5 Search Results for "Wang, Quanlong"

Document
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.
Cite as

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.FSCD.2025.22
Branch Sequentialization in Quantum Polytime

Authors: Emmanuel Hainry, Romain Péchoux, and Mário Silva

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
Quantum algorithms leverage the use of quantumly-controlled data in order to achieve computational advantage. This implies that the programs use constructs depending on quantum data and not just classical data such as measurement outcomes. Current compilation strategies for quantum control flow involve compiling the branches of a quantum conditional, either in-depth or in-width, which in general leads to circuits of exponential size. This problem is coined as the branch sequentialization problem. We introduce and study a compilation technique for avoiding branch sequentialization on a language that is sound and complete for quantum polynomial time, thus, improving on existing polynomial-size-preserving compilation techniques.
Cite as

Emmanuel Hainry, Romain Péchoux, and Mário Silva. Branch Sequentialization in Quantum Polytime. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 22:1-22:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hainry_et_al:LIPIcs.FSCD.2025.22,
  author =	{Hainry, Emmanuel and P\'{e}choux, Romain and Silva, M\'{a}rio},
  title =	{{Branch Sequentialization in Quantum Polytime}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{22:1--22:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.22},
  URN =		{urn:nbn:de:0030-drops-236373},
  doi =		{10.4230/LIPIcs.FSCD.2025.22},
  annote =	{Keywords: Quantum Programs, Implicit Computational Complexity, Quantum Circuits}
}
Document
DOI: 10.4230/LIPIcs.TQC.2020.11
Fast and Effective Techniques for T-Count Reduction via Spider Nest Identities

Authors: Niel de Beaudrap, Xiaoning Bian, and Quanlong Wang

Published in: LIPIcs, Volume 158, 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)

Abstract
In fault-tolerant quantum computing systems, realising (approximately) universal quantum computation is usually described in terms of realising Clifford+T operations, which is to say a circuit of CNOT, Hadamard, and π/2-phase rotations, together with T operations (π/4-phase rotations). For many error correcting codes, fault-tolerant realisations of Clifford operations are significantly less resource-intensive than those of T gates, which motivates finding ways to realise the same transformation involving T-count (the number of T gates involved) which is as low as possible. Investigations into this problem [Matthew Amy et al., 2013; Gosset et al., 2014; Matthew Amy et al., 2014; Matthew Amy et al., 2018; Earl T. Campbell and Mark Howard, 2017; Matthew Amy and Michele Mosca, 2019] has led to observations that this problem is closely related to NP-hard tensor decomposition problems [Luke E. Heyfron and Earl T. Campbell, 2018] and is tantamount to the difficult problem of decoding exponentially long Reed-Muller codes [Matthew Amy and Michele Mosca, 2019]. This problem then presents itself as one for which must be content in practise with approximate optimisation, in which one develops an array of tactics to be deployed through some pragmatic strategy. In this vein, we describe techniques to reduce the T-count, based on the effective application of "spider nest identities": easily recognised products of parity-phase operations which are equivalent to the identity operation. We demonstrate the effectiveness of such techniques by obtaining improvements in the T-counts of a number of circuits, in run-times which are typically less than the time required to make a fresh cup of coffee.
Cite as

Niel de Beaudrap, Xiaoning Bian, and Quanlong Wang. Fast and Effective Techniques for T-Count Reduction via Spider Nest Identities. In 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 11:1-11:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{debeaudrap_et_al:LIPIcs.TQC.2020.11,
  author =	{de Beaudrap, Niel and Bian, Xiaoning and Wang, Quanlong},
  title =	{{Fast and Effective Techniques for T-Count Reduction via Spider Nest Identities}},
  booktitle =	{15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)},
  pages =	{11:1--11:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-146-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{158},
  editor =	{Flammia, Steven T.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2020.11},
  URN =		{urn:nbn:de:0030-drops-120705},
  doi =		{10.4230/LIPIcs.TQC.2020.11},
  annote =	{Keywords: T-count, Parity-phase operations, Phase gadgets, Clifford hierarchy, ZX calculus}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.11
ZX-Calculus: Cyclotomic Supplementarity and Incompleteness for Clifford+T Quantum Mechanics

Authors: Emmanuel Jeandel, Simon Perdrix, Renaud Vilmart, and Quanlong Wang

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract
The ZX-Calculus is a powerful graphical language for quantum mechanics and quantum information processing. The completeness of the language - i.e. the ability to derive any true equation - is a crucial question. In the quest of a complete ZX-calculus, supplementarity has been recently proved to be necessary for quantum diagram reasoning (MFCS 2016). Roughly speaking, supplementarity consists in merging two subdiagrams when they are parameterized by antipodal angles. We introduce a generalised supplementarity - called cyclotomic supplementarity - which consists in merging n subdiagrams at once, when the n angles divide the circle into equal parts. We show that when n is an odd prime number, the cyclotomic supplementarity cannot be derived, leading to a countable family of new axioms for diagrammatic quantum reasoning. We exhibit another new simple axiom that cannot be derived from the existing rules of the ZX-Calculus, implying in particular the incompleteness of the language for the so-called Clifford+T quantum mechanics. We end up with a new axiomatisation of an extended ZX-Calculus, including an axiom schema for the cyclotomic supplementarity.
Cite as

Emmanuel Jeandel, Simon Perdrix, Renaud Vilmart, and Quanlong Wang. ZX-Calculus: Cyclotomic Supplementarity and Incompleteness for Clifford+T Quantum Mechanics. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 11:1-11:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{jeandel_et_al:LIPIcs.MFCS.2017.11,
  author =	{Jeandel, Emmanuel and Perdrix, Simon and Vilmart, Renaud and Wang, Quanlong},
  title =	{{ZX-Calculus: Cyclotomic Supplementarity and Incompleteness for Clifford+T Quantum Mechanics}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{11:1--11:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.11},
  URN =		{urn:nbn:de:0030-drops-81173},
  doi =		{10.4230/LIPIcs.MFCS.2017.11},
  annote =	{Keywords: Categorical Quantum Mechanincs, ZX-Calculus, Completeness, Cyclotomic Supplmentarity, Clifford+T}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2016.76
Supplementarity is Necessary for Quantum Diagram Reasoning

Authors: Simon Perdrix and Quanlong Wang

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract
The ZX-calculus is a powerful diagrammatic language for quantum mechanics and quantum information processing. We prove that its pi/4-fragment is not complete, in other words the ZX-calculus is not complete for the so called "Clifford+T quantum mechanics". The completeness of this fragment was one of the main open problems in categorical quantum mechanics, a programme initiated by Abramsky and Coecke. The ZX-calculus was known to be incomplete for quantum mechanics. On the other hand, its pi/2-fragment is known to be complete, i.e. the ZX-calculus is complete for the so called "stabilizer quantum mechanics". Deciding whether its pi/4-fragment is complete is a crucial step in the development of the ZX-calculus since this fragment is approximately universal for quantum mechanics, contrary to the pi/2-fragment. To establish our incompleteness result, we consider a fairly simple property of quantum states called supplementarity. We show that supplementarity can be derived in the ZX-calculus if and only if the angles involved in this equation are multiples of pi/2. In particular, the impossibility to derive supplementarity for pi/4 implies the incompleteness of the ZX-calculus for Clifford+T quantum mechanics. As a consequence, we propose to add the supplementarity to the set of rules of the ZX-calculus. We also show that if a ZX-diagram involves antiphase twins, they can be merged when the ZX-calculus is augmented with the supplementarity rule. Merging antiphase twins makes diagrammatic reasoning much easier and provides a purely graphical meaning to the supplementarity rule.
Cite as

Simon Perdrix and Quanlong Wang. Supplementarity is Necessary for Quantum Diagram Reasoning. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 76:1-76:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{perdrix_et_al:LIPIcs.MFCS.2016.76,
  author =	{Perdrix, Simon and Wang, Quanlong},
  title =	{{Supplementarity is Necessary for Quantum Diagram Reasoning}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{76:1--76:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.76},
  URN =		{urn:nbn:de:0030-drops-65062},
  doi =		{10.4230/LIPIcs.MFCS.2016.76},
  annote =	{Keywords: quantum diagram reasoning, completeness, ZX-calculus, quantum computing, categorical quantum mechanics}
}
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