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Efficient Implementation of LIMDDs for Quantum Circuit Simulation

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Model Checking Software (SPIN 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13872))

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Abstract

Realizing the promised advantage of quantum computers over classical computers requires both physical devices and corresponding methods for the design, verification and analysis of quantum circuits. In this regard, decision diagrams have proven themselves to be an indispensable tool due to their capability to represent both quantum states and unitaries (circuits) compactly. Nonetheless, recent results show that decision diagrams can grow to exponential size even for the ubiquitous stabilizer states, which are generated by Clifford circuits. Since Clifford circuits can be efficiently simulated classically, this is surprising. Moreover, since Clifford circuits play a crucial role in many quantum computing applications, from networking, to error correction, this limitation forms a major obstacle for using decision diagrams for the design, verification and analysis of quantum circuits. The recently proposed Local Invertible Map Decision Diagram (LIMDD) solves this problem by combining the strengths of decision diagrams and the stabilizer formalism that enables efficient simulation of Clifford circuits. However, LIMDDs have only been introduced on paper thus far and have not been implemented yet—preventing an investigation of their practical capabilities through experiments. In this work, we present the first implementation of LIMDDs for quantum circuit simulation. A case study confirms the improved performance in both worlds for the Quantum Fourier Transform applied to a stabilizer state. The resulting package is available under a free license at https://github.com/cda-tum/ddsim/tree/limdd.

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Acknowledgment

This work received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 101001318) and was part of the Munich Quantum Valley, which is supported by the Bavarian state government with funds from the Hightech Agenda Bayern Plus.

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Authors and Affiliations

  1. Leiden University, Leiden, The Netherlands

    Lieuwe Vinkhuijzen, Sebastiaan Brand & Alfons Laarman

  2. Secure Information Systems, University of Applied Sciences Upper Austria, Wels, Austria

    Thomas Grurl

  3. Institute for Integrated Circuits, Johannes Kepler University Linz, Linz, Austria

    Thomas Grurl & Stefan Hillmich

  4. Chair for Design Automation, Technical University of Munich, Munich, Germany

    Robert Wille

  5. Software Competence Center Hagenberg Gmbh (SCCH), Hagenberg Im Mühlkreis, Austria

    Robert Wille

Authors
  1. Lieuwe Vinkhuijzen
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  2. Thomas Grurl
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  3. Stefan Hillmich
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  4. Sebastiaan Brand
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  5. Robert Wille
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  6. Alfons Laarman
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Correspondence to Lieuwe Vinkhuijzen .

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Editors and Affiliations

  1. University of Twente, Enschede, The Netherlands

    Georgiana Caltais

  2. Aalborg University, Aalborg, Denmark

    Christian Schilling

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Vinkhuijzen, L., Grurl, T., Hillmich, S., Brand, S., Wille, R., Laarman, A. (2023). Efficient Implementation of LIMDDs for Quantum Circuit Simulation. In: Caltais, G., Schilling, C. (eds) Model Checking Software. SPIN 2023. Lecture Notes in Computer Science, vol 13872. Springer, Cham. https://doi.org/10.1007/978-3-031-32157-3_1

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  • DOI: https://doi.org/10.1007/978-3-031-32157-3_1

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