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<!DOCTYPE html>
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<h4>🔬 Dark Mode</h4>
<p>Manual Controls</p>
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QASM: Single Gate Multiple-Qubits
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/qasm-qubit-initialization-and-measurement/" class="page-menu__link">
QASM: Qubit initialization and measurement
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/qasm-binary-controlled-gates/" class="page-menu__link">
QASM: Binary controlled gates
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/qasm-display-commands/" class="page-menu__link">
QASM: Display commands
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/qasm-error-models/" class="page-menu__link">
QASM: Error models
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/optimization-of-simulations/" class="page-menu__link">
Optimization of simulations
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/gate-decomposition/" class="page-menu__link">
Gate decomposition
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/optimizing-quantum-circuits/" class="page-menu__link">
Optimizing quantum circuits
</a>
</li>
</ul>
</section>
<section class="page-menu__group">
<h3 class="h3 page-menu__group-title">cQASM instructions</h3>
<ul class="page-menu__list">
<li>
<a href="https://www.quantum-inspire.com/kbase/qubits/" class="page-menu__link">
Qubits
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/prep-z/" class="page-menu__link">
Prep_z
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/prep-y/" class="page-menu__link">
Prep_y
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/prep-x/" class="page-menu__link">
Prep_x
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/pauli-x/" class="page-menu__link">
Pauli-X gate
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/pauli-y/" class="page-menu__link">
Pauli-Y gate
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/pauli-z/" class="page-menu__link">
Pauli-Z gate
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/hadamard/" class="page-menu__link">
Hadamard gate
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/identity-gate/" class="page-menu__link">
Identity gate
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/rx-gate/" class="page-menu__link">
Rx Gate
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/ry-gate/" class="page-menu__link">
Ry Gate
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/rz-gate/" class="page-menu__link">
Rz Gate
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/90-degree-rotations/" class="page-menu__link">
90 degree rotations
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/s-gate/" class="page-menu__link">
S Gate
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/s-dagger-gate/" class="page-menu__link">
S dagger Gate
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/t-gate/" class="page-menu__link">
T Gate
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/t-dagger-gate/" class="page-menu__link">
T dagger Gate
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/cnot/" class="page-menu__link">
CNOT Gate
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/cz-gate/" class="page-menu__link">
CZ Gate
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/swap/" class="page-menu__link">
Swap Gate
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/cr-gate/" class="page-menu__link">
CR gate
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/crk-gate/" class="page-menu__link">
CRk gate
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/toffoli/" class="page-menu__link">
Toffoli Gate
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/measure-z/" class="page-menu__link">
Measure_z
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/measure-y/" class="page-menu__link">
Measure_y
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/measure-x/" class="page-menu__link">
Measure_x
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/measure-all/" class="page-menu__link">
Measure_all
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/measure_parity/" class="page-menu__link">
Measure_parity
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/display/" class="page-menu__link">
Display
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/display-binary/" class="page-menu__link">
Display_binary
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/binary-controlled-gates/" class="page-menu__link">
Binary controlled gates
</a>
</li>
<li>
<a href="https://www.quantum-inspire.com/kbase/not/" class="page-menu__link">
Not
</a>
</li>
</ul>
</section>
<section class="page-menu__group">
<h3 class="h3 page-menu__group-title">Hardware backends</h3>
<ul class="page-menu__list">
<li>
<a href="https://www.quantum-inspire.com/kbase/hardware-backends/" class="page-menu__link">
Hardware backends
</a>
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</ul>
</section>
<section class="page-menu__group">
<h3 class="h3 page-menu__group-title">Simulator backends</h3>
<ul class="page-menu__list">
<li>
<a href="https://www.quantum-inspire.com/kbase/simulator-backends/" class="page-menu__link">
Simulator backends
</a>
</li>
</ul>
</section>
</nav>
</div>
</div>
<div class="page-layout__content">
<article>
<h1 class="h1">What is a quantum algorithm?</h1>
<div class="page-content">
<div class="rich-text">
<div class="rich-text">
<h2 class="h2" id="quantum-algorithms" name="quantum-algorithms">
Quantum Algorithms
</h2>
<p>
An algorithm is a step-by-step procedure to perform a
calculation, or a sequence of instructions to solve a
problem, where each step can be performed on a computer.
Therefore, an algorithm is a quantum algorithm when it can
be performed on a quantum computer. In principle it is
possible to run all classical algorithms on a quantum
computer. However, the term quantum algorithm is applied
to algorithms of which at least one of the steps is
distinctly ‘quantum’, using
<a href="https://www.quantum-inspire.com/kbase/superposition-and-entanglement/">superposition or
entanglement</a>.
</p>
</div>
<div class="responsive-video">
<figure>
<div class="fixed-ratio responsive-video__canvas" style="padding-bottom: 56.25%;">
<div class="fixed-ratio__content">
<div class="responsive-video__lazy-load">
<div class="responsive-video__background" style="background-image: url("https://i.ytimg.com/vi/V0ssQZBS8-U/maxresdefault.jpg");"></div>
<!---->
</div>
<!----><a href="https://youtu.be/V0ssQZBS8-U" class="responsive-video__button"><span class="sr-only">Play</span><img
src="../original_files/play.svg" class="responsive-video__icon" /></a>
</div>
</div>
<figcaption class="responsive-video__caption">
<a target="_blank" rel="noopener" href="https://youtu.be/V0ssQZBS8-U" class="responsive-video__caption-anchor">
Quantum algorithms explained by Qutech Academy
</a>
</figcaption>
</figure>
</div>
<h2 class="h2" id="quantum-circuits" name="quantum-circuits">
Quantum circuits
</h2>
<p>
Quantum algorithms are most commonly described by a quantum
circuit, of which a simple example is shown in the figure
below. A quantum circuit is a model for quantum computation,
where the steps to solve the problem are quantum gates
performed on one or more qubits. A quantum gate is an
operation applied to a qubit that changes the quantum state
of the qubit. Quantum gates can be divided into single-qubit
gates and two-qubit gates, depending on the number of qubits
on which they are applied at the same time. Three-qubit
gates and other multi-qubit gates can also be defined. A
quantum circuit is concluded with a measurement on one or
more qubits.
</p>
<p>
<em>When your algorithm is executed on a simulator backend,
instead of a hardware backend, it is usually very
beneficial in terms of execution time, to omit the
measurement at the end of the algorith. This is eplained
in more detail in the
<a href="https://www.quantum-inspire.com/kbase/optimization-of-simulations">section on simulation
optimization</a></em>
</p>
</div>
<div class="code-preview">
<div class="code-preview__pane code-preview__pane--light">
<div class="vue-codemirror">
<textarea placeholder="" style="display: none;"></textarea>
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1
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<pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-comment">version 1.0</span></span></pre>
</div>
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2
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<pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre>
</div>
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<div class="CodeMirror-gutter-wrapper" style="left: -31px;">
<div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 21px;">
3
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<pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-comment"># define a quantum register of 2 qubits</span></span></pre>
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4
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<pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-keyword">qubits</span><span class="cm-number"> 2</span></span></pre>
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5
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<pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text=""></span></span></pre>
</div>
<div style="position: relative;">
<div class="CodeMirror-gutter-wrapper" style="left: -31px;">
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6
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</div>
<pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-operator cm-box">h</span> q[<span class="cm-number">0</span>]</span></pre>
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7
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<pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-operator cm-box">cnot</span> q[<span class="cm-number">0</span>],q[<span class="cm-number">1</span>]</span></pre>
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<pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-keyword cm-box">measure_all</span></span></pre>
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<div style="position: absolute; height: 15px; width: 1px; border-bottom: 0px solid transparent; top: 208px;"></div>
<div class="CodeMirror-gutters" style="height: 223px; left: 0px;">
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</div>
</div>
</div>
<div class="code-preview__pane code-preview__pane--visualiser">
<figure class="circuit-visualiser circuit-visualiser--light">
<table class="circuit-visualiser__table">
<thead>
<td></td>
<td class="circuit-visualiser__subcircuit-heading">
<!---->
</td>
<td class="circuit-visualiser__subcircuit-heading">
<!---->
</td>
<td class="circuit-visualiser__subcircuit-heading">
<!---->
</td>
<td></td>
</thead>
<tr class="circuit-visualiser__row">
<th class="circuit-visualiser__register-heading">
q[0]
</th>
<td>
<figure class="gate-icon gate-icon--singleGate gate-icon--h circuit-gate circuit-gate--singleGate circuit-gate--h circuit-gate--light
circuit-gate--target">
<svg xmlns="http://www.w3.org/2000/svg" width="28" height="28">
<path fill="currentColor" d="M19.64 20.42H16.4v-5.64h-4.8v5.64H8.35V6.91h3.25v5.37h4.8V6.91h3.24z"></path>
</svg>
<!---->
</figure>
<div class="circuit-connection circuit-connection--operator circuit-connection--none">
</div>
</td>
<td>
<figure class="gate-icon gate-icon--dualGate gate-icon--cnot circuit-gate circuit-gate--dualGate circuit-gate--cnot circuit-gate--light
circuit-gate--control">
<svg xmlns="http://www.w3.org/2000/svg" width="18" height="18">
<path fill="currentColor" d="M9 0a9 9 0 1 0 9 9 9 9 0 0 0-9-9zm4 10h-3v3a1 1 0 0 1-2 0v-3H5a1 1 0 0 1 0-2h3V5a1 1 0 0 1 2 0v3h3a1 1 0 0 1 0 2z"></path>
</svg>
<!---->
</figure>
<div class="circuit-connection circuit-connection--operator circuit-connection--start">
</div>
</td>
<td>
<figure class="gate-icon gate-icon--measure gate-icon--measure_all circuit-gate circuit-gate--measure circuit-gate--measure_all circuit-gate--light
circuit-gate--target">
<svg xmlns="http://www.w3.org/2000/svg" width="28" height="28">
<path fill="currentColor" d="M17 18.4v-1h-6.6v1.5h4.1l-4.1 5.9v1.1H17v-1.6h-4l4-5.9zm8.5-16.1l-4.2.9a.2.2 0 0 0-.1.3l1 1-1.4 1.3A10.6 10.6 0 0 0 3.4 14a1 1 0 0 0 2 0 8.6 8.6 0 0 1 14-6.8l-6 6a1 1 0 0 0 0 1.5 1 1 0 0 0 .6.3 1 1 0 0 0 .7-.3l6-6a8.5 8.5 0 0 1 2 5.3 1 1 0 0 0 2 0 10.6 10.6 0 0 0-2.5-6.8L23.6 6l1 1a.2.2 0 0 0 .3-.1l.9-4.2a.2.2 0 0 0-.3-.3z"></path>
</svg>
<!---->
</figure>
<div class="circuit-connection circuit-connection--keyword circuit-connection--none">
</div>
<!---->
<div class="circuit-connection circuit-connection--keyword circuit-connection--none">
</div>
</td>
<td></td>
</tr>
<tr class="circuit-visualiser__row">
<th class="circuit-visualiser__register-heading">
q[1]
</th>
<td>
<!---->
<div class="circuit-connection circuit-connection--operator circuit-connection--none">
</div>
</td>
<td>
<figure class="gate-icon gate-icon--dualGate gate-icon--cnot circuit-gate circuit-gate--dualGate circuit-gate--cnot circuit-gate--light
circuit-gate--target">
<svg xmlns="http://www.w3.org/2000/svg" width="18" height="18">
<path fill="currentColor" d="M9 0a9 9 0 1 0 9 9 9 9 0 0 0-9-9zm4 10h-3v3a1 1 0 0 1-2 0v-3H5a1 1 0 0 1 0-2h3V5a1 1 0 0 1 2 0v3h3a1 1 0 0 1 0 2z"></path>
</svg>
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</figure>
<div class="circuit-connection circuit-connection--operator circuit-connection--end">
</div>
</td>
<td>
<!---->
<div class="circuit-connection circuit-connection--keyword circuit-connection--none">
</div>
<figure class="gate-icon gate-icon--measure gate-icon--measure_all circuit-gate circuit-gate--measure circuit-gate--measure_all circuit-gate--light
circuit-gate--target">
<svg xmlns="http://www.w3.org/2000/svg" width="28" height="28">
<path fill="currentColor" d="M17 18.4v-1h-6.6v1.5h4.1l-4.1 5.9v1.1H17v-1.6h-4l4-5.9zm8.5-16.1l-4.2.9a.2.2 0 0 0-.1.3l1 1-1.4 1.3A10.6 10.6 0 0 0 3.4 14a1 1 0 0 0 2 0 8.6 8.6 0 0 1 14-6.8l-6 6a1 1 0 0 0 0 1.5 1 1 0 0 0 .6.3 1 1 0 0 0 .7-.3l6-6a8.5 8.5 0 0 1 2 5.3 1 1 0 0 0 2 0 10.6 10.6 0 0 0-2.5-6.8L23.6 6l1 1a.2.2 0 0 0 .3-.1l.9-4.2a.2.2 0 0 0-.3-.3z"></path>
</svg>
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</figure>
<div class="circuit-connection circuit-connection--keyword circuit-connection--none">
</div>
</td>
<td></td>
</tr>
</table>
</figure>
</div>
</div>
<div class="rich-text">
<h2 class="h2" id="reversibility-of quantum circuits" name="reversibility-of quantum circuits">
Reversibility of quantum circuits
</h2>
<p>
A difference with a classical algorithm is that a quantum
algorithm is always reversible. This means that if
measurements are not a part of the circuit, a reverse
traversal of the quantum circuit will undo the operations
brought about by a forward traversal of that circuit.
</p>
<h2 class="h2" id="the-power of quantum algorithms" name="the-power of quantum algorithms">
The power of quantum algorithms
</h2>
<p>
Problems that are fundamentally unsolvable by classical
algorithms (so called undecidable problems) cannot be solved
by quantum algorithms either. The added value of quantum
algorithms is that they can solve some problems
significantly faster than classical algorithms. The best
known examples are Shor’s algorithm and
<a href="https://www.quantum-inspire.com/kbase/grover-algorithm/">Grover’s algorithm</a>. Shor’s
algorithm is a quantum algorithm for integer
factorization. Simply put, when given a integer N, it will
find its prime factors. It can solve this problem
exponentially faster than the best known classical algorithm
can. Grover’s algorithm can search an unstructured database
or unordered list quadratically faster then the best
classical algorithm with this purpose.
</p>
</div>
</div>
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