{"content":[{"text":"Quantum Computing with Quantum-dot Cellular Automata using Coherence Vector \n Formalism","bbox":{"left":0.088186,"top":0.09078,"width":0.8158449999999999,"height":0.04585600000000001}},{"text":"Géza Tóth1, John Timler and Craig S. Lent","bbox":{"left":0.329363,"top":0.153032,"width":0.337431,"height":0.02308199999999999}},{"text":"Department of Electrical Engineering \n University of Notre Dame, Notre Dame, IN 46556 \n e-mail: Geza.Toth.17@nd.edu, John.Timler.2@nd.edu, Lent@nd.edu","bbox":{"left":0.227206,"top":0.191205,"width":0.5423129999999999,"height":0.05551499999999998}},{"text":"1Department of Electrical Engineering \n Technical University of Budapest, Muegyetem rakpart 3-9., Budapest 1111, Hungary","bbox":{"left":0.165441,"top":0.259092,"width":0.6660200000000001,"height":0.04065800000000003}},{"text":"A coherence vector formalism is used to describe quantum computing with Quantum-dot \n Cellular Automata, and the realizations of basic quantum gates are also discussed.","bbox":{"left":0.152108,"top":0.314992,"width":0.6943149999999999,"height":0.03794000000000003}},{"text":"1. Introduction","bbox":{"left":0.088382,"top":0.370886,"width":0.125961,"height":0.020984999999999976}},{"text":"mathematical simplicity and the ability of this description to \n include dissipation. \n In Section 2 the physical background will be summa- \n rized, while Section 3 and 4 are about the realization of the \n Quantum Computing with QCA. Three basic operations will \n be implemented: the NOT, the controlled NOT and a \n three-bit quantum gate, that will be called modified con- \n trolled controlled NOT (MCCNOT) in this paper.","bbox":{"left":0.514853,"top":0.371792,"width":0.39703599999999994,"height":0.12283500000000003}},{"text":"A nanoelectronics technology that would enable device scal- \n ing down to molecular levels will almost certainly entail a \n cellular architecture with near-neighbor connectivity. One \n scheme that has been developed for physically realizing such \n a concept is termed Quantum-dot Cellular Automata (QCA) \n [1-8] The basic cell is comprised of four or five dots which \n can hold two extra electrons. Information is encoded in the \n geometrical charge configuration within the cell. The Cou- \n lomb interaction between cells provides the inter-cellular \n coupling. This interaction produces a sufficiently rich system \n that it has been shown that could be implemented in such a \n scheme. \n The two basis states of the QCA cell with polarization \n P=+1 and P=-1, respectively, are shown in Fig. 1.","bbox":{"left":0.088382,"top":0.40725,"width":0.397929,"height":0.21374300000000002}},{"text":"2. Application of the coherence vector \n formalism for QCA","bbox":{"left":0.514853,"top":0.509826,"width":0.315099,"height":0.03871200000000008}},{"text":"The Hamiltonian of a single QCA cell of a 1D array is [7]:","bbox":{"left":0.514853,"top":0.563765,"width":0.38276,"height":0.016776000000000013}},{"text":"EkP \n E0 – ---------- – γ \n 2 \n EkP \n –γ E0 + ---------- \n 2","bbox":{"left":0.661524,"top":0.600561,"width":0.1499290000000001,"height":0.08789899999999995}},{"text":"H ( γ ) =","bbox":{"left":0.589559,"top":0.630824,"width":0.05496999999999985,"height":0.018556999999999935}},{"text":"where γ is the interdot tunneling energy and Ek is the electro- \n static cost of two adjacent fully polarized cells having oppo- \n site polarization. The cell is coupled to its left and right \n neighbors through P which is the sum of the adjacent cell \n polarizations. \n The state vector of one cell can be given as the linear \n combination of the fully polarized P=+1 and P=-1 basis \n states. \n α \n |Ψ 〉 = α 1| 〉 + β –| 1 〉 = \n β \n Thus the state of a cell is described by two complex num- \n bers, α and β.","bbox":{"left":0.514853,"top":0.706947,"width":0.39721300000000004,"height":0.20707799999999998}},{"text":"P=+1","bbox":{"left":0.17799,"top":0.72619,"width":0.035641000000000006,"height":0.016776000000000013}},{"text":"P=-1","bbox":{"left":0.367067,"top":0.72619,"width":0.03188200000000002,"height":0.016776000000000013}},{"text":"FIGURE 1. Schematic representation of the QCA cells. Two \n electrons tunnel between the four dots in the cell. The two \n arrangements of charge shown are used to encode information \n in the cell.","bbox":{"left":0.097794,"top":0.755648,"width":0.373089,"height":0.05682600000000004}},{"text":"The empty circles denote a quantum dot, the lines show the \n possibility of interdot tunneling, and the solid circles indi- \n cate extra electron. Logical circuits (AND, OR, NOT gates) \n and Cellular Nonlinear Network [7,9-11] architectures can \n be both realized by this paradigm. \n In this paper the so-called coherence vector formalism \n [12] will be applied to the QCA. Its main advantages are the \n 0-7803-46369-7 / 98 $10.00 ©1998 IEEE \n 42","bbox":{"left":0.088382,"top":0.821793,"width":0.41764799999999996,"height":0.14886600000000005}}],"images_bbox":[],"images_bbox_not_text_overlap":[]}