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Minimization of Quantum Multiple-valued Decision Diagrams Using Data Structure Metrics.

David Y. Feinstein, Mitchell Aaron Thornton, D. Michael Miller

Published Jan 1, 2009• 3 citations
OpenAlex

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On the Data Structure Metrics of Quantum Multiple-Valued Decision Diagrams

David Y. Feinstein, Mitchell Aaron Thornton, D. Michael Miller

This paper describes new metrics for the data structure referred to as quantum multiple-valued decision diagrams (QMDD) which are used to represent the matrices describing reversible and quantum gates and circuits. These metrics provide information about QMDD that allows for improvement of minimization techniques. We explore metrics related to the frequency of edges with non-zero weight for the entire QMDD data structure and their histograms with respect to each variable. We observe some unique regularity particular to the methodology of the QMDD. We develop new heuristics for QMDD dynamic variable ordering (DVO) that are guided by the proposed metrics. Experimental results show the effectiveness of the proposed techniques.

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On the Skipped Variables of Quantum Multiple-Valued Decision Diagrams

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The data structure referred to as quantum multiple-valued decision diagrams (QMDD) is used to efficiently represent the unitary matrices describing reversible and quantum circuits. This paper investigates the conditions that cause skipped variables to appear in the QMDD of some binary and ternary quantum circuits. We have found that a unitary matrix that produces a skipped variable in a QMDD is likely to cause a specific anomaly when it is decomposed into a cascade of two-level unitary matrices by the Beck-Zeilinger-Bernstein-Bertani algorithm.

IEEE International Symposium on Multiple-Valued Logic (ISMVL)•May 1, 2011•5 citations
This paper describes new metrics for the data structure referred to as quantum multiple-valued decision diagrams (QMDD) which are used to represent the matrices describing reversible and quantum gates and circuits. These metrics provide information about QMDD that allows for improvement of minimization techniques. We explore metrics related to the frequency of edges with non-zero weight for the entire QMDD data structure and their histograms with respect to each variable. We observe some unique regularity particular to the methodology of the QMDD. We develop new heuristics for QMDD dynamic variable ordering (DVO) that are guided by the proposed metrics. Experimental results show the effectiveness of the proposed techniques.
The data structure referred to as quantum multiple-valued decision diagrams (QMDD) is used to efficiently represent the unitary matrices describing reversible and quantum circuits. This paper investigates the conditions that cause skipped variables to appear in the QMDD of some binary and ternary quantum circuits. We have found that a unitary matrix that produces a skipped variable in a QMDD is likely to cause a specific anomaly when it is decomposed into a cascade of two-level unitary matrices by the Beck-Zeilinger-Bernstein-Bertani algorithm.