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Quantum Circuits for Functionally Controlled NOT Gates
Open accessAbstract
We generalize quantum circuits for the Toffoli gate presented by Selinger [1] and Jones [2] for functionally controlled NOT gates, i.e.,$X$gates controlled by arbitrary n- variable Boolean functions. Our constructions target the gate set consisting of Clifford gates and single qubit rotations by arbitrary angles. Our constructions use the Walsh-Hadamard spectrum of Boolean functions and build on the work by Schuch and Siewert [3] and Welch et al [4]. We present quantum circuits for the case where the target qubit is in an arbitrary state as well as the special case where the target is in a known state. Additionally, we present constructions that require no auxiliary qubits and constructions that have a rotation depth of 1.
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“The Fredkin gate and CNOT gate offer additional security benefits; the Fredkin gate performs controlled swaps based on the input condition, and the CNOT gate provides a bitwise conditional operation that is fundamental in quantum computing and adds a layer of complexity and robustness to the encryption process, enhancing its resistance to cryptographic attacks25.”
From A chaos-based augmented image encryption scheme for satellite images using Fredkin logic (2025) · cites this paper as [25]
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Cites
A fast quantum mechanical algorithm for database search
Grover, L. K. (1996) · Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96 · doi:10.1145/237814.237866 · Cited by 8,830
A Meet-in-the-Middle Algorithm for Fast Synthesis of Depth-Optimal Quantum Circuits
Amy, M., Maslov, D., Mosca, M., & Roetteler, M. (2013) · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · doi:10.1109/tcad.2013.2244643 · Cited by 549
Self-citationHalving the cost of quantum addition
Gidney, C. (2018) · Quantum · doi:10.22331/q-2018-06-18-74 · Cited by 279
Efficient quantum circuits for diagonal unitaries without ancillas
Welch, J., Greenbaum, D., Mostame, S., & Aspuru-Guzik, A. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/3/033040 · Cited by 114
T-Count Optimization and Reed–Muller Codes
Amy, M., & Mosca, M. (2019) · IEEE Transactions on Information Theory · doi:10.1109/tit.2019.2906374 · Cited by 49
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A chaos-based augmented image encryption scheme for satellite images using Fredkin logic
Alexan, W., Maher, E. A., Mamdouh, E., Youssef, M., & Ehab, N. (2025) · Scientific Reports · doi:10.1038/s41598-025-22008-z · Cited by 20
“…Fredkin gate performs controlled swaps based on the input condition, and the CNOT gate provides a bitwise conditional operation that is fundamental in quantum computing and adds a layer of complexity and robustness to the encryption process, enhancing its resistance to cryptographic attacks 25 .”
Metadata
- Authors
- Soeken, M., & Roetteler, M.
- Affiliations
- Microsoft (United States) (US)
- Venue
- 2020 IEEE International Conference on Quantum Computing and Engineering (QCE)
- Publisher
- IEEE
- Published
- 2020-10
- Pages
- 366-371
- OpenAlex
- W3030680142
- Cited by
- 4
- References
- 5
- Citations by year
- 2025: 2 · 2022: 1 · 2021: 1
- FWCI
- 0.19
- Type
- conference paper
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- IEEE International Conference on Quantum Computing and Engineering (QCE) (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Coding theory and cryptography
- Keywords
- Toffoli gate, quantum circuits, Boolean functions, Clifford gates, single-qubit rotations, quantum gates
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