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ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL)

QWIRE: a core language for quantum circuits

Jennifer Paykin, Robert W. Rand, Steve Zdancewic

Published Dec 22, 2016• 131 citations
Publisher

Abstract

This paper introduces QWIRE (``choir''), a language for defining quantum circuits and an interface for manipulating them inside of an arbitrary classical host language. QWIRE is minimal---it contains only a few primitives---and sound with respect to the physical properties entailed by quantum mechanics. At the same time, QWIRE is expressive and highly modular due to its relationship with the host language, mirroring the QRAM model of computation that places a quantum computer (controlled by circuits) alongside a classical computer (controlled by the host language).

DOI
10.1145/3009837.3009894

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This paper introduces QWIRE (``choir''), a language for defining quantum circuits and an interface for manipulating them inside of an arbitrary classical host language. QWIRE is minimal---it contains only a few primitives---and sound with respect to the physical properties entailed by quantum mechanics. At the same time, QWIRE is expressive and highly modular due to its relationship with the host language, mirroring the QRAM model of computation that places a quantum computer (controlled by circuits) alongside a classical computer (controlled by the host language). We present QWIRE along with its type system and operational semantics, which we prove is safe and strongly normalizing whenever the host language is. We give circuits a denotational semantics in terms of density matrices. Throughout, we investigate examples that demonstrate the expressive power of QWIRE, including extensions to the host language that (1) expose a general analysis framework for circuits, and (2) provide dependent types.

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This paper introduces QWIRE (``choir''), a language for defining quantum circuits and an interface for manipulating them inside of an arbitrary classical host language. QWIRE is minimal---it contains only a few primitives---and sound with respect to the physical properties entailed by quantum mechanics. At the same time, QWIRE is expressive and highly modular due to its relationship with the host language, mirroring the QRAM model of computation that places a quantum computer (controlled by circuits) alongside a classical computer (controlled by the host language).
This paper introduces QWIRE (``choir''), a language for defining quantum circuits and an interface for manipulating them inside of an arbitrary classical host language. QWIRE is minimal---it contains only a few primitives---and sound with respect to the physical properties entailed by quantum mechanics. At the same time, QWIRE is expressive and highly modular due to its relationship with the host language, mirroring the QRAM model of computation that places a quantum computer (controlled by circuits) alongside a classical computer (controlled by the host language). We present QWIRE along with its type system and operational semantics, which we prove is safe and strongly normalizing whenever the host language is. We give circuits a denotational semantics in terms of density matrices. Throughout, we investigate examples that demonstrate the expressive power of QWIRE, including extensions to the host language that (1) expose a general analysis framework for circuits, and (2) provide dependent types.
We describe an embedding of the QWIRE quantum circuit language in the Coq proof assistant. This allows programmers to write quantum circuits using high-level abstractions and to prove properties of those circuits using Coq's theorem proving features. The implementation uses higher-order abstract syntax to represent variable binding and provides a type-checking algorithm for linear wire types, ensuring that quantum circuits are well-formed. We formalize a denotational semantics that interprets QWIRE circuits as superoperators on density matrices, and prove the correctness of some simple quantum programs.
The field of quantum mechanics predates computer science by at least ten years, the time between the publication of the Schrodinger equation and the Church-Turing thesis. It took another fifty years for Feynman to recognize that harnessing quantum mechanics is necessary to efficiently simulate physics and for David Deutsch to propose the quantum Turing machine. After thirty more years, we are finally getting close to the first general-purpose quantum computers based upon prototypes by IBM, Intel, Google and others.\nWhile physicists and engineers have worked on building scalable quantum computers, theoretical computer scientists have made their own advances. Complexity theorists introduced quantum complexity classes like BQP and QMA; Shor and Grover developed their famous algorithms for factoring and unstructured search. Programming languages researchers pursued two main research directions: Small-scale languages like QPL and the quantum lambda-calculi for reasoning about quantum computation and large-scale languages like Quipper and Q# for industrial-scale quantum software development. This thesis aims to unify these two threads while adding a third one: formal verification.\nWe argue that quantum programs demand machine-checkable proofs of correctness. We justify this on the basis of the complexity of programs manipulating quantum states, the expense of running quantum programs, and the inapplicability of traditional debugging techniques to programs whose states cannot be examined. We further argue that the existing mathematical models of quantum computation make this an easier task than one could reasonably expect. In light of these observations we introduce QWIRE, a tool for writing verifiable, large scale quantum programs.\nQWIRE is not merely a language for writing and verifying quantum circuits: it is a verified circuit description language. This means that the semantics of QWIRE circuits are verified in the Coq proof assistant. We also implement verified abstractions, like ancilla management and reversible circuit compilation. Finally, we turn QWIRE and Coq's abilities outwards, towards verifying popular quantum algorithms like quantum teleportation. We argue that this tool provides a solid foundation for research into quantum programming languages and formal verification going forward.
It is becoming increasingly clear that, if a useful device for quantum computation will ever be built, it will be embodied by a classical computing machine with control over a truly quantum subsystem, this apparatus performing a mixture of classical and quantum computation. This paper investigates a possible approach to the problem of programming such machines: a template high level quantum language is presented which complements a generic general purpose classical language with a set of quantum primitives. The underlying scheme involves a run-time environment which calculates the byte-code for the quantum operations and pipes it to a quantum device controller or to a simulator. This language can compactly express existing quantum algorithms and reduce them to sequences of elementary operations; it also easily lends itself to automatic, hardware independent, circuit simplification. A publicly available preliminary implementation of the proposed ideas has been realized using the C++ language. 1 Quantum programming
We describe categorical models of a circuit-based (quantum) functional programming language. We show that enriched categories play a crucial role. Following earlier work on QWire by Paykin et al., we consider both a simple first-order linear language for circuits, and a more powerful host language, such that the circuit language is embedded inside the host language. Our categorical semantics for the host language is standard, and involves cartesian closed categories and monads. We interpret the circuit language not in an ordinary category, but in a category that is enriched in the host category. As an extended example, we recall an earlier result that the category of W*-algebras is dcpo-enriched, and we use this model to extend the circuit language with some recursive types.
Models of quantum computation and quantum programming languages The goal of the presented paper is to provide an introduction to the basic computational models used in quantum information theory. We review various models of quantum Turing machine, quantum circuits and quantum random access machine (QRAM) along with their classical counterparts. We also provide an introduction to quantum programming languages, which are developed using the QRAM model. We review the syntax of several existing quantum programming languages and discuss their features and limitations.