Contraction Heuristics for Tensor Decision Diagrams

In this paper, we study the equivalence problem for quantum circuits: Given two quantum circuits, are they equivalent? We reduce this problem to the contraction problem of a tensor network. The order in which the contraction operations between tensors are applied has a crucial impact on efficiency,...

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Veröffentlicht in:	Entropy (Basel, Switzerland) Jg. 26; H. 12; S. 1058
Hauptverfasser:	Larsen, Christian Bøgh, Olsen, Simon Brun, Larsen, Kim Guldstrand, Schilling, Christian
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Switzerland MDPI AG 05.12.2024 MDPI
Schlagworte:	Algorithms Circuit diagrams Circuits Computers contraction planning Equivalence equivalence checking Heuristic heuristics Integrated circuits quantum circuit Quantum computing Semiconductor chips tensor decision diagram tensor network Tensors New York United States quantum circuit tensor decision diagram heuristics equivalence checking tensor network contraction planning
ISSN:	1099-4300, 1099-4300
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Abstract	In this paper, we study the equivalence problem for quantum circuits: Given two quantum circuits, are they equivalent? We reduce this problem to the contraction problem of a tensor network. The order in which the contraction operations between tensors are applied has a crucial impact on efficiency, which is why many heuristics have been proposed. In this work, we use an efficient representation of tensors as a tensor decision diagram. Since existing contraction heuristics do not perform well in combination with these diagrams, we propose two new contraction heuristics. We demonstrate experimentally that our heuristics outperform other state-of-the-art heuristics. We also demonstrate that our framework yields state-of-the-art performance for equivalence checking.
AbstractList	In this paper, we study the equivalence problem for quantum circuits: Given two quantum circuits, are they equivalent? We reduce this problem to the contraction problem of a tensor network. The order in which the contraction operations between tensors are applied has a crucial impact on efficiency, which is why many heuristics have been proposed. In this work, we use an efficient representation of tensors as a tensor decision diagram. Since existing contraction heuristics do not perform well in combination with these diagrams, we propose two new contraction heuristics. We demonstrate experimentally that our heuristics outperform other state-of-the-art heuristics. We also demonstrate that our framework yields state-of-the-art performance for equivalence checking. In this paper, we study the equivalence problem for quantum circuits: Given two quantum circuits, are they equivalent? We reduce this problem to the contraction problem of a tensor network. The order in which the contraction operations between tensors are applied has a crucial impact on efficiency, which is why many heuristics have been proposed. In this work, we use an efficient representation of tensors as a tensor decision diagram. Since existing contraction heuristics do not perform well in combination with these diagrams, we propose two new contraction heuristics. We demonstrate experimentally that our heuristics outperform other state-of-the-art heuristics. We also demonstrate that our framework yields state-of-the-art performance for equivalence checking.In this paper, we study the equivalence problem for quantum circuits: Given two quantum circuits, are they equivalent? We reduce this problem to the contraction problem of a tensor network. The order in which the contraction operations between tensors are applied has a crucial impact on efficiency, which is why many heuristics have been proposed. In this work, we use an efficient representation of tensors as a tensor decision diagram. Since existing contraction heuristics do not perform well in combination with these diagrams, we propose two new contraction heuristics. We demonstrate experimentally that our heuristics outperform other state-of-the-art heuristics. We also demonstrate that our framework yields state-of-the-art performance for equivalence checking.
Audience	Academic
Author	Olsen, Simon Brun Larsen, Kim Guldstrand Schilling, Christian Larsen, Christian Bøgh
AuthorAffiliation	Department of Computer Science, Aalborg University, 9220 Aalborg, Denmark kgl@cs.aau.dk (K.G.L.)
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Keywords	quantum circuit tensor decision diagram heuristics equivalence checking tensor network contraction planning
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SubjectTerms	Algorithms Circuit diagrams Circuits Computers contraction planning Equivalence equivalence checking Heuristic heuristics Integrated circuits quantum circuit Quantum computing Semiconductor chips tensor decision diagram tensor network Tensors
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Title	Contraction Heuristics for Tensor Decision Diagrams
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