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Paper 1
A four-dimensional toric code with non-Clifford transversal gates
Tomas Jochym-O'Connor, Theodore J. Yoder
- Year
- 2020
- Journal
- arXiv preprint
- DOI
- arXiv:2010.02238
- arXiv
- 2010.02238
The design of a four-dimensional toric code is explored with the goal of finding a lattice capable of implementing a logical $\mathsf{CCCZ}$ gate transversally. The established lattice is the octaplex tessellation, which is a regular tessellation of four-dimensional Euclidean space whose underlying 4-cell is the octaplex, or hyper-diamond. This differs from the conventional 4D toric code lattice, based on the hypercubic tessellation, which is symmetric with respect to logical $X$ and $Z$ and only allows for the implementation of a transversal Clifford gate. This work further develops the established connection between topological dimension and transversal gates in the Clifford hierarchy, generalizing the known designs for the implementation of transversal $\mathsf{CZ}$ and $\mathsf{CCZ}$ in two and three dimensions, respectively.
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Quantum circuit design for accurate simulation of qudit channels
Dong-Sheng Wang, Barry C. Sanders
- Year
- 2014
- Journal
- arXiv preprint
- DOI
- arXiv:1407.7251
- arXiv
- 1407.7251
We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm distance. The classical algorithm is constructed by decomposing a quantum channel into a convex combination of generalized extreme channels by optimization of a set of nonlinear coupled algebraic equations. The resultant circuit is a randomly chosen generalized extreme channel circuit whose run-time is logarithmic with respect to the error tolerance and quadratic with respect to Hilbert space dimension, which requires only a single ancillary qudit plus classical dits.
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