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Quantitative Robustness Analysis of quantum Programs

PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2019年第POPL期3卷 1-29页

作者： Hung, Shih-Han Hietala, Kesha Zhu, Shaopeng Ying, Mingsheng Hicks, Michael Wu, Xiaodi Univ Maryland College Pk MD 20742 USA Univ Technol Sydney Sydney NSW Australia Chinese Acad Sci Inst Software State Key Lab Comp Sci Beijing Peoples R China Tsinghua Univ Beijing Peoples R China

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 c-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.

关键词： quantum programming quantum noise approximate computing

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Twist: Sound Reasoning for Purity and Entanglement in quantum Programs

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2022年第POPL期6卷 1–32页

作者： Yuan, Charles McNally, Christopher Carbin, Michael MIT CSAIL 32 Vassar St Cambridge MA 02139 USA MIT RLE 32 Vassar St Cambridge MA 02139 USA

quantum programming languages enable developers to implement algorithms for quantum computers that promise computational breakthroughs in classically intractable tasks. programming quantum computers requires awareness of entanglement, the phenomenon in which measurement outcomes of qubits are correlated. Entanglement can determine the correctness of algorithms and suitability of programming patterns. In this work, we formalize purity as a central tool for automating reasoning about entanglement in quantum programs. A pure expression is one whose evaluation is unaffected by the measurement outcomes of qubits that it does not own, implying freedom from entanglement with any other expression in the computation. We present Twist, the first language that features a type system for sound reasoning about purity. The type system enables the developer to identify pure expressions using type annotations. Twist also features purity assertion operators that state the absence of entanglement in the output of quantum gates. To soundly check these assertions, Twist uses a combination of static analysis and runtime verification. We evaluate Twist's type system and analyses on a benchmark suite of quantum programs in simulation, demonstrating that Twist can express quantum algorithms, catch programming errors in them, and support programs that existing languages disallow, while incurring runtime verification overhead of less than 3.5%.

关键词： quantum programming entanglement purity type systems

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quantum Arrows in Haskell

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ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE 2008年第C期210卷 139-152页

作者： Vizzotto, Juliana Kaizer da Rocha Costa, Antonio Carlos Sabry, Amr Univ Fed Rio Grande do Sul Porto Alegre RS Brazil Univ Catolica Pelotas Pelotas Brazil Indiana Univ Bloomington IN 47405 USA

We argue that a realistic model for quantum computations should be general with respect to measurements, and complete with respect to the information flow between the quantum and classical worlds. We discuss two alternative models for general and complete quantum computations based on probability distributions of quantum state vectors and on density matrices with classical outputs. We show that both models can be structured using a generalization of monads called arrows.

关键词： quantum programming density matrices probabilities

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Extending Python for quantum-classical Computing via quantum Just-in-time Compilation

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ACM TRANSACTIONS ON quantum COMPUTING 2022年第4期3卷 1–25页

作者： Nguyen, Thien Mccaskey, Alexander J. Oak Ridge Natl Lab Comp Sci & Math Div Oak Ridge TN 37831 USA

Python is a popular programming language known for its flexibility, usability, readability, and focus on developer productivity. The quantum software community has adopted Python on a number of large-scale efforts due to these characteristics, as well as the remote nature of near-term quantum processors. The use of Python has enabled quick prototyping for quantum code that directly benefits pertinent research and development efforts in quantum scientific computing. However, this rapid prototyping ability comes at the cost of future performant integration for tightly coupled CPU-QPU architectures with fast-feedback. Here, we present a language extension to Python that enables heterogeneous quantum-classical computing via a robust C++ infrastructure for quantum just-in-time (QJIT) compilation. Our work builds off the QCOR C++ language extension and compiler infrastructure to enable a single-source, quantum hardware-agnostic approach to quantum-classical computing that retains the performance required for tightly coupled CPU-QPU compute models. We detail this Python extension, its programming model and underlying software architecture, and provide a robust set of examples to demonstrate the utility of our approach.

关键词： quantum computing compilers domain specific languages quantum programming

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Algorithmic Analysis of Termination Problems for quantum Programs

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PROCEEDINGS OF THE ACM ON programming LANGUAGES-PACMPL 2018年第POPL期2卷 1-29页

作者： Li, Yangjia Ying, Mingsheng Chinese Acad Sci Inst Software State Key Lab Comp Sci Beijing 100190 Peoples R China Univ Technol Sydney Sydney NSW Australia Tsinghua Univ Beijing 100084 Peoples R China

We introduce the notion of linear ranking super-martingale (LRSM) for quantum programs (with nondeterministic choices, namely angelic and demonic choices). Several termination theorems are established showing that the existence of the LRSMs of a quantum program implies its termination. Thus, the termination problems of quantum programs is reduced to realisability and synthesis of LRSMs. We further show that the realisability and synthesis problem of LRSMs for quantum programs can be reduced to an SDP (Semi-Definite programming) problem, which can be settled with the existing SDP solvers. The techniques developed in this paper are used to analyse the termination of several example quantum programs, including quantum random walks and quantum Bernoulli factory for random number generation. This work is essentially a generalisation of constraint-based approach to the corresponding problems for probabilistic programs developed in the recent literature by adding two novel ideas: (1) employing the fundamental Gleason's theorem in quantum mechanics to guide the choices of templates;and (2) a generalised Farkas' lemma in terms of observables (Hermitian operators) in quantum physics.

关键词： quantum programming termination ranking function super-martingale SDP (Semi-Definite programming) quantum random walk quantum Bernoulli factory

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Type Your Matrices for Great Good A Haskell Library of Typed Matrices and Applications (Functional Pearl) 13

Type Your Matrices for Great Good A Haskell Library of Typed...

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13th International Symposium on Haskell (Haskell)

作者： Santos, Armando Oliveira, Jose N. INESC TEC High Assurance Software Lab Braga Portugal Univ Minho Braga Portugal

ISBN: (纸本)9781450380508

We study a simple inductive data type for representing correctby-construction matrices. Despite its simplicity, it can be used to implement matrix-manipulation algorithms efficiently and safely, performing in some cases faster than existing alternatives even though the algorithms are written in a direct and purely functional style. A rich collection of laws makes it possible to derive and optimise these algorithms using equational reasoning, avoiding the notorious off-by-one indexing errors when fiddling with matrix dimensions. We demonstrate the usefulness of the data type on several examples, and highlight connections to related topics in category theory.

关键词： Haskell Linear Algebra of programming Matrices Probabilistic programming quantum programming Data Analysis

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quantum Vs Classical Computing: a Comparative Analysis 7

Quantum Vs Classical Computing: a Comparative Analysis

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7th International Conference on Fog and Mobile Edge Computing (FMEC)

作者： Belkhir, Maria Benkaouha, Haroun Benkhelifa, Elhadj USTHB Univ LSI Lab Comp Sci Fac Algiers Algeria Staffordshire Univ Smart Syst AI& Cybersecur Res Ctr Stoke On Trent England

ISBN: (纸本)9798350334524

Despite the significant technological advancements, the amount of data to be processed remains enormous, and certain problems remain unsolved or take millions of years to be solved. The advent of quantum computing, with its unique properties, represents a pivotal point in the technological world. Although quantum computers are still under development in the laboratories, research is progressing in parallel with the aim of creating a good basis for any contribution in order to be ready for the commercialization of the first computer. This article clarifies the essential basics required before entering the quantum realm. We present the basic properties of quantum computing based on four fondations and their differences from classical computing.

关键词： quantum Computing quantum algorithmic quantum networking quantum programming quantum databases qubits

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A MLIR Dialect for quantum Assembly Languages 2

A MLIR Dialect for Quantum Assembly Languages

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IEEE International Conference on quantum Computing and Engineering (QCE) / quantum Week

作者： McCaskey, Alexander Thien Nguyen Oak Ridge Natl Lab Comp Sci & Math Div Oak Ridge TN 37831 USA Oak Ridge Natl Lab Quantum Sci Ctr Oak Ridge TN 37831 USA

ISBN: (纸本)9781665416917

We demonstrate the utility of the Multi-Level Intermediate Representation (MLIR) for quantum computing. Specifically, we extend MLIR with a new quantum dialect that enables the expression and compilation of common quantum assembly languages. The true utility of this dialect is in its ability to be lowered to the LLVM intermediate representation (IR) in a manner that is adherent to the quantum intermediate representation (QIR) specification recently proposed by Microsoft. We leverage a qcor-enabled implementation of the QIR quantum runtime API to enable a retargetable (quantum hardware agnostic) compiler workflow mapping quantum languages to hybrid quantum-classical binary executables and object code. We evaluate and demonstrate this novel compiler workflow with quantum programs written in OpenQASM 2.0. We provide concrete examples detailing the generation of MLIR from OpenQASM source files, the lowering process from MLIR to LLVM IR, and ultimately the generation of executable binaries targeting available quantum processors.

关键词： quantum computing quantum programming quantum simulation programming languages

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An Automated Deductive Verification Framework for Circuit-building quantum Programs 1

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30th European Symposium on programming (ESOP) Held as Part of the 24th European Joint Conferences on Theory and Practice of Software (ETAPS)

作者： Chareton, Christophe Bardin, Sebastien Bobot, Francois Perrelle, Valentin Valiron, Benoit Univ Paris Saclay Cent Supelec LMF Gif Sur Yvette France Univ Paris Saclay LIST CEA Palaiseau France

ISBN: (数字)9783030720193

ISBN: (纸本)9783030720193;9783030720186

While recent progress in quantum hardware open the door for significant speedup in certain key areas, quantum algorithms are still hard to implement right, and the validation of such quantum programs is a challenge. In this paper we propose QBRICKS, a formal verification environment for circuit-building quantum programs, featuring both parametric specifications and a high degree of proof automation. We propose a logical framework based on first-order logic, and develop the main tool we rely upon for achieving the automation of proofs of quantum specification: PPS, a parametric extension of the recently developed path sum semantics. To back-up our claims, we implement and verify parametric versions of several famous and non-trivial quantum algorithms, including the quantum parts of Shor's integer factoring, quantum phase estimation (QPE) and Grover's search.

关键词： deductive verification quantum programming quantum circuits

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Experiments with IBM quantum Devices for Random Number Generation and String Matching 28

Experiments with IBM Quantum Devices for Random Number Gener...

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28th Telecommunications Forum (TELFOR)

作者： Savvas, I. K. Chernov, A., V Butakova, M. A. Univ Thessaly Dept Digital Syst Larisa Greece Southern Fed Univ Smart Mat Res Inst Rostov Na Donu Russia

ISBN: (纸本)9780738142432

quantum physics is old and mature. quantum computing and algorithms arose 3 decades ago. quantum programming on real quantum Computational Devices (QCD) is something new. Less than the last five years, researchers and scientists could apply quantum programming to QCD since several vendors like IBM, Rigetti, Microsoft or Google could provide access to real machines. In this paper, we experiment and investigate the accuracy of a 5-qubits QCD applying a string search algorithm. Simulating environment used also in order to evaluate the technique and the results obtained were very promising. Even if the accuracy of a real device was around 48% since the possibilities of the other outcomes were extremely low proved the reliability of the real machine. The number of existing qubits was the main obstacle that limits their processing power. In addition, a random number generator was implemented which overcomes all the disadvantages of pseudo-random generators.

关键词： Qiskit quantum programming Random number generator string matching

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