There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The organization of behavior: A neuropsychological theory

The Personal Interview

What is modal logic

IEEE transactions on computer-aided design of integrated circuits and systems : a publication of the IEEE Circuits and Systems Society

Finding appropriate bound sets of variables is the most zmportant task of functional decomposition. When sohing some problems the bound sets need to be large: for instance in decomposition to symmetric subfunctions realized in MOPS arrays for submicron technologaes, or when, no good small bound sets exist. In such cases the creation of the incompatibility graph, that is necessary to evaluate good variable partationings, becomes very inefficient. Therefore an algorithm is proposed here, that can speed up this process by orders of magnitude without sacrifying the quality of the decomposation, because the same graph coloring algorithms (exact or approximate) is still applied to the created graph:

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An efficient approach to decomposition with large sets of bound variables of multi-output boolean functions

Reversible logic is becoming more and more popular due to the fact that many novel technologies such as quantum computing, low power CMOS circuit design or quantum optical computing are becoming more and more realistic. In quantum computing, reversible computing is the main venue for the realization and design of classical functions and circuits. We present a new approach to synthesis of reversible circuits using Kronecker Functional Lattice Diagrams (KFLD). Unlike many of contemporary algorithms for synthesis of reversible functions that use n×n Toffoli gates, our method synthesizes functions using 3 × 3 Toffoli gates, Feynman gates and NOT gates. This reduces the quantum cost of the designed circuit but adds additional ancilla bits. The resulting circuits are always regular in a 4-neighbor model and all connections are predictable. Consequently resulting circuits can be directly mapped in to a quantum device such as quantum FPGA [14]. This is a significant advantage of our method, as it allows us to design optimum circuits for a given quantum technology. key words: reversible circuits synthesis, kronecker lattices, quantum computing

Synthesis of Quantum Arrays from Kronecker Functional Lattice Diagrams

Efficiently mapping binary functions to adiabatic quantum computers is an important problem because the resulting circuits can be used as oracles in Grover's algorithm. This paper presents a method for mapping binary functions to a two-dimensional grid of qubits with nearest neighbor interactions which is used in a prototype from D-Wave Systems. This is done by writing the binary function in a special form. This allows the binary function to be implemented by converting each gate into a 3-local Hamiltonian. These 3-local Hamiltonians are then converted into two-local Hamiltonians which are mapped to the grid of qubits.

/pdf/mapping-binary-functions-to-a-practical-adiabatic-quantum-2cvz095zxa.pdf

Mapping Binary Functions to a Practical Adiabatic Quantum Computer

Self-repairable GALs

Regular structures in Quantum-dot Cellular Automata (QCA) allow for ease of design and uniform clocking structure. The paper presents a comparative analysis of QCA realization using regular structures: Shannon-Lattices and Programmable Logic Arrays (PLAs). A software tool was developed that generates complete QCA-Shannon-Lattice and QCA-PLA Layouts for Boolean functions based on an input characterized macro-cell library. The correctness of equations were verified by performing simulations of the generated layouts. It is shown that the new regular lattices outperform PLAs and are closer to full custom design on Full Adders.

Marek Perkowski

Papers

An efficient approach to decomposition with large sets of bound variables of multi-output boolean functions

Synthesis of Quantum Arrays from Kronecker Functional Lattice Diagrams

Mapping Binary Functions to a Practical Adiabatic Quantum Computer

Self-repairable GALs

Comparative Analysis of Full Adder Custom Design Circuit using Two Regular Structures in Quantum-Dot Cellular Automata (QCA)