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Paper 1
Entanglement-assisted Quantum Codes from Cyclic Codes
Francisco Revson F. Pereira
- Year
- 2019
- Journal
- arXiv preprint
- DOI
- arXiv:1911.06384
- arXiv
- 1911.06384
Entanglement-assisted quantum (QUENTA) codes are a subclass of quantum error-correcting codes which use entanglement as a resource. These codes can provide error correction capability higher than the codes derived from the traditional stabilizer formalism. In this paper, it is shown a general method to construct QUENTA codes from cyclic codes. Afterwards, the method is applied to Reed-Solomon codes, BCH codes, and general cyclic codes. We use the Euclidean and Hermitian construction of QUENTA codes. Two families of QUENTA codes are maximal distance separable (MDS), and one is almost MDS or almost near MDS. The comparison of the codes in this paper is mostly based on the quantum Singleton bound.
Open paperPaper 2
Synthesis of Arbitrary Quantum Circuits to Topological Assembly: Systematic, Online and Compact
Alexandru Paler, Austin G. Fowler, Robert Wille
- Year
- 2017
- Journal
- arXiv preprint
- DOI
- arXiv:1711.01387
- arXiv
- 1711.01387
It is challenging to transform an arbitrary quantum circuit into a form protected by surface code quantum error correcting codes (a variant of topological quantum error correction), especially if the goal is to minimise overhead. One of the issues is the efficient placement of magic state distillation sub circuits, so-called distillation boxes, in the space-time volume that abstracts the computation's required resources. This work presents a general, systematic, online method for the synthesis of such circuits. Distillation box placement is controlled by so-called schedulers. The work introduces a greedy scheduler generating compact box placements. The implemented software, whose source code is available online, is used to illustrate and discuss synthesis examples. Synthesis and optimisation improvements are proposed.
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