Quantum computational networks
Abstract
The theory of quantum computational networks is the quantum generalization of the theory of logic circuits used in classical computing machines. Quantum gates are the generalization of classical logic gates. A single type of gate, the universal quantum gate, together with quantum ‘unit wires’, is adequate for constructing networks with any possible quantum computational property.
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Toffoli (and single) gates are universal.
“First, Toffoli (and single) gates are universal [33][34][35].”
From Time–space complexity of quantum search algorithms in symmetric cryptanalysis: applying to AES and SHA-2 (2018) · cites this paper as [33]
A sequence of quantum-phase gates supplemented by one-bit rotations in the (a,b) subspaces could serve as a universal element for quantum computation.
“A sequence of such gates (supplemented by one bit rotations in the (a; b) subspaces) could be combined to serve as a universal element for quantum computation [9].”
From Measurement of Conditional Phase Shifts for Quantum Logic (1995) · cites this paper as [9]
A random bilateral rotation on each shared pair transforms any initial general two-spin mixed state M into a rotationally symmetric Werner state W_F of the same purity F.
“Because of the singlet's invariance under bilateral rotations, the symmetrized state W F , which we shall call a Werner state [7] of purity F , has the same F as the initial mixed state M from which it was derived.”
From Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels (1996) · cites this paper as [7]
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- Authors
- Deutsch, D. E.
- Affiliations
- University of Oxford (GB)
- Corresponding author
- Deutsch, David Elieser
- Venue
- Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- Publisher
- The Royal Society
- Published
- 1989-09-08
- Volume
- 425
- Issue
- 1868
- Pages
- 73-90
- ISSN
- 0080-4630 (ISSN-L)
- 2053-9169
- OpenAlex
- W2101088258
- Semantic Scholar
- 539357be9d9b2939ccc15a83f3a177cd28caa04d
- Cited by
- 1,270
- References
- 1
- Citations by year
- 2026: 14 · 2025: 33 · 2024: 37 · 2023: 55 · 2022: 38 · 2021: 43 · 2020: 43 · 2019: 33 · 2018: 27 · 2017: 32 · 2016: 38 · 2015: 34 · 2014: 36 · 2013: 34 · 2012: 43
- FWCI
- 1.52
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Proceedings of the Royal Society of London A Mathematical and Physical Sciences (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum gates, universal quantum gates, quantum circuits, quantum computing, logic circuits
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