Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
Quantum Query Complexity of Some Graph Problems
SIAM Journal on Computing
QMDD: A Decision Diagram Structure for Reversible and Quantum Circuits
ISMVL '06 Proceedings of the 36th International Symposium on Multiple-Valued Logic
Quantum Computer Science: An Introduction
Quantum Computer Science: An Introduction
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
An XQDD-Based Verification Method for Quantum Circuits
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Equivalence Checking of Reversible Circuits
ISMVL '09 Proceedings of the 2009 39th International Symposium on Multiple-Valued Logic
Quantum Circuit Simulation
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The Quantum Multiple-valued Decision Diagram (QMDD) data-structure has been introduced as a means for an efficient representation and manipulation of transformation matrices realized by quantum or reversible logic circuits. A particular challenge is the handling of arbitrary complex numbers as they frequently occur in quantum functionality. These numbers are represented through edge weights which, however, represent a severe obstacle with respect to canonicity, modifiability, and applicability of QMDDs. Previously introduced approaches did not provide a satisfactory solution to these obstacles. In this paper, we propose an improved factorization scheme for complex numbers that ensures a canonical representation while, at the same time, allows for local changes. We demonstrate how the proposed solution can be exploited to improve the data-structure itself (e.g. through variable re-ordering enabled by the advanced modifiability) and how applications such as equivalence checking benefit from that.