02180nas a2200181 4500008004100000245003100041210003100072260001200103520171100115100001901826700001301845700001701858700001701875700001701892700001501909700001901924856005501943 2021 eng d00aExpanding the VOQC Toolkit0 aExpanding the VOQC Toolkit c06/20213 a

voqc [Hietala et al. 2021b] (pronounced “vox”) is a compiler for quantum circuits, in the style of
tools like Qiskit [Aleksandrowicz et al. 2019], tket [Cambridge Quantum Computing Ltd 2019],
Quilc [Rigetti Computing 2019], and Cirq [Developers 2021]. What makes voqc different from these
tools is that it has been formally verified in the Coq proof assistant [Coq Development Team 2019].
voqc source programs are expressed in sqir, a simple quantum intermediate representation, which
has a precise mathematical semantics. We use Gallina, Coq’s programming language, to implement
voqc transformations over sqir programs, and use Coq to prove the source program’s semantics
are preserved. We then extract these Gallina definitions to OCaml, and compile the OCaml code to
a library that can operate on standard-formatted circuits.
voqc, and sqir, were built to be general-purpose. For example, while we originally designed sqir
for use in verified optimizations, we subsequently found sqir could also be suitable for writing, and
proving correct, source programs [Hietala et al. 2021a]. We have continued to develop the voqc
codebase to expand its reach and utility.
In this abstract, we present new extensions to voqc as an illustration of its flexibility. These
include support for calling voqc transformations from Python, added support for new gate sets
and optimizations, and the extension of our notion of correctness to include mapping-preservation,
which allows us to apply optimizations after mapping, reducing the cost introduced by making a
program conform to hardware constraints.

1 aHietala, Kesha1 aLi, Liyi1 aGaur, Akshaj1 aGreen, Aaron1 aRand, Robert1 aWu, Xiaodi1 aHicks, Michael uhttp://rand.cs.uchicago.edu/files/planqc_2021c.pdf01160nas a2200157 4500008004100000245003700041210003700078260001400115520074900129100001900878700001700897700001900914700001300933700001900946856003700965 2021 eng d00aProving Quantum Programs Correct0 aProving Quantum Programs Correct c7/13/20213 a

As quantum computing steadily progresses from theory to practice, programmers are faced with 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 Simon's algorithm, 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.

1 aHietala, Kesha1 aRand, Robert1 aHung, Shih-Han1 aLi, Liyi1 aHicks, Michael uhttps://arxiv.org/abs/2010.0124001742nas a2200169 4500008004100000245004400041210004400085260001500129520128400144100001301428700002301441700001901464700001801483700001501501700001901516856003701535 2021 eng d00aVerified Compilation of Quantum Oracles0 aVerified Compilation of Quantum Oracles c12/13/20213 a

Quantum algorithms often apply classical operations, such as arithmetic or predicate checks, over a quantum superposition of classical data; these so-called oracles are often the largest components of a quantum algorithm. To ease the construction of efficient, correct oracle functions, this paper presents VQO, a high-assurance framework implemented with the Coq proof assistant. The core of VQO is OQASM, the oracle quantum assembly language. OQASM operations move qubits among three different bases via the Quantum Fourier Transform and Hadamard operations, thus admitting important optimizations, but without inducing entanglement and the exponential blowup that comes with it. OQASM's design enabled us to prove correct VQO's compilers -- from a simple imperative language called OQIMP to OQASM, and from OQASM to SQIR, a general-purpose quantum assembly language -- and allowed us to efficiently test properties of OQASM programs using the QuickChick property-based testing framework. We have used VQO to implement oracles used in Shor's and Grover's algorithms, as well as several common arithmetic operators. VQO's oracles have performance comparable to those produced by Quipper, a state-of-the-art but unverified quantum programming platform.

1 aLi, Liyi1 aVoichick, Finnegan1 aHietala, Kesha1 aPeng, Yuxiang1 aWu, Xiaodi1 aHicks, Michael uhttps://arxiv.org/abs/2112.0670001145nas a2200169 4500008004100000245004600041210004400087260001500131490000600146520069700152100001900849700001700868700001900885700001500904700001900919856003700938 2021 eng d00aA Verified Optimizer for Quantum Circuits0 aVerified Optimizer for Quantum Circuits c11/12/20200 v53 a

We present VOQC, the first fully verified compiler for quantum circuits, written using the Coq proof assistant. Quantum circuits are expressed as programs in a simple, low-level language called SQIR, which is deeply embedded in Coq. Optimizations and other transformations are expressed as Coq functions, which are proved correct with respect to a semantics of SQIR programs. We evaluate VOQC's verified optimizations on a series of benchmarks, and it performs comparably to industrial-strength compilers. VOQC's optimizations reduce total gate counts on average by 17.7% on a benchmark of 29 circuit programs compared to a 10.7% reduction when using IBM's Qiskit compiler.

1 aHietala, Kesha1 aRand, Robert1 aHung, Shih-Han1 aWu, Xiaodi1 aHicks, Michael uhttps://arxiv.org/abs/1912.0225000982nas a2200157 4500008004100000245006700041210006700108260001500175520050800190100001900698700001700717700001900734700001500753700001900768856003700787 2019 eng d00aVerified Optimization in a Quantum Intermediate Representation0 aVerified Optimization in a Quantum Intermediate Representation c04/12/20193 a

We present sqire, a low-level language for quantum computing and verification. sqire uses a global register of quantum bits, allowing easy compilation to and from existing `quantum assembly' languages and simplifying the verification process. We demonstrate the power of sqire as an intermediate representation of quantum programs by verifying a number of useful optimizations, and we demonstrate sqire's use as a tool for general verification by proving several quantum programs correct.

1 aHietala, Kesha1 aRand, Robert1 aHung, Shih-Han1 aWu, Xiaodi1 aHicks, Michael uhttps://arxiv.org/abs/1904.0631901816nas a2200193 4500008004100000245007600041210006900117260001400186300001500200490000600215520125400221100001901475700001901494700001801513700002001531700001901551700001501570856003701585 2018 eng d00aQuantitative Robustness Analysis of Quantum Programs (Extended Version)0 aQuantitative Robustness Analysis of Quantum Programs Extended Ve c2018/12/1 aArticle 310 v33 a

Quantum computation is a topic of significant recent interest, with practical advances coming from both research and industry. A major challenge in quantum programming is dealing with errors (quantum noise) during execution. Because quantum resources (e.g., qubits) are scarce, classical error correction techniques applied at the level of the architecture are currently cost-prohibitive. But while this reality means that quantum programs are almost certain to have errors, there as yet exists no principled means to reason about erroneous behavior. This paper attempts to fill this gap by developing a semantics for erroneous quantum while-programs, as well as a logic for reasoning about them. This logic permits proving a property we have identified, called ε-robustness, which characterizes possible "distance" between an ideal program and an erroneous one. We have proved the logic sound, and showed its utility on several case studies, notably: (1) analyzing the robustness of noisy versions of the quantum Bernoulli factory (QBF) and quantum walk (QW); (2) demonstrating the (in)effectiveness of different error correction schemes on single-qubit errors; and (3) analyzing the robustness of a fault-tolerant version of QBF.

1 aHung, Shih-Han1 aHietala, Kesha1 aZhu, Shaopeng1 aYing, Mingsheng1 aHicks, Michael1 aWu, Xiaodi uhttps://arxiv.org/abs/1811.03585