QMDD: A Decision Diagram Structure for Reversible and Quantum Circuits

Miller, David M.; Thornton, Mitchell A.

doi:10.1109/ismvl.2006.35

Cited by 130 publications

(108 citation statements)

References 11 publications

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“…Quantum Multiple Valued Decision Diagrams (QMDDs) [38], provide a more specific data-structure for reversible functions. Hence, developing synthesis based on these DDs seems plausible.…”

Section: Future Directionsmentioning

confidence: 99%

Synthesis of Reversible Circuits Using Decision Diagrams

Drechsler

Wille

2012

2012 International Symposium on Electronic System Design (ISED)

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Abstract-Due to its promising applications in domains like quantum computation or low-power design, synthesis of reversible circuits has become an intensely studied topic. However, many synthesis methods are limited by non-scalable function representations like truth tables. As an alternative, synthesis exploiting graph-based representations have been suggested. The underlying structure is a decision diagram (DD) that may vary regarding reduction methods, decomposition rules, or ordering restrictions.In this work, we review the progress of DD-based synthesis. It is shown that dedicated transformation rules can be applied to generate circuits for functions with a large number of inputs. We discuss the effect of different decomposition types or typical DD improvements like complement edges and re-ordering. Furthermore, we describe how DD-based synthesis can be exploited to transfer theoretical results known from decision diagrams into the domain of reversible circuits. Finally, further directions for future work are outlined.

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“…Quantum Multiple Valued Decision Diagrams (QMDDs) [38], provide a more specific data-structure for reversible functions. Hence, developing synthesis based on these DDs seems plausible.…”

Section: Future Directionsmentioning

confidence: 99%

Synthesis of Reversible Circuits Using Decision Diagrams

Drechsler

Wille

2012

2012 International Symposium on Electronic System Design (ISED)

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“…Note that we use the notation for controlled qudit gates as that used in [5] where the controlled qudit value is indicated numerically at the control point. The circuit in Figure 3 was generated with a version of the automatic synthesis method from [6] adapted to QMDDs [13]. The quantum ternary circuit in Figure 5 results when a digit encoding of 0→(-1), 1→0, 2→(+1) is used.…”

Section: Ternary Modular Multiplicative Inverse Circuitmentioning

confidence: 99%

“…Both of these circuits were verified through equivalence checking using QMDDs [13]. The manually designed circuit is shown in Figure 6 and the automatically synthesized circuit is shown in Figure 7.…”

Section: Ternary Discrete Logarithm Circuit Cascadesmentioning

confidence: 99%

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Quantum Logic Implementation of Unary Arithmetic Operations

Thornton

Matula

Spenner

et al. 2008

38th International Symposium on Multiple Valued Logic (Ismvl 2008)

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“…not only the Boolean values 0 and 1 known from conventional computations need to be considered, but also quantum states representing the superposition of them. To address this problem, approaches have been introduced which (1) rely on simulation [15] and often require an exhaustive consideration of the input vectors or (2) make use of decision diagram-like data-structures [16], [9], [10], [12], [14] that suffer from memory explosion.…”

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confidence: 99%

A compact and efficient SAT encoding for quantum circuits

2013

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Abstract-Promising applications of quantum computation motivated the consideration of corresponding design methods for this emerging technology. Here, researchers are faced with the problem that signals in quantum circuits may (theoretically) assume an infinite number of states. As a consequence, design approaches based on Boolean satisfiability (SAT) were subject to restrictions so far. In this work, we propose a compact and efficient SAT encoding for quantum circuits that loses these restrictions. For this purpose, a structural analysis is introduced which determines an upper bound on possible quantum states. The applicability of the encoding is exemplarily demonstrated by a SAT-based equivalence checker.

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QMDD: A Decision Diagram Structure for Reversible and Quantum Circuits

Abstract: In this paper, we present a novel structure, Quantum Multiple-valued Decision Diagrams (QMDD)

Cited by 130 publications

References 11 publications

Synthesis of Reversible Circuits Using Decision Diagrams

Synthesis of Reversible Circuits Using Decision Diagrams

Quantum Logic Implementation of Unary Arithmetic Operations

A compact and efficient SAT encoding for quantum circuits

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