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Derivatives of Perkowski’s Gate

k. f2. t. t. . g. h. P. A. B. Q. f 2. R. C. . Toffoli gates. Derivatives of Perkowski’s Gate. Generalized multi-input multiplexer. f2. De Vos gates. . A. P. Feynman gates. Many other gate families. f 1. Q. P. B. A. . B. Q. f 2. R. C. 01. CMOS gates. S. D.

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Derivatives of Perkowski’s Gate

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  1. k f2 t t ... g h P A B Q f2 R C  Toffoli gates Derivatives of Perkowski’s Gate Generalized multi-input multiplexer f2 De Vos gates  A P Feynman gates Many other gate families f 1 Q P B A  B Q f 2 R C 01 CMOS gates S D Kerntopf gates 0 1 Generalized Maitra gates Maitra gates Fredkin gates

  2. Structure of Wave Cascade • The definitions presented in this section are based on and , with some modifications. • Definition. A complex Maitra term is recursively defined as follows: • (1) Constant 0 (1) Boolean function is a Maitra term. • (2) A literal is a Maitra term. • (3) If Mi is a Maitra term, a is a literal, and G is an arbitrary two-input Boolean function, then Mi+1 = G( a, Mi+1 ) is a Maitra term. • Additionally, it is required that each variable appears in each Maitra term only once and that the same variable ordering is used to represent all Maitra terms. • Previous authors restricted the two-input functions used in the Maitra terms to only functions AND, OR, and EXOR. • For the purposes of reversible logic synthesis, on the other hand, it is better to use the above more general definition. • In a variation of our algorithm targeting low-power CMOS implementation, G cannot be an EXOR function and its complement, NEXOR.

  3. Generalized Maitra Gate, Maitra Gate or CMOS Gate Reversible Wave Cascade

  4. Material for exam • Definition of reversible functions. • Balanced and Conservative functions. Interaction and other optically-realizable reversible gates that are not n*n gates. • Toffoli, Feynman, Peres, Fredkin, Miller, Margolus and Kerntopf gates. Properties. Be able to synthesize one from another one. SWAP gates. • Convertion of irreversible circuit to reversible quantum array. • Concepts of garbage, input constants and ancilla bits. • Mirrors, local mirrors, spies, folding of constants. • Generalized controlled gates (so-called Perkowski’s gates). • Transposition vector, vs set of cycles, vs Kmap vs truth table vs BDD notations. Go from one to another. • MMD algorithm and synthesis without ancilla bits. • EXOR Lattice for symmetric and non-symmetric functions. Understanding of symmetry and its uses. • Naïve methods of converting from irreversible netlist to reversible quantum cascade. • Billard Ball model. • KFDD and function graphs with linear and nonlinear preprocessors. Davio versus Shannon expansions. • Synthesis of linear reversible circuits. • Nets versus lattices, single-output versus multi-output • Multiple-valued reversible logic. Fundamentals. (no advanced methods).

  5. Material for exam 17. PPRM, FPRM and ESOP. Synthesis and use in reversible logic. 18. Kronecker Products and matrix representation of logic. 19. QUIDDs. 20. Analyze a circuit with CV, CV+ and CNOT gates. 21. Analyze Mitra cascades or other complex realizations. No synthesis. 22. Being able to use symmetry or other properties such as balancedness, or NPNP classification classes in problems formulated in natural language. 23. Being able to combine several methods to design a practical quantum oracle, such as a spectral transform or arithmetic circuit. 24. Being able to combine several methods, or at least select one good method to analyze a reversible circuit. Binary of multi-valued. 25. Being able to analyze a reversible fuzzy circuit. 26. Being able to solve linear equations to solve some problem in reversible logic. (1) expansions of non-symmetric functions. (2) inverse gate. (3) find inputs states from output states. 27. Testability of simple cascades. EXOR cascade. Cascade from PPRM.

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