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Quantum Computation Language

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Quantum Computation Language (QCL) is one of the first implemented <a href="Quantum_programming" title="Quantum programming">quantum programming</a> <a href="Programming_languages" class="mw-redirect" title="Programming languages">languages</a>.<a href="#cite_note-1">[1]</a> The most important feature of QCL is the support for user-defined operators and functions. Its <a href="Syntax" title="Syntax">syntax</a> resembles the syntax of the <a href="C_programming_language" class="mw-redirect" title="C programming language">C programming language</a> and its classical <a href="Data_type" title="Data type">data types</a> are similar to primitive data types in C. One can combine classical code and quantum code in the same program.

The language was created before there were multi-qubit quantum computers and the only implementation of QCL uses an interpreter with a built-in classically simulated quantum computer.

QCL was created to explore programming concepts for quantum computers.<a href="#cite_note-2">[2]</a><a href="#cite_note-3">[3]</a><a href="#cite_note-4">[4]</a>

The QCL library provides standard quantum operators used in quantum algorithms such as:<a href="#cite_note-5">[5]</a>

<ul><li>Controlled-not with many target qubits,</li>

<li><a href="Hadamard_operation" class="mw-redirect" title="Hadamard operation">Hadamard operation</a> on many qubits,</li>

<li>Phase and controlled phase.</li>

<li>Quantum algorithms for addition, multiplication and exponentiation with binary constants (all modulus n)</li>

<li>The <a href="Quantum_Fourier_transform" title="Quantum Fourier transform">quantum fourier transform</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Syntax">Syntax</h2></div>

<ul><li>Data types

<ul><li>Quantum - qureg, quvoid, quconst, quscratch, qucond</li>

<li>Classical - int, real, complex, boolean, string, vector, matrix, tensor</li></ul></li>

<li>Function types

<ul><li>qufunct - Pseudo-classic operators. Can only change the permutation of basis states.</li>

<li>operator - General unitary operators. Can change the amplitude.</li>

<li>procedure - Can call measure, print, and dump inside this function. This function is non-invertible.</li></ul></li>

<li>Built-in functions

<ul><li>Quantum

<ul><li>qufunct - Fanout, Swap, Perm2, Perm4, Perm8, Not, CNot</li>

<li>operator - Matrix2x2, Matrix4x4, Matrix8x8, Rot, Mix, H, CPhase, SqrtNot, X, Y, Z, S, T</li>

<li>procedure - measure, dump, reset</li></ul></li>

<li>Classical

<ul><li>Arithmetic - sin, cos, tan, log, sqrt, ...</li>

<li>Complex - Re, Im, conj</li></ul></li></ul></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2></div>

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).

<div class="mw-highlight mw-highlight-lang-cpp mw-content-ltr" dir="ltr"><pre>qureg x1[2]; // 2-qubit quantum register x1

qureg x2[2]; // 2-qubit quantum register x2

H(x1); // Hadamard operation on x1

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.

<div class="mw-highlight mw-highlight-lang-text mw-content-ltr" dir="ltr"><pre>qcl> dump

: STATE: 4 / 32 qubits allocated, 28 / 32 qubits free

0.35355 |0> + 0.35355 |1> + 0.35355 |2> + 0.35355 |3>

+ 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 realized only using a simulator.

Like in modern programming languages, it is possible to define new operations which can be used to manipulate quantum data. For example:

<div class="mw-highlight mw-highlight-lang-cpp mw-content-ltr" dir="ltr"><pre>operator diffuse (qureg q) {

H(q); // Hadamard Transform

Not(q); // Invert q

CPhase(pi, q); // Rotate if q=1111..

!Not(q); // undo inversion

!H(q); // undo Hadamard Transform

}

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defines inverse about the mean operator used in <a href="Grover's_algorithm" title="Grover's algorithm">Grover's algorithm</a> (it is sometimes called Grover's diffusion operator). This allows one to define algorithms on a higher level of abstraction and extend the library of functions available for programmers.

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://tph.tuwien.ac.at/~oemer/qcl.html">"QCL - A Programming Language for Quantum Computers"</a>. tuwien.ac.at. Retrieved 2017-07-20.</cite>

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<li id="cite_note-2"><a href="#cite_ref-2">^</a> <cite id="CITEREFÖmer2000" class="citation thesis cs1">Ömer, Bernhard (2000-01-20). <a rel="nofollow" class="external text" href="http://tph.tuwien.ac.at/~oemer/doc/quprog.pdf">Quantum Programming in QCL</a> (PDF) (Thesis). Institute for Theoretical Physics, Vienna University of Technology. Retrieved 2021-05-24.</cite>

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<li id="cite_note-3"><a href="#cite_ref-3">^</a> <cite id="CITEREFÖmer2003" class="citation journal cs1">Ömer, Bernhard (29 Apr 2003). "Classical Concepts in Quantum Programming". International Journal of Theoretical Physics. 44 (7): 943–955. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/quant-ph/0211100">quant-ph/0211100</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10773-005-7071-x">10.1007/s10773-005-7071-x</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:119373370">119373370</a>.</cite>

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<li id="cite_note-4"><a href="#cite_ref-4">^</a> <cite id="CITEREFÖmer2009" class="citation web cs1">Ömer, Bernhard (2 September 2009). <a rel="nofollow" class="external text" href="http://tph.tuwien.ac.at/~oemer/doc/structquprog.pdf">"Structured Quantum Programming"</a> (PDF). Institute for Theoretical Physics, Vienna University of Technology.</cite>

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