Towards topological quantum computer
2018
Abstract Quantum R -matrices, the entangling deformations of non-entangling (classical) permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates) for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R -matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R -matrix calculus and propose to look at the R -matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern–Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.
Keywords:
- Discrete mathematics
- Quantum error correction
- Quantum electrodynamics
- Quantum phase estimation algorithm
- Topological quantum computer
- Quantum process
- Physics
- Quantum t-design
- Quantum mechanics
- Quantum algorithm
- Quantum network
- Open quantum system
- Theoretical physics
- Quantum information
- Quantum computer
- Quantum Fourier transform
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