Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2504.07732

Efficient Formal Verification of Quantum Error Correcting Programs

Qifan Huang·Li Zhou·Wang Fang·Mengyu Zhao·Mingsheng Ying
View original source ↗Read source document ↗Export metadata ↓

Abstract

Quantum error correction (QEC) is fundamental for suppressing noise in quantum hardware and enabling fault-tolerant quantum computation. In this paper, we propose an efficient verification framework for QEC programs. We define an assertion logic and a program logic specifically crafted for QEC programs and establish a sound proof system. We then develop an efficient method for handling verification conditions (VCs) of QEC programs: for Pauli errors, the VCs are reduced to classical assertions that can be solved by SMT solvers, and for non-Pauli errors, we provide a heuristic algorithm. We formalize the proposed program logic in Coq proof assistant, making it a verified QEC verifier. Additionally, we implement an automated QEC verifier, Veri-QEC, for verifying various fault-tolerant scenarios. We demonstrate the efficiency and broad functionality of the framework by performing different verification tasks across various scenarios. Finally, we present a benchmark of 14 verified stabilizer codes.

Explore related subjects

cs.PLquant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Qifan Huang, Li Zhou, Wang Fang, Mengyu Zhao, Mingsheng Ying. 2025-10-29. Efficient Formal Verification of Quantum Error Correcting Programs. https://doi.org/10.1145/3729293

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

From Rocq to Metal: A Pipeline for Formally Verified Microcontroller Firmware

Enforcing invariants in safety-critical firmware is increasingly urgent as generated code becomes widespread, but standard extraction targets for proof assistants require runtimes too large for many embedded devices. We present a pipeline for running formally verified Rocq firmware logic on Cortex-M microcontrollers. The pipeline extracts Gallina to Scheme, compiles it with Encore!, a bare-metal Continuation Passing Style (CPS) bytecode virtual machine, and embeds the result in no_std Rust firmware. We structure applications as pure state-transition functions, so the business logic is proved in Rocq while the event/effect boundary, host callbacks, compiler, and VM remain explicit trusted components. On ST33-class targets with a 50 KB RAM lower bound, Encore! executes Rocq-extracted code end-to-end, stays within the target memory budget on our benchmarks, and validates a transaction-signing application on physical Ledger Flex hardware.

cs.PL↗
arXiv2026

Practical Range Refinement Types with Inference

Refinement types are a static verification technique that aims at increasing the expressivity of traditional type systems while remaining easy and natural to use. While systems based on refinement types have been developed for several mainstream languages, their practical adoption remains limited by their annotation overhead, which is often a more significant burden than when using the "plain" type annotations of languages like Java or Scala. To improve the state of the art, this paper introduces Ranger: a refinement type system designed to keep the annotation overhead small and to seamlessly integrate with imperative-style constructs like variables and loops. As the name suggests, Ranger focuses on integer range types: a particular kind of refinement types that express bounded integer ranges. Such types are widely useful to verify correct index manipulation and in-bounds data accesses, among others. To combine expressiveness and succinctness, Ranger is based on a bidirectional type system, which runs a type inference algorithm to provide the typechecking pass with information useful to reduce the need for user-written auxiliary annotations. Ranger also integrates other forms of lightweight flow-sensitive static analysis techniques that precisely capture the program's behavior without explicit annotations. We implemented Ranger on top of the Licorne experimental programming language. Our experiments show that Ranger's implementation can concisely express and verify a variety of useful properties that fall beyond the capabilities of standard static type systems like those of Java and Scala, and that Ranger compares favorably to other extended type systems, such as the Java Checker Framework and Liquid Java, that can also check properties about ranges.

cs.PL↗
arXiv2026

Djinnlang: Higher-Level Programming by Unambiguous Specification with an LLM in the Compiler

Programmers write formal specifications, and LLMs implement them, proving that each implementation matches its spec. Taken to its extreme, this makes specification languages the new programming languages. We argue that an unambiguity constraint is key: in addition to proving that its implementation satisfies the specification, the LLM must also prove that any other implementation satisfying it must produce the same outputs on the same inputs, i.e. that the relation formed by the constraints is deterministic. This leaves the LLM no leeway on program semantics: as with a conventional compiler, the generated code never needs to be read and can be regenerated from the spec at any time. Under this constraint and with a powerful LLM, the difference between a specification language and a programming language becomes essentially meaningless, and the LLM essentially becomes a part of the compiler toolchain. The arrangement doubles as a strong form of AI control: an untrusted model writes the code, yet its work is tightly checked by a verifier. To demonstrate that our LLM-in-the-compiler paradigm is feasible when supported by our unambiguity constraint, we present Djinnlang, a high-level specification language built for this future. A Djinnlang program consists only of specifications --- the programmer never writes executable code. In place of a traditional compiler, a symbolic translator lowers each spec to Dafny stubs and proof obligations, and a driver harness orchestrates an LLM that fills in implementations and proofs, all checked by the Dafny verifier. We evaluate our language and implementation on multiple examples and we show that it is self-hosting: an LLM can implement the Djinnlang translator from its specification and the reimplementation can verify itself.

cs.PL↗