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Paper 1

Edge local complementation for logical cluster states

Jaewoo Joo, David L. Feder

Year

2011

Journal

arXiv preprint

DOI

arXiv:1105.3921

arXiv

1105.3921

A method is presented for the implementation of edge local complementation in graph states, based on the application of two Hadamard operations and a single controlled-phase (CZ) gate. As an application, we demonstrate an efficient scheme to construct a one-dimensional logical cluster state based on the five-qubit quantum error-correcting code, using a sequence of edge local complementations. A single physical CZ operation, together with local operations, is sufficient to create a logical CZ operation between two logical qubits. The same construction can be used to generate any encoded graph state. This approach in concatenation may allow one to create a hierarchical quantum network for quantum information tasks.

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Paper 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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