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DOI: 10.4230/LIPIcs.MFCS.2025.85

Cutoff Theorems for the Equivalence of Parameterized Quantum Circuits

Authors: Neil J. Ross and Scott Wesley

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract

Many promising quantum algorithms in economics, medical science, and material science rely on circuits that are parameterized by a large number of angles. To ensure that these algorithms are efficient, these parameterized circuits must be heavily optimized. However, most quantum circuit optimizers are not verified, so this procedure is known to be error-prone. For this reason, there is growing interest in the design of equivalence checking algorithms for parameterized quantum circuits. In this paper, we define a generalized class of parameterized circuits with arbitrary rotations and show that this problem is decidable for cyclotomic gate sets. We propose a cutoff-based procedure which reduces the problem of verifying the equivalence of parameterized quantum circuits to the problem of verifying the equivalence of finitely many parameter-free quantum circuits. Because the number of parameter-free circuits grows exponentially with the number of parameters, we also propose a probabilistic variant of the algorithm for cases when the number of parameters is intractably large. We show that our techniques extend to equivalence modulo global phase, and describe an efficient angle sampling procedure for cyclotomic gate sets.

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Neil J. Ross and Scott Wesley. Cutoff Theorems for the Equivalence of Parameterized Quantum Circuits. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 85:1-85:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ross_et_al:LIPIcs.MFCS.2025.85,
  author =	{Ross, Neil J. and Wesley, Scott},
  title =	{{Cutoff Theorems for the Equivalence of Parameterized Quantum Circuits}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{85:1--85:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.85},
  URN =		{urn:nbn:de:0030-drops-241921},
  doi =		{10.4230/LIPIcs.MFCS.2025.85},
  annote =	{Keywords: Quantum Circuits, Parameterized Equivalence Checking}
}

Document

DOI: 10.4230/LIPIcs.ECOOP.2024.43

Inductive Predicate Synthesis Modulo Programs

Authors: Scott Wesley, Maria Christakis, Jorge A. Navas, Richard Trefler, Valentin Wüstholz, and Arie Gurfinkel

Published in: LIPIcs, Volume 313, 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract

A growing trend in program analysis is to encode verification conditions within the language of the input program. This simplifies the design of analysis tools by utilizing off-the-shelf verifiers, but makes communication with the underlying solver more challenging. Essentially, the analysis tools operates at the level of input programs, whereas the solver operates at the level of problem encodings. To bridge this gap, the verifier must pass along proof-rules from the analysis tool to the solver. For example, an analysis tool for concurrent programs built on an inductive program verifier might need to declare Owicki-Gries style proof-rules for the underlying solver. Each such proof-rule further specifies how a program should be verified, meaning that the problem of passing proof-rules is a form of invariant synthesis. Similarly, many program analysis tasks reduce to the synthesis of pure, loop-free Boolean functions (i.e., predicates), relative to a program. From this observation, we propose Inductive Predicate Synthesis Modulo Programs (IPS-MP) which extends high-level languages with minimal synthesis features to guide analysis. In IPS-MP, unknown predicates appear under assume and assert statements, acting as specifications modulo the program semantics. Existing synthesis solvers are inefficient at IPS-MP as they target more general problems. In this paper, we show that IPS-MP admits an efficient solution in the Boolean case, despite being generally undecidable. Moreover, we show that IPS-MP reduces to the satisfiability of constrained Horn clauses, which is less general than existing synthesis problems, yet expressive enough to encode verification tasks. We provide reductions from challenging verification tasks - such as parameterized model checking - to IPS-MP. We realize these reductions with an efficient IPS-MP-solver based on SeaHorn, and describe a real-world application to smart-contract verification.

Cite as

Scott Wesley, Maria Christakis, Jorge A. Navas, Richard Trefler, Valentin Wüstholz, and Arie Gurfinkel. Inductive Predicate Synthesis Modulo Programs. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 43:1-43:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{wesley_et_al:LIPIcs.ECOOP.2024.43,
  author =	{Wesley, Scott and Christakis, Maria and Navas, Jorge A. and Trefler, Richard and W\"{u}stholz, Valentin and Gurfinkel, Arie},
  title =	{{Inductive Predicate Synthesis Modulo Programs}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{43:1--43:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-341-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{313},
  editor =	{Aldrich, Jonathan and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2024.43},
  URN =		{urn:nbn:de:0030-drops-208926},
  doi =		{10.4230/LIPIcs.ECOOP.2024.43},
  annote =	{Keywords: Software Verification, Invariant Synthesis, Model-Checking}
}

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Documents authored by Wesley, Scott

Cutoff Theorems for the Equivalence of Parameterized Quantum Circuits

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Inductive Predicate Synthesis Modulo Programs

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