DDMF: An Efficient Decision Diagram Structure for Design Verification of Quantum Circuits under a Practical Restriction

Recently much attention has been paid to quantum circuit design to prepare for the future "quantum computation era." Like the conventional logic synthesis, it should be important to verify and analyze the functionalities of generated quantum circuits. For that purpose, we propose an efficient verification method for quantum circuits under a practical restriction. Thanks to the restriction, we can introduce an efficient verification scheme based on decision diagrams called Decision Diagrams for Matrix Functions (DDMFs). Then, we show analytically the advantages of our approach based on DDMFs over the previous verification techniques. In order to introduce DDMFs, we also introduce new concepts, quantum functions and matrix functions, which may also be interesting and useful on their own for designing quantum circuits.Comment: 15 pages, 14 figures, to appear IEICE Trans. Fundamentals, Vol. E91-A, No.1

Synthesis and Optimization of Reversible Circuits - A Survey

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table

GENETIC ALGORITHM FOR BINARY AND FUNCTIONAL DECISION DIAGRAMS OPTIMIZATION

Decision diagrams (DD) are a widely used data structure for discrete functions representation. The major problem in DD-based applicationsis the DD size minimization (reduction of the number of nodes), because their size is dependent on the variables order. Genetic algorithms are often used in different optimization problems including the DD size optimization. In this paper, we apply the genetic algorithm to minimize the size of both Binary Decision Diagrams (BDDs) and Functional Decision Diagrams (FDDs). In both cases, in the proposed algorithm, a Bottom-Up Partially Matched Crossover (BU-PMX) is used as the crossover operator. In the case of BDDs, mutation is done in the standard way by variables exchanging. In the case of FDDs, the mutation by changing the polarity of variables is additionally used. Experimental results of optimization of the BDDs and FDDs of the set of benchmark functions are also presented

Minimization of lines in reversible circuits

Reversible computing has been theoretically shown to be an efficient approach over conventional computing due to the property of virtually zero power dissipation. A major concern in reversible circuits is the number of circuit lines or qubits which are a limited resource. In this thesis we explore the line reduction problem using a decision diagram based synthesis approach and introduce a line reduction algorithm— Minimization of lines using Ordered Kronecker Functional Decision Diagrams (MOKFDD). The algorithm uses a new sub-circuit for a positive Davio node structure in addition to the existing node structures. We also present a shared node ordering for OKFDDs. OKFDDs are a combination of OBDDs and OFDDs. The experimental results shows that the number of circuit lines and quantum cost can be reduced with our proposed approach.NSER