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Documents authored by Li, Liyi

Document
DOI: 10.4230/LIPIcs.ECOOP.2024.24
Qafny: A Quantum-Program Verifier

Authors: Liyi Li, Mingwei Zhu, Rance Cleaveland, Alexander Nicolellis, Yi Lee, Le Chang, and Xiaodi Wu

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

Abstract
Because of the probabilistic/nondeterministic behavior of quantum programs, it is highly advisable to verify them formally to ensure that they correctly implement their specifications. Formal verification, however, also traditionally requires significant effort. To address this challenge, we present Qafny, an automated proof system based on the program verifier Dafny and designed for verifying quantum programs. At its core, Qafny uses a type-guided quantum proof system that translates quantum operations to classical array operations modeled within a classical separation logic framework. We prove the soundness and completeness of our proof system and implement a prototype compiler that transforms Qafny programs and specifications into Dafny for automated verification purposes. We then illustrate the utility of Qafny’s automated capabilities in efficiently verifying important quantum algorithms, including quantum-walk algorithms, Grover’s algorithm, and Shor’s algorithm.
Cite as

Liyi Li, Mingwei Zhu, Rance Cleaveland, Alexander Nicolellis, Yi Lee, Le Chang, and Xiaodi Wu. Qafny: A Quantum-Program Verifier. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 24:1-24:31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{li_et_al:LIPIcs.ECOOP.2024.24,
  author =	{Li, Liyi and Zhu, Mingwei and Cleaveland, Rance and Nicolellis, Alexander and Lee, Yi and Chang, Le and Wu, Xiaodi},
  title =	{{Qafny: A Quantum-Program Verifier}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{24:1--24:31},
  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.2024.24},
  URN =		{urn:nbn:de:0030-drops-208735},
  doi =		{10.4230/LIPIcs.ECOOP.2024.24},
  annote =	{Keywords: Quantum Computing, Automated Verification, Separation Logic}
}
Document
Artifact
DOI: 10.4230/DARTS.10.2.12
Qafny: A Quantum-Program Verifier (Artifact)

Authors: Liyi Li, Mingwei Zhu, Rance Cleaveland, Alexander Nicolellis, Yi Lee, Le Chang, and Xiaodi Wu

Published in: DARTS, Volume 10, Issue 2, Special Issue of the 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract
This artifact contains the Coq theory files for the Qafny proof system, including the formalism of the Qafny syntax, semantics, type system, and proof system, with the theorem proofs of type soundness, proof system soundness and completeness. It also contains a the compiled Dafny example programs generated from our Qafny-to-Dafny prototype compiler. These example programs serve as the validations of our Qafny-to-Dafny prototype compiler mechanism. The main work is introduced in the Qafny paper, which develops a separation logic style verification framework for quantum programs.
Cite as

Liyi Li, Mingwei Zhu, Rance Cleaveland, Alexander Nicolellis, Yi Lee, Le Chang, and Xiaodi Wu. Qafny: A Quantum-Program Verifier (Artifact). In Special Issue of the 38th European Conference on Object-Oriented Programming (ECOOP 2024). Dagstuhl Artifacts Series (DARTS), Volume 10, Issue 2, pp. 12:1-12:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{li_et_al:DARTS.10.2.12,
  author =	{Li, Liyi and Zhu, Mingwei and Cleaveland, Rance and Nicolellis, Alexander and Lee, Yi and Chang, Le and Wu, Xiaodi},
  title =	{{Qafny: A Quantum-Program Verifier (Artifact)}},
  pages =	{12:1--12:2},
  journal =	{Dagstuhl Artifacts Series},
  ISBN =	{978-3-95977-342-3},
  ISSN =	{2509-8195},
  year =	{2024},
  volume =	{10},
  number =	{2},
  editor =	{Li, Liyi and Zhu, Mingwei and Cleaveland, Rance and Nicolellis, Alexander and Lee, Yi and Chang, Le and Wu, Xiaodi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DARTS.10.2.12},
  URN =		{urn:nbn:de:0030-drops-209104},
  doi =		{10.4230/DARTS.10.2.12},
  annote =	{Keywords: Quantum Computing, Automated Verification, Separation Logic}
}
Document
DOI: 10.4230/LIPIcs.ITP.2021.21
Proving Quantum Programs Correct

Authors: Kesha Hietala, Robert Rand, Shih-Han Hung, Liyi Li, and Michael Hicks

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
As quantum computing progresses steadily from theory into practice, programmers will face a common problem: How can they be sure that their code does what they intend it to do? This paper presents encouraging results in the application of mechanized proof to the domain of quantum programming in the context of the SQIR development. It verifies the correctness of a range of a quantum algorithms including Grover’s algorithm and quantum phase estimation, a key component of Shor’s algorithm. In doing so, it aims to highlight both the successes and challenges of formal verification in the quantum context and motivate the theorem proving community to target quantum computing as an application domain.
Cite as

Kesha Hietala, Robert Rand, Shih-Han Hung, Liyi Li, and Michael Hicks. Proving Quantum Programs Correct. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 21:1-21:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{hietala_et_al:LIPIcs.ITP.2021.21,
  author =	{Hietala, Kesha and Rand, Robert and Hung, Shih-Han and Li, Liyi and Hicks, Michael},
  title =	{{Proving Quantum Programs Correct}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{21:1--21:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.21},
  URN =		{urn:nbn:de:0030-drops-139160},
  doi =		{10.4230/LIPIcs.ITP.2021.21},
  annote =	{Keywords: Formal Verification, Quantum Computing, Proof Engineering}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2020.7
K-LLVM: A Relatively Complete Semantics of LLVM IR

Authors: Liyi Li and Elsa L. Gunter

Published in: LIPIcs, Volume 166, 34th European Conference on Object-Oriented Programming (ECOOP 2020)

Abstract
LLVM [Lattner and Adve, 2004] is designed for the compile-time, link-time and run-time optimization of programs written in various programming languages. The language supported by LLVM targeted by modern compilers is LLVM IR [llvm.org, 2018]. In this paper we define K-LLVM, a reference semantics for LLVM IR. To the best of our knowledge, K-LLVM is the most complete formal LLVM IR semantics to date, including all LLVM IR instructions, intrinsic functions in the LLVM documentation and Standard-C library functions that are necessary to execute many LLVM IR programs. Additionally, K-LLVM formulates an abstract machine that executes all LLVM IR instructions. The machine allows to describe our formal semantics in terms of simulating a conceptual virtual machine that runs LLVM IR programs, including non-deterministic programs. Even though the K-LLVM memory model in this paper is assumed to be a sequentially consistent memory model and does not include all LLVM concurrency memory behaviors, the design of K-LLVM’s data layout allows the K-LLVM abstract machine to execute some LLVM IR programs that previous semantics did not cover, such as the full range of LLVM IR behaviors for the interaction among LLVM IR casting, pointer arithmetic, memory operations and some memory flags (e.g. readonly) of function headers. Additionally, the memory model is modularized in a manner that supports investigating other memory models. To validate K-LLVM, we have implemented it in 𝕂 [Roşu, 2016], which generated an interpreter for LLVM IR. Using this, we ran tests including 1,385 unit test programs and around 3,000 concrete LLVM IR programs, and K-LLVM passed all of them.
Cite as

Liyi Li and Elsa L. Gunter. K-LLVM: A Relatively Complete Semantics of LLVM IR. In 34th European Conference on Object-Oriented Programming (ECOOP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 166, pp. 7:1-7:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{li_et_al:LIPIcs.ECOOP.2020.7,
  author =	{Li, Liyi and Gunter, Elsa L.},
  title =	{{K-LLVM: A Relatively Complete Semantics of LLVM IR}},
  booktitle =	{34th European Conference on Object-Oriented Programming (ECOOP 2020)},
  pages =	{7:1--7:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-154-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{166},
  editor =	{Hirschfeld, Robert and Pape, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2020.7},
  URN =		{urn:nbn:de:0030-drops-131649},
  doi =		{10.4230/LIPIcs.ECOOP.2020.7},
  annote =	{Keywords: LLVM, formal semantics, K framework, memory model, abstract machine}
}
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