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Non-deterministic quantum programming

Paolo Zuliani

Published Dec 31, 2004• 19 citations
Publisher

Abstract

In standard computation, non-determinism is used for specifying programs’ behaviour, without having to specify details of implementation. In quantum computation, non-determinism is either meant to be “classical” probabilism or it is not considered at all, since quantum computation is the physical theory of computation and thus it does not deal with non-implementable features. In this work we will instead show that non-determinism may be useful also in quantum computation. In particular, we consider non-determinism embedded in a programming language for quantum computation, the quantum Guarded-Command Language (qGCL), and use that for describing and reasoning about counterfactual computation and mixed-state systems.

DOI
10.25405/ncl.34193379

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In standard computation, non-determinism is used for specifying programs’ behaviour, without having to specify details of implementation. In quantum computation, non-determinism is either meant to be “classical” probabilism or it is not considered at all, since quantum computation is the physical theory of computation and thus it does not deal with non-implementable features. In this work we will instead show that non-determinism may be useful also in quantum computation. In particular, we consider non-determinism embedded in a programming language for quantum computation, the quantum Guarded-Command Language (qGCL), and use that for describing and reasoning about counterfactual computation and mixed-state systems.
While classical computing science has developed a variety of methods and programming languages around the concept of the universal computer, the typical description of quantum algorithms still uses a purely mathematical, non‐constructive formalism which makes no difference between a hydrogen atom and a quantum computer. This paper investigates, how the concept of procedural programming languages, the most widely used classical formalism for describing and implementing algorithms, can be adopted to the field of quantum computing, and how non‐classical features like the reversibility of unitary transformations, the non‐observability of quantum states or the lack of copy and erase operations can be reflected semantically. It introduces the key concepts of procedural quantum programming (hybrid target architecture, operator hierarchy, quantum data types, memory management, etc.) and presents the experimental language QCL, which implements these principles.
Despite many common concepts with classical computer science, quantum computing is still widely considered as a special discipline within the broad field of theoretical physics. One reason for the slow adoption of QC by the computer science community is the confusing variety of formalisms (Dirac notation, matrices, gates, operators, etc.), none of which has any similarity with classical programming languages, as well as the rather “physical” terminology in most of the available literature. QCL (Quantum Computation Language) tries to fill this gap: QCL is a hight level, architecture independent programming language for quantum computers, with a syntax derived from classical procedural languages like C or Pascal. This allows for the complete implementation and simulation of quantum algorithms (including classical components) in one consistent formalism. Chapter 1 is an introduction into the basic concepts of quantum programming,
In this paper a programming language, qGCL, is presented for the expression of quantum algorithms. It contains the features required to program a 'universal' quantum computer (including initialisation and observation), has a formal semantics and body of laws, and provides a refinement calculus supporting the verification and derivation of programs against their specifications. A representative selection of quantum algorithms are expressed in the language and one of them is derived from its specification.
Nondeterministic choice is a useful program construct that provides a way to describe the behaviour of a program without specifying the details of possible implementations. It supports the stepwise refinement of programs, a method that has proven useful in software development. Nondeterminism has also been introduced in quantum programming, and termination of nondeterministic quantum programs has been extensively analysed. In this paper, we go beyond termination analysis to investigate the verification of nondeterministic quantum programs where properties are given by sets of hermitian operators on the associated Hilbert space. Hoare-type logic systems for partial and total correctness are proposed which turn out to be both sound and relatively complete with respect to their corresponding semantic correctness. To show the utility of these proof systems, we analyse some quantum algorithms such as quantum error correction scheme, Deutsch algorithm, and a nondeterministic quantum walk. Finally, a proof assistant prototype is implemented to aid in the automated reasoning of nondeterministic quantum programs.
Has conducted research to determine the derivation of quantum guarded command language (qGCL) program for average. Initially calculation of average value was made in guaded command language (GCL) which is then implemented on a digital computer into the Pascal programming language. Furthermore GCL to calculate the average value was analyzed again to be made in the quantum guarded command language (qGCL). qGCL implementation is on a quantum computer is a future computer could perform calculations very quickly because it uses a superposition state is referred to as quantum bits (qubits). Keywords : GCL, qGCL, Quantum Computer