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

We propose an approach to optimally synthesize quantum circuits from non-permutative quantum gates such as Controlled-Square-Root-of-Not (i.e. Controlled-V). Our approach reduces the synthesis problem to multiple-valued optimization and uses group theory. We devise a novel technique that transforms the quantum logic synthesis problem from a multi-valued constrained optimization problem to a group permutation problem. The transformation enables us to utilize group theory to exploit the properties of the synthesis problem. Assuming a cost of one for each two-qubit gate, we found all reversible circuits with quantum costs of 4, 5, 6, etc, and give another algorithm to realize these reversible circuits with quantum gates.

/pdf/exact-synthesis-of-3-qubit-quantum-circuits-from-non-binary-50dcot3tx8.pdf

Exact Synthesis of 3-Qubit Quantum Circuits from Non-Binary Quantum Gates Using Multiple-Valued Logic and Group Theory

Finding column multiplicity index is one of important component processes in functional decomposition of discrete functions for circuit design and especially Data Mining appli cations How important it is to solve this problem exactly from the point of view of the minimum complexity of decomposition and related to it error in Machine Learning type of applications In order to investigate this problem we wrote two graph coloring programs exact program EXOC and approximate program DOM DOM can give provably exact results on some types of graphs These programs were next incorporated into the multi valued decomposer of functions and rela tionsMVGUD Extensive testing of MVGUD with these programs has been performed on various kinds of data Based on these tests we demonstrated that exact graph coloring is not necessary for high quality functional decomposers especially in Data Mining applications giving thus an other argument that e cient and e ective Machine Learning approach based on decomposition is possible

/pdf/exact-graph-coloring-for-functional-decomposition-do-we-need-5645bn44ip.pdf

Exact Graph Coloring for Functional Decomposition: Do We Need It?

Spectral representation of multiple-valued input binary functions is proposed for the first time. Such a representation is composed of a vector of Walsh transforms, each of which is defined for one pair of the input variables of the function. The new representation has the advantage of being real valued and having, therefore, an easy interpretation. Since two types of binary function value codings are used, two different spectra are introduced. The meaning of each spectral coefficient is discussed in classical logic terms. The mathematical relationships between the number of true, false, and don't care minterms and spectral coefficients are stated. These relationships can be used to calculate the spectral coefficients directly from the graphical representations of binary functions. As do the spectral methods in classical logic design, the new spectral representation of binary functions find applications in many problems of analysis, synthesis, and testing of circuits described by such functions. >

Walsh type transforms for completely and incompletely specified multiple-valued input binary functions

We describe the use of Grovers algorithm as implemented in a quantum logic circuit that produces a solution for a classical switching circuit design problem. The particular application described here is to determine a Fixed Polarity Reed-Muller (FPRM) form that satisfies a threshold value constraint, thus we find a particular FPRM form among all 2^n FPRM forms that has a number of terms less than or equal to the threshold value. Grovers algorithm is implemented in a quantum logic circuit that also contains a subcircuit that expresses all possible FPRM solutions of a given function. This approach illustrates how fast transforms as known from spectral theory can be combined with quantum computing as a part of an oracle.

http://lyle.smu.edu/~mitch/ftp_dir/pubs/ismvl06b.pdf

A Quantum CAD Accelerator Based on Grover&#146;s Algorithm for Finding the Minimum Fixed Polarity Reed-Muller Form

An efficient algorithm is presented for ternary Reed-Muller expansions under fixed polarities. It involves less computation cost than previous algorithms.

Marek Perkowski

Papers

Exact Synthesis of 3-Qubit Quantum Circuits from Non-Binary Quantum Gates Using Multiple-Valued Logic and Group Theory

Exact Graph Coloring for Functional Decomposition: Do We Need It?

Walsh type transforms for completely and incompletely specified multiple-valued input binary functions

A Quantum CAD Accelerator Based on Grovers Algorithm for Finding the Minimum Fixed Polarity Reed-Muller Form

Efficient computation for ternary Reed-Muller expansions under fixed polarities

Marek Perkowski

Papers

Exact Synthesis of 3-Qubit Quantum Circuits from Non-Binary Quantum Gates Using Multiple-Valued Logic and Group Theory

Exact Graph Coloring for Functional Decomposition: Do We Need It?

Walsh type transforms for completely and incompletely specified multiple-valued input binary functions

A Quantum CAD Accelerator Based on Grover&#146;s Algorithm for Finding the Minimum Fixed Polarity Reed-Muller Form

Efficient computation for ternary Reed-Muller expansions under fixed polarities

A Quantum CAD Accelerator Based on Grovers Algorithm for Finding the Minimum Fixed Polarity Reed-Muller Form