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| '''Quantum programming''' is a set of computer [[programming language]]s that allow the expression of [[quantum algorithm]]s using high-level constructs. The point of quantum languages is not so much to provide a tool for programmers, but to provide tools for researchers to understand better how quantum computation works and how to formally reason about quantum algorithms.
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| One can single out two main groups of quantum programming languages: imperative quantum programming languages and functional quantum programming languages.
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| The most prominent representatives of the first group are QCL and LanQ.<ref>{{cite web |author=Hynek Mlnařík |title=LanQ – a quantum imperative programming language |url=http://lanq.sourceforge.net/}}</ref>
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| Efforts are underway to develop [[functional programming languages]] for [[quantum computing]]. Examples include Selinger's QPL,<ref name="qpl">Peter Selinger, [http://www.mathstat.dal.ca/~selinger/papers.html#qpl "Towards a quantum programming language"], Mathematical Structures in Computer Science 14(4):527-586, 2004.</ref> and the [[Haskell (programming language)|Haskell-like]] language QML by Altenkirch and Grattage.<ref name="qml1">[http://www.cs.nott.ac.uk/~jjg/qml.html Jonathan Grattage: QML Research<!-- Bot generated title -->] (website)</ref><ref name="qml2">T. Altenkirch, V. Belavkin, J. Grattage, A. Green, A. Sabry, J. K. Vizzotto, [http://sneezy.cs.nott.ac.uk/qml QML: A Functional Quantum Programming Language] (website)</ref> Higher-order quantum programming languages, based on [[lambda calculus]], have been proposed by van Tonder,<ref>Andre van Tonder, [http://dx.doi.org/10.1137/S0097539703432165 "A Lambda Calculus for Quantum Computation"], SIAM J. Comput., 33(5), 1109–1135. (27 pages), 2004. Also available from [http://arxiv.org/abs/quant-ph/0307150 arXiv:quant-ph/0307150]</ref> Selinger and Valiron <ref>Peter Selinger and Benoît Valiron, [http://www.mathstat.dal.ca/~selinger/papers/#qlambda "A lambda calculus for quantum computation with classical control"], Mathematical Structures in Computer Science 16(3):527-552, 2006.</ref> and by Arrighi and Dowek.<ref>Pablo Arrighi, Gilles Dowek, [http://www.arxiv.org/abs/quant-ph/0612199 "Linear-algebraic lambda-calculus: higher-order, encodings and confluence"], 2006</ref>
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| Simon Gay's [http://www.dcs.gla.ac.uk/~simon/quantum Quantum Programming Languages Survey] provides information on the state of research and a comprehensive bibliography of resources about quantum programming as of 2007.
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| == Imperative quantum programming languages ==
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| === Quantum pseudocode ===
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| Quantum pseudocode proposed by E. Knill is the first formalised language for description of [[quantum algorithm]]s was introduced and, moreover, it was tightly connected with a model of quantum machine called [[Quantum Random Access Machine]] (QRAM).
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| === Quantum computing language ===
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| [http://tph.tuwien.ac.at/~oemer/qcl.html QCL] (Quantum Computation Language) is one of the first implemented quantum [[programming languages]]. Its [[syntax]] resembles the syntax of the [[C programming language]] and its classical [[data type]]s are similar to primitive data types in C. One can combine classical code and quantum code in the same program.
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| The basic built-in quantum data type in QCL is the qureg (quantum register). It can be interpreted as an array of qubits (quantum bits).
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| qureg x1[2]; // 2-qubit quantum register x1
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| qureg x2[2]; // 2-qubit quantum register x2
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| H(x1); // Hadamard operation on x1
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| H(x2[1]); // Hadamard operation on the first qubit of the register x2
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| Since the qcl interpreter uses qlib simulation library, it is possible to observe the internal state of the quantum machine during execution of the quantum program.
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| qcl> dump
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| : STATE: 4 / 32 qubits allocated, 28 / 32 qubits free
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| 0.35355 |0> + 0.35355 |1> + 0.35355 |2> + 0.35355 |3>
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| + 0.35355 |8> + 0.35355 |9> + 0.35355 |10> + 0.35355 |11>
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| Note that the dump operation is different from measurement, since it does not influence the state of the quantum machine and can be realised only using a simulator.
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| The QCL standard library provides standard quantum operators used in quantum algorithms such as:
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| * controlled-not with many target qubits,
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| * Hadamard operation on many qubits,
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| * parse and controlled phase.
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| But the most important feature of QCL is the support for user-defined operators and functions. Like in modern programming languages, it is possible to define new operations which can be used to manipulate quantum data. For example:
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| operator diffuse (qureg q) {
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| H(q); // Hadamard Transform
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| Not(q); // Invert q
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| CPhase(pi, q); // Rotate if q=1111..
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| !Not(q); // undo inversion
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| !H(q); // undo Hadamard Transform
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| }
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| defines inverse about the mean operator used in [[Grover's algorithm]]. This allows one to define algorithms on a higher level of abstraction and extend the library of functions available for programmers.
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| ====Syntax====
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| *Data types
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| **Quantum - qureg, quvoid, quconst, quscratch, qucond
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| **Classical - int, real, complex, boolean, string, vector, matrix, tensor
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| *Function types
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| **qufunct - Pseudo-classic operators. Can only change the permutation of basic states.
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| **operator - General unitary operators. Can change the amplitude.
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| **procedure - Can call measure, print, and dump inside this function. This function is non-invertible.
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| *Built-in functions
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| **Quantum
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| ***qufunct - Fanout, Swap, Perm2, Perm4, Perm8, Not, CNot
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| ***operator - Matrix2x2, Matrix4x4, Matrix8x8, Rot, Mix, H, CPhase, SqrtNot, X, Y, Z, S, T
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| ***procedure - measure, dump, reset
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| **Classical
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| ***Arithmetic - sin, cos, tan, log, sqrt, ...
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| ***Complex - Re, Im, conj
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| === Q language ===
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| [http://sra.itc.it/people/serafini/qlang/ Q Language] is the second implemented imperative quantum programming language. | |
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| Q Language was implemented as an extension of C++ programming language. It
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| provides classes for basic quantum operations like QHadamard,
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| QFourier, QNot, and QSwap, which are derived from the base class Qop.
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| New operators can be defined using C++ class mechanism.
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| Quantum memory is represented by class Qreg.
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| Qreg x1; // 1-qubit quantum register with initial value 0
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| Qreg x2(2,0); // 2-qubit quantum register with initial value 0
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| The computation process is executed using a provided simulator. Noisy environment can be
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| simulated using parameters of the simulator.
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| === qGCL === | |
| Quantum Guarded Command Language (qGCL) was defined by P. Zuliani in his PhD thesis. It is based on [[Guarded Command Language]] created by [[Edsger Dijkstra]].
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| It can be described as a language of quantum programmes specification.
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| == Functional quantum programming languages ==
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| During the last few years many quantum programming languages based on the [[functional programming]] paradigm were proposed. Functional programming languages are well-suited for reasoning about programs.
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| === QFC and QPL ===
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| QFC and QPL are two closely related quantum programming languages defined by Peter Selinger. They differ only in their syntax: QFC uses a flow chart syntax, whereas QPL uses a textual syntax. These languages have classical control flow, but can operate on quantum or classical data. Selinger gives a denotational semantics for these languages in a category of
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| [[superoperator]]s.
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| === QML ===
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| [http://sneezy.cs.nott.ac.uk/QML/ QML] is a [[Haskell (programming language)|Haskell]]-like quantum programming language by Altenkirch and Grattage.<ref name="qml1"/> Unlike Selinger's QPL, this language takes duplication, rather than discarding, of quantum information as a primitive operation. Duplication in this context is understood to be the operation that maps <math>|\phi\rangle</math> to <math>|\phi\rangle\otimes|\phi\rangle</math>, and is not to be confused with the impossible operation of [[no cloning theorem|cloning]]; the authors claim it is akin to how sharing is modelled in classical languages. QML also introduces both classical and
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| quantum control operators, whereas most other languages rely on classical control.
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| An [[operational semantics]] for QML is given in terms of [[quantum circuit]]s, while a [[denotational semantics]] is presented in terms of [[superoperator]]s, and these are shown to agree. Both the operational and denotational semantics have been implemented (classically) in Haskell.<ref>Jonathan Grattage, [http://sneezy.cs.nott.ac.uk/qml/compiler QML: A Functional Quantum Programming Language (compiler)], 2005–2008</ref>
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| === Quantum lambda calculi ===
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| Quantum lambda calculi are extensions of the [[lambda calculus]], introduced by [[Alonzo Church]] and [[Stephen Cole Kleene]] in the 1930s. The purpose of quantum lambda calculi is to extend quantum programming languages with a theory of [[higher-order functions]].
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| The first attempt to define a quantum lambda calculus was made by Philip Maymin in 1996.<ref>Philip Maymin, [http://arxiv.org/abs/quant-ph/9612052 "Extending the Lambda Calculus to Express Randomized and Quantumized Algorithms"], 1996</ref>
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| His lambda-q calculus is powerful enough to express any quantum computation. However, this language can efficiently solve [[NP-complete]] problems, and therefore appears to be strictly stronger than the standard quantum computational models (such as the [[quantum Turing machine]] or the [[quantum circuit]] model). Therefore, Maymin's lambda-q calculus is probably not implementable on a physical device.
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| In 2003, André van Tonder defined an extension of the [[lambda calculus]] suitable for proving correctness of quantum programs. He also provided an implementation in the [[Scheme (programming language)|Scheme]] programming language.<ref>{{cite web |author=André van Tonder |title=A lambda calculus for quantum computation (website) |url=http://www.het.brown.edu/people/andre/qlambda}}</ref>
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| In 2004, Selinger and Valiron defined a [[strongly typed]] lambda calculus for quantum computation with a type system based on [[linear logic]].
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| === Quipper ===
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| Quipper has been published in 2013.<ref>{{cite web |author=Alexander S. Green, Peter LeFanu Lumsdaine, Neil J. Ross, Peter Selinger, Benoît Valiron |title=The Quipper Language (website) |url=http://www.mathstat.dal.ca/~selinger/quipper/}}</ref> It is implemented as an embedded language, using [[Haskell (programming language)|Haskell]] as the host language.<ref>{{cite web |author=Alexander S. Green, Peter LeFanu Lumsdaine, Neil J. Ross, Peter Selinger, Benoît Valiron |title=An Introduction to Quantum Programming in Quipper |url=http://arxiv.org/abs/1304.5485 |year=2013}}</ref> For this reason, quantum programms written in Quipper are written in [[Haskell (programming language)|Haskell]] using provided libraries. For example, the following code implements preparation of a superposition
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| import Quipper
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|
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| spos :: Bool -> Circ Qubit
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| spos b = do
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| q <- qinit b
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| r <- hadamard q
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| return r
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| == References ==
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| <references /> | |
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| == External links ==
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| * [http://www.comlab.ox.ac.uk/people/bob.coecke/DCM_QPL_08.html 5th International Workshop on Quantum Physics and Logic]
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| * [http://www.mathstat.dal.ca/~selinger/qpl2006/ 4th International Workshop on Quantum Programming Languages]
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| * [http://www.mathstat.dal.ca/~selinger/qpl2005/ 3rd International Workshop on Quantum Programming Languages]
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| * [http://www.mathstat.dal.ca/~selinger/qpl2004/ 2nd International Workshop on Quantum Programming Languages]
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| * [http://www.dcs.gla.ac.uk/~simon/quantum/ Bibliography on Quantum Programming Languages] (updated in May 2007)
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| * [http://www.quantiki.org/wiki/index.php/Quantum_Programming_Language Quantum programming language] in [http://www.quantiki.org/ Quantiki]
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| {{Quantum computing}}
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| [[Category:Programming language classification]]
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| [[Category:Quantum information science]]
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| [[Category:Programming paradigms]]
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