Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

New Generation Computing

Transformation rules for CNOT-based quantum circuits and their applications

Kazuo Iwama, Shigeru Yamashita

Published Dec 1, 2003• 5 citations
Publisher
DOI
10.1007/bf03037305

Related papers

A complete set of transformation rules for quantum Boolean circuits with CNOT gates

Kazuo Iwama, Shigeru Yamashita

Superlattices and Microstructures•Feb 1, 2002•2 citations

Circular CNOT Circuits: Definition, Analysis and Application to Fault-Tolerant Quantum Circuits

Alexandru Paler

arXiv:1604.02931•Lecture notes in computer science•Jan 1, 2016•2 citations

Transformation rules for designing CNOT-based quantum circuits

Kazuo Iwama, Yahiko Kambayashi, Shigeru Yamashita

This paper gives a simple but nontrivial set of local transformation rules for Control-NOT(CNOT)-based combinatorial circuits. It is shown that this rule set is complete, namely, for any two equivalent circuits, S1 and S2, there is a sequence of transformations, each of them in the rule set, which changes S1 to S2. Our motivation is to use this rule set for developing a design theory for quantum circuits whose Boolean logic parts should be implemented by CNOT based circuits. As a preliminary example, we give a design procedure based on our transformation rules which reduces the cost of CNOT-based circuits.

ACM/IEEE Design Automation Conference (DAC)•Jan 1, 2002•39 citations

Transformation rules for designing CNOT-based quantum circuits

K. Iwama, Y. Kambayashi, S. Yamashita

This paper gives a simple but nontrivial set of local transformation rules for control-NOT (CNOT)-based combinatorial circuits. It is shown that this rule set is complete, namely, for any two equivalent circuits, S/sub 1/ and S/sub 2/, there is a sequence of transformations, each of them in the rule set, which changes S/sub 1/ to S/sub 2/. Our motivation is to use this rule set for developing a design theory for quantum circuits whose Boolean logic parts should be implemented by CNOT-based circuits. As a preliminary example, we give a design procedure based on the transformation rules which reduces the cost of CNOT-based circuits.

ACM/IEEE Design Automation Conference (DAC)•Jan 1, 2002•50 citations

A study on CNOT−based quantum circuits using rewriting systems

Issei Sakashita

•Oct 31, 2013•0 citations

A complete transformation rule set and a minimal equation set for CNOT-based 3 qubits quantum circuits

Issei Sakashita

We introduce a complete transformation rule set and a minimal equation set for controlled-NOT (CNOT)-based quantum circuits. Using these rules, quantum circuits that compute the same Boolean function are reduced to a same normal form. We can thus easily check the equivalence of circuits by comparing their normal forms. By applying the Knuth-Bendix completion algorithm to a set of modified 18 equations introduced by Iwama et al. 2002 [IKY02], we obtain a complete transformation rule set (i.e., a set of transformation rules with the properties of `termination' and `confluence'). Our transformation rule set consists of 114 rules. Moreover, we found a minimal subset of equations for the initial equation set.

•Apr 1, 2013•0 citations
This paper gives a simple but nontrivial set of local transformation rules for Control-NOT(CNOT)-based combinatorial circuits. It is shown that this rule set is complete, namely, for any two equivalent circuits, S1 and S2, there is a sequence of transformations, each of them in the rule set, which changes S1 to S2. Our motivation is to use this rule set for developing a design theory for quantum circuits whose Boolean logic parts should be implemented by CNOT based circuits. As a preliminary example, we give a design procedure based on our transformation rules which reduces the cost of CNOT-based circuits.
This paper gives a simple but nontrivial set of local transformation rules for control-NOT (CNOT)-based combinatorial circuits. It is shown that this rule set is complete, namely, for any two equivalent circuits, S/sub 1/ and S/sub 2/, there is a sequence of transformations, each of them in the rule set, which changes S/sub 1/ to S/sub 2/. Our motivation is to use this rule set for developing a design theory for quantum circuits whose Boolean logic parts should be implemented by CNOT-based circuits. As a preliminary example, we give a design procedure based on the transformation rules which reduces the cost of CNOT-based circuits.
We introduce a complete transformation rule set and a minimal equation set for controlled-NOT (CNOT)-based quantum circuits. Using these rules, quantum circuits that compute the same Boolean function are reduced to a same normal form. We can thus easily check the equivalence of circuits by comparing their normal forms. By applying the Knuth-Bendix completion algorithm to a set of modified 18 equations introduced by Iwama et al. 2002 [IKY02], we obtain a complete transformation rule set (i.e., a set of transformation rules with the properties of `termination' and `confluence'). Our transformation rule set consists of 114 rules. Moreover, we found a minimal subset of equations for the initial equation set.