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

A Common Algorithm of Construction a New Quantum Logic Gate for Exact Minimization of Quantum Circuits

Zhiqiang Li, Sai Chen, Wei Kang Zhu, Hanwu Chen

Published Dec 22, 2017• 0 citations
Publisher
DOI
10.1515/9783110584974-041

Related papers

Realization of a new permutative gate library using controlled-kth-root-of-NOT quantum gates for exact minimization of quantum circuits

Zhiqiang Li, Xiaoyu Song B, Marek A. Perkowski +2 more

Since non-permutative quantum gates have more complex rules than permutative quantum gates, it is very hard to synthesize quantum logic circuits using non-permutative quantum gates, such as controlled-square-root-of-NOT gates (CV∕CV+ gates). In the efficient synthesis algorithm, direct use of quantum non-permutative gates should be avoided. Rather, the key method is to use quantum gates to create new permutative quantum gates that then replace non-permutative quantum gates. This method assumes the library of quantum gate primitives are constructed so as to have the lowest possible quantum cost. In this paper, we first propose some new CV∕CV+-like gates, i.e. controlled-kth-root-of-NOT gates where k = 2,4,8,…, and give all corresponding matrixes. Further, we also present a novel generic method to quickly and directly construct this new optimal quantum logic gate library using CNOT and these non-permutative quantum gates. Our method introduces new means to find permutative quantum gates with lower quantum cost.

International Journal of Quantum Information•Aug 1, 2014•2 citations

Quantum Circuit Designs for Gate Model Quantum Computers

László Gyöngyösi, Sándor Imre

Bulletin of the American Physical Society•Mar 5, 2018•0 citations

Construction of Quantum Circuits for Classical Logical Gates Using Quantum Gates with Qiskit

Sumathi Pawar, Suchetha N V, Ramasubramanian Murugesan +2 more

International Conference Computational Vision and Bio Inspired Computing•Aug 1, 2026•0 citations

Efficient Algorithm for Synthesis of Optimal NCV 3-Qubit Reversible Circuits Using New Quantum Logic Gate Library

Xiao Fang-ying

Owing to the exponential nature of the memory or run-time complexity,many existing methods can only synthesize 3-qubit logic circuits using quantum logic gate library,however,a few can optimally synthesize 3-qubit logic circuits for quantum NOT,CNOT,Controlled-V and Controlled-V+(NCV)gates,the key approach reduces the NCV quantum circuit synthesis problem to four-valued logic synthesis.This paper proposes using NCV gates to create a new quantum logic gate library,which is exactly the same as NCV gate library in the synthesis of all optimal 3-qubit circuits,thus it also reduces the four-valued logic synthesis to easily solved two-valued logic synthesis.We present a 3-qubit efficient synthesis algorithms based on perfect hash function,which can quickly construct all optimal 3-qubit circuits——the average speed that synthesizes circuits with minimum cost is nearly 127 times faster than that of the best result of Maslov 2007.

Dianzi xuebao•Jan 1, 2013•2 citations

Search for Universal Ternary Quantum Gate Sets with Exact Minimum Costs

Marek A. Perkowski, Normen Giesecke, Dong Hwa Kim +1 more

The choice of the best set of universal ternary gates for quantum circuits is an open problem. We create exact minimum cost ternary reversible gates with quantum multiplexers using the method of iterative deepening depth-first search (IDDFS) [25]. Such search is better for small problems than evolutionary algorithms or other search methods. Several new gates that are provably exact minimum cost have been discovered. These gates are next used as library building blocks in the minimization of larger ternary quantum circuits like highly testable GFSOP cascades [15,16] (that generalize ESOP) as well as the wave cascades [24] generalized to ternary logic. They are useful to design oracles for multivalued algorithms such as Deutsch-Jozsa [26] and Grover.

•Jan 1, 2007•10 citations

Minimization of AND-XOR Expressions with Decoders for Quantum Circuits

Sonia Yang, Ali Al-Bayaty, Marek Perkowski

This paper introduces a new logic structure for reversible quantum circuit synthesis. Our synthesis method aims to minimize the quantum cost of reversible quantum circuits with decoders. In this method, multi-valued input, binary output (MVI) functions are utilized as a mathematical concept only, but the circuits are binary. We introduce the new concept of ``Multi-Valued Input Fixed Polarity Reed-Muller (MVI-RM)" forms. Our decoder-based circuit uses three logical levels in contrast to commonly-used methods based on Exclusive-or Sum of Products (ESOP) with two levels (AND-XOR expressions), realized by Toffoli gates. In general, the high number of input qubits in the resulting Toffoli gates is a problem that greatly impacts the quantum cost. Using decoders decreases the number of input qubits in these Toffoli gates. We present two practical algorithms for three-level circuit synthesis by finding the MVI-FPRM: products-matching and the newly developed butterfly diagrams. The best MVI-FPRM forms are factorized and reduced to approximate Multi-Valued Input Generalized Reed-Muller (MVI-GRM) forms.

quant-pharXiv:2601.02515•Jan 7, 2026•0 citations
Since non-permutative quantum gates have more complex rules than permutative quantum gates, it is very hard to synthesize quantum logic circuits using non-permutative quantum gates, such as controlled-square-root-of-NOT gates (CV∕CV+ gates). In the efficient synthesis algorithm, direct use of quantum non-permutative gates should be avoided. Rather, the key method is to use quantum gates to create new permutative quantum gates that then replace non-permutative quantum gates. This method assumes the library of quantum gate primitives are constructed so as to have the lowest possible quantum cost. In this paper, we first propose some new CV∕CV+-like gates, i.e. controlled-kth-root-of-NOT gates where k = 2,4,8,…, and give all corresponding matrixes. Further, we also present a novel generic method to quickly and directly construct this new optimal quantum logic gate library using CNOT and these non-permutative quantum gates. Our method introduces new means to find permutative quantum gates with lower quantum cost.
Owing to the exponential nature of the memory or run-time complexity,many existing methods can only synthesize 3-qubit logic circuits using quantum logic gate library,however,a few can optimally synthesize 3-qubit logic circuits for quantum NOT,CNOT,Controlled-V and Controlled-V+(NCV)gates,the key approach reduces the NCV quantum circuit synthesis problem to four-valued logic synthesis.This paper proposes using NCV gates to create a new quantum logic gate library,which is exactly the same as NCV gate library in the synthesis of all optimal 3-qubit circuits,thus it also reduces the four-valued logic synthesis to easily solved two-valued logic synthesis.We present a 3-qubit efficient synthesis algorithms based on perfect hash function,which can quickly construct all optimal 3-qubit circuits——the average speed that synthesizes circuits with minimum cost is nearly 127 times faster than that of the best result of Maslov 2007.
The choice of the best set of universal ternary gates for quantum circuits is an open problem. We create exact minimum cost ternary reversible gates with quantum multiplexers using the method of iterative deepening depth-first search (IDDFS) [25]. Such search is better for small problems than evolutionary algorithms or other search methods. Several new gates that are provably exact minimum cost have been discovered. These gates are next used as library building blocks in the minimization of larger ternary quantum circuits like highly testable GFSOP cascades [15,16] (that generalize ESOP) as well as the wave cascades [24] generalized to ternary logic. They are useful to design oracles for multivalued algorithms such as Deutsch-Jozsa [26] and Grover.
This paper introduces a new logic structure for reversible quantum circuit synthesis. Our synthesis method aims to minimize the quantum cost of reversible quantum circuits with decoders. In this method, multi-valued input, binary output (MVI) functions are utilized as a mathematical concept only, but the circuits are binary. We introduce the new concept of ``Multi-Valued Input Fixed Polarity Reed-Muller (MVI-RM)" forms. Our decoder-based circuit uses three logical levels in contrast to commonly-used methods based on Exclusive-or Sum of Products (ESOP) with two levels (AND-XOR expressions), realized by Toffoli gates. In general, the high number of input qubits in the resulting Toffoli gates is a problem that greatly impacts the quantum cost. Using decoders decreases the number of input qubits in these Toffoli gates. We present two practical algorithms for three-level circuit synthesis by finding the MVI-FPRM: products-matching and the newly developed butterfly diagrams. The best MVI-FPRM forms are factorized and reduced to approximate Multi-Valued Input Generalized Reed-Muller (MVI-GRM) forms.