2D Quon Language: Unifying Framework for Cliffords, Matchgates, and Beyond
Byungmin Kang, Chen Zhao, Zhengwei Liu, Xun Gao, Soonwon Choi

TL;DR
This paper introduces the 2D Quon language, a unifying diagrammatic framework that captures Clifford and matchgate classes as special cases, enabling efficient representation and analysis of quantum states and processes.
Contribution
The authors develop the 2D Quon language, a universal diagrammatic approach that unifies Clifford and matchgate classes and introduces new tensor network families for quantum computation.
Findings
2D Quon language can represent arbitrary quantum states and dynamics.
Efficient characterization of Clifford and matchgate classes within the Quon framework.
New tensor networks exhibit high entanglement and non-Cliffordness, useful for quantum applications.
Abstract
Simulating generic quantum states and dynamics is practically intractable using classical computers. However, certain special classes -- namely Clifford and matchgate circuits -- permit efficient computation. They provide invaluable tools for studying many-body physics, quantum chemistry, and quantum computation. While both play foundational roles across multiple disciplines, the origins of their tractability seem disparate, and their relationship remain unclear. A deeper understanding of such tractable classes could expand their scope and enable a wide range of new applications. In this work, we make progress toward the unified understanding of the Clifford and matchgate -- these two classes are, in fact, distinct special cases of a single underlying structure. Specifically, we introduce the 2D Quon language, which combines Majorana worldlines with their underlying spacetime topology…
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum many-body systems · Machine Learning in Materials Science
