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Compaction of Topological Quantum Circuits by Modularization
Kota ASAI Shigeru YAMASHITA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E102A
No.4
pp.624632 Publication Date: 2019/04/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E102.A.624
Type of Manuscript: PAPER Category: VLSI Design Technology and CAD Keyword: topological quantum computation, qubit layout, circuit optimization, simulated annealing,
Full Text: PDF(2.1MB)>>
Summary:
A topological quantum circuit is a representation model for topological quantum computation, which attracts much attention recently as a promising faulttolerant quantum computation model by using 3D cluster states. A topological quantum circuit can be considered as a set of “loops,” and we can transform the topology of loops without changing the functionality of the circuit if the transformation satisfies certain conditions. Thus, there have been proposed many researches to optimize topological quantum circuits by transforming the topology. There are two directions of research to optimize topological quantum circuits. The first group of research considers socalled a placement and wiring problem where we consider how to place “parts” in a 3D space which corresponds to already optimized subcircuits. The second group of research focuses on how to optimize the structure and locations of loops in a relatively small circuit which is treated as one part in the abovementioned first group of research. This paper proposes a new idea for the second group of research; our idea is to consider topological transformations as a placement and wiring problem for modules which we derive from the information how loops are crossed. By using such a formulation, we can use the techniques for placement and wiring problems, and successfully obtain an optimized solution. We confirm by our experiment that our method indeed can reduce the cost much more than the method by Paetznick and Fowler.

