Analysis and Synthesis of Quantum Circuits by Using Quantum Decision Diagrams

Abdollahi, Afshin; Pedram, Massoud

doi:10.1109/date.2006.244176

Cited by 54 publications

(54 citation statements)

References 25 publications

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“…As described, they should be useful for the analysis and the verification of quantum circuits with a practical restriction. It should be noted that DDMFs are provably useful even for quantum circuit design methods since DDMFs can be considered as a generalization of the data structure used in the design method in [5].…”

Section: Discussionmentioning

confidence: 99%

“…Thus, we can use this circuit (as a part of a quantum algorithm) to calculate the Boolean function f (x 1 , x 2 ) = x 1 · x 2 + x 1 · x 2 . As mentioned before, although our goal is to construct such a quantum circuit that calculates a Boolean function, quantum specific gates (such as R(θ) and V ) are useful [5,6,7,13] to make the circuit size smaller. For example, the circuit as shown in Fig.…”

Section: Semi-classical Quantum Circuit (Scqc)mentioning

confidence: 99%

“…However, the quantum decision diagrams in [5] are used to represent conventional Boolean functions whereas DDMFs are used for representing matrix functions: the terminal node of a DDMF is a matrix I. Also a weight on an edge in DDMFs is generalized to any matrix.…”

Section: ) (3) the Root Node Has One Incoming Edge That Has A Matrixmentioning

confidence: 99%

“…However, even if we consider quantum circuits calculating only Boolean functions, it is known that non-classical (quantum specific) gates are useful to reduce the circuit size [5,6,7,13]. Thus we need to verify quantum circuits with non-classical gates.…”

Section: Introductionmentioning

confidence: 99%

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

Yamashita

Minato

Miller

2008

IEICE Transactions on Fundamentals of Electronics, Communicatio

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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.

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Section: Discussionmentioning

confidence: 99%

Section: Semi-classical Quantum Circuit (Scqc)mentioning

confidence: 99%

Section: ) (3) the Root Node Has One Incoming Edge That Has A Matrixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Yamashita

Minato

Miller

2008

IEICE Transactions on Fundamentals of Electronics, Communicatio

View full text Add to dashboard Cite

show abstract

“…In [17], Shende et al presented a top-down structure based on Cosine-Sine decomposition to introduce quantum multiplexer and used it to propose a synthesis algorithm in terms of quantum multiplexers. In [18] a quantum decision diagram (QDD) structure was introduced and used to synthesize quantum circuits using R x (θ) rotation gates. However, they assumed that the QDD control variables are pure quantum states.…”

Section: Previous Workmentioning

confidence: 99%