characteristics. If one places four QDs in a square array to form a QCA, such that the electrons can tunnel betweens QDs but cannot leave the array, then Coulomb repulsion will force the electrons to occupy QDs on opposite corners of the array. By aligning groups of QCAs, then one could transmit potentials from one end of the line to the other, essentially doing computations. 

J. Twamley, Quantum-Cellular-Automata Quantum Computing with Endohedral Fullerenes, Phys. Rev. A67,052318(2003). 

Ordered arrays of nanocrystals can be thought of as arrays of SETs, where the electrostatic interaction between neighboring SETs acts as wireless communication means. It has been suggested by Korotkov [64] and Lent [961] that simple logical operations can be performed on a circuitry consisting of arrays of SETs in the form of chains or cells with suitable insulating spacers. An electric field applied in one direction polarizes the strings into either the 0 or the 1 state. Lent s scheme, named quantum cellular automata, instead... 

Jiao J, Long GJ, Rebbouh L, Grandjean F, Beatty AM, Fehlner TP (2005) Properties of a mixed-valence (Fe )2(Fe )2 square ceU for utilization in the quantum cellular automata paradigm for molecular electronics. J Am Chem Soc 127 17819-17831. doi 10.1021/ja0550935... 

Lent CS (2006) Quantum cellular automata. Imperial College Press, London... 

The first approach to molecular computing is based on quantum cellular automata (QCA) and related electrostatic information transfers. This method relies on electrostatic field repulsions to transport information throughout the circuitry. One major benefit of the QCA or electrostatics approach is that heat dissipation is less of an issue because only a few or fractions of an electron are used for each bit of information in classical solid-state devices. 

Nemykin VN, Rohde GT, Barrett CD, Hadt RG, Bizzarri C, Galloni P, Floris B, Nowik I, Heiber RH, Marrani AG, Zanoni R, Loim NM (2009) Electron-transfer processes in metal-free tetraferrocenylpoiphyrin. Understanding internal interactions to access mixed-valence states potentially useful for quantum cellular automata. J Am Chem Soc 131(41) 14969-14978... 

Grossing, G., and Zeilinger, A. (1988) Structures in quantum cellular automata. Physica B151, pp. 366-370. 

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