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commit dff65bbae55259bb9d33ed6d24c1f6aeb9b7a96b
Author: GitHub Actions Bot <>
AuthorDate: Wed Jan 22 04:10:11 2025 +0000
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---
feed.xml | 2 +-
quantum-computing-primer/03_qubits/index.html | 69 +++++++---------------
.../04_quantum_gates/index.html | 27 ++-------
.../07_quantum_algorithms/index.html | 30 ++++++++--
.../10_advanced_topics/index.html | 34 +++++------
5 files changed, 68 insertions(+), 94 deletions(-)
diff --git a/feed.xml b/feed.xml
index 32f1dd844..0682a611a 100644
--- a/feed.xml
+++ b/feed.xml
@@ -1,4 +1,4 @@
-<?xml version="1.0" encoding="utf-8"?><feed
xmlns="http://www.w3.org/2005/Atom"; ><generator uri="https://jekyllrb.com/";
version="4.3.2">Jekyll</generator><link
href="http://mahout.apache.org//feed.xml"; rel="self"
type="application/atom+xml" /><link href="http://mahout.apache.org//";
rel="alternate" type="text/html"
/><updated>2025-01-21T23:09:14+00:00</updated><id>http://mahout.apache.org//feed.xml</id><title
type="html">Apache Mahout</title><subtitle>Distributed Linear
Algebra</subtitle> [...]
+<?xml version="1.0" encoding="utf-8"?><feed
xmlns="http://www.w3.org/2005/Atom"; ><generator uri="https://jekyllrb.com/";
version="4.3.2">Jekyll</generator><link
href="http://mahout.apache.org//feed.xml"; rel="self"
type="application/atom+xml" /><link href="http://mahout.apache.org//";
rel="alternate" type="text/html"
/><updated>2025-01-22T04:10:03+00:00</updated><id>http://mahout.apache.org//feed.xml</id><title
type="html">Apache Mahout</title><subtitle>Distributed Linear
Algebra</subtitle> [...]
<p><a href="mailto:[email protected]";>Subscribe</a> to the
Mahout User list to ask for details on joining.</p>
<h3 id="attendees">Attendees</h3>
diff --git a/quantum-computing-primer/03_qubits/index.html
b/quantum-computing-primer/03_qubits/index.html
index 2fde1a9ce..816ad5e63 100644
--- a/quantum-computing-primer/03_qubits/index.html
+++ b/quantum-computing-primer/03_qubits/index.html
@@ -224,50 +224,32 @@
\[|\psi\rangle = \alpha|0\rangle + \beta|1\rangle\]
-<table>
- <tbody>
- <tr>
- <td>where (\alpha) and (\beta) are complex numbers representing the
probability amplitudes of the qubit being in the (</td>
- <td>0\rangle) and (</td>
- <td>1\rangle) states, respectively. The probabilities of measuring the
qubit in either state are given by (</td>
- <td>\alpha</td>
- <td>^2) and (</td>
- <td>\beta</td>
- <td>^2), and they must satisfy the normalization condition:</td>
- </tr>
- </tbody>
-</table>
+<p>where $\alpha$ and $\beta$ are complex numbers representing the probability
+amplitudes of the qubit being in the $|0\rangle$ and $|1\rangle$ states,
+respectively. The probabilities of measuring the qubit in either state are
given
+by $|\alpha|^2$ and $|\beta|^2$, and they must satisfy the normalization
condition:</p>
\[|\alpha|^2 + |\beta|^2 = 1\]
<h2 id="32-representing-qubits">3.2 Representing Qubits</h2>
-<table>
- <tbody>
- <tr>
- <td>Qubits can be visualized using the <strong>Bloch sphere</strong>, a
geometric representation of the quantum state of a single qubit. The Bloch
sphere is a unit sphere where the north and south poles represent the (</td>
- <td>0\rangle) and (</td>
- <td>1\rangle) states, respectively. Any point on the surface of the
sphere represents a valid quantum state of the qubit.</td>
- </tr>
- </tbody>
-</table>
+<p>Qubits can be visualized using the <strong>Bloch sphere</strong>, a
geometric representation
+of the quantum state of a single qubit. The Bloch sphere is a unit sphere
where
+the north and south poles represent the $|0\rangle$ and $|1\rangle$ states,
+respectively. Any point on the surface of the sphere represents a valid
quantum
+state of the qubit.</p>
-<table>
- <tbody>
- <tr>
- <td>The state of a qubit can also be described using a <strong>state
vector</strong> in a two-dimensional complex vector space. For example, the
state (</td>
- <td>0\rangle) is represented as:</td>
- </tr>
- </tbody>
-</table>
+<p>The state of a qubit can also be described using a <strong>state
vector</strong> in a
+two-dimensional complex vector space. For example, the state $|0\rangle$ is
+represented as:</p>
\[|0\rangle = \begin{pmatrix} 1 \\ 0 \end{pmatrix}\]
<table>
<tbody>
<tr>
- <td>and the state (</td>
- <td>1\rangle) is represented as:</td>
+ <td>and the state $</td>
+ <td>1\rangle$ is represented as:</td>
</tr>
</tbody>
</table>
@@ -297,14 +279,9 @@
<h3 id="example-applying-a-hadamard-gate">Example: Applying a Hadamard
Gate</h3>
-<table>
- <tbody>
- <tr>
- <td>The Hadamard gate ((H)) is a fundamental quantum gate that puts a
qubit into a superposition state. Applying the Hadamard gate to a qubit
initially in the (</td>
- <td>0\rangle) state results in the state:</td>
- </tr>
- </tbody>
-</table>
+<p>The Hadamard gate ((H)) is a fundamental quantum gate that puts a qubit
into a
+superposition state. Applying the Hadamard gate to a qubit initially in the
+$|0\rangle$ state results in the state:</p>
\[H|0\rangle = \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)\]
@@ -318,15 +295,9 @@
<span class="nf">print</span><span class="p">(</span><span
class="n">result</span><span class="p">)</span>
</code></pre></div></div>
-<table>
- <tbody>
- <tr>
- <td>In this example, the Hadamard gate is applied to the qubit at index
0, and the circuit is executed to obtain the measurement results. The output
will show the probabilities of measuring the qubit in the (</td>
- <td>0\rangle) and (</td>
- <td>1\rangle) states.</td>
- </tr>
- </tbody>
-</table>
+<p>In this example, the Hadamard gate is applied to the qubit at index 0, and
the
+circuit is executed to obtain the measurement results. The output will show
the
+probabilities of measuring the qubit in the $|0\rangle$ and $|1\rangle$
states.</p>
<h3 id="visualizing-the-circuit">Visualizing the Circuit</h3>
diff --git a/quantum-computing-primer/04_quantum_gates/index.html
b/quantum-computing-primer/04_quantum_gates/index.html
index f10231572..b468c744c 100644
--- a/quantum-computing-primer/04_quantum_gates/index.html
+++ b/quantum-computing-primer/04_quantum_gates/index.html
@@ -250,29 +250,14 @@
<h2 id="42-multi-qubit-gates">4.2 Multi-Qubit Gates</h2>
-<p>Multi-qubit gates operate on two or more qubits, enabling entanglement and
more complex quantum operations. Some of the most common multi-qubit gates
include:</p>
+<p>Multi-qubit gates operate on two or more qubits, enabling entanglement and
more
+complex quantum operations. Some of the most common multi-qubit gates
include:</p>
<ul>
- <li>
- <table>
- <tbody>
- <tr>
- <td><strong>CNOT Gate (Controlled-NOT)</strong>: Flips the target
qubit if the control qubit is in the state</td>
- <td>1⟩.</td>
- </tr>
- </tbody>
- </table>
- </li>
- <li>
- <table>
- <tbody>
- <tr>
- <td><strong>Toffoli Gate (CCNOT)</strong>: A
controlled-controlled-NOT gate that flips the target qubit if both control
qubits are in the state</td>
- <td>1⟩.</td>
- </tr>
- </tbody>
- </table>
- </li>
+ <li><strong>CNOT Gate (Controlled-NOT)</strong>: Flips the target qubit if
the control qubit is
+in the state $|1\rangle$.</li>
+ <li><strong>Toffoli Gate (CCNOT)</strong>: A controlled-controlled-NOT gate
that flips the
+target qubit if both control qubits are in the state $|1\rangle$.</li>
<li><strong>SWAP Gate</strong>: Exchanges the states of two qubits.</li>
</ul>
diff --git a/quantum-computing-primer/07_quantum_algorithms/index.html
b/quantum-computing-primer/07_quantum_algorithms/index.html
index 55b6eee63..6fefae048 100644
--- a/quantum-computing-primer/07_quantum_algorithms/index.html
+++ b/quantum-computing-primer/07_quantum_algorithms/index.html
@@ -224,13 +224,20 @@
<h2 id="71-deutsch-jozsa-algorithm">7.1 Deutsch-Jozsa Algorithm</h2>
-<p>The Deutsch-Jozsa algorithm is one of the earliest quantum algorithms that
demonstrates the potential of quantum computing. It solves a specific problem
exponentially faster than any classical algorithm.</p>
+<p>The Deutsch-Jozsa algorithm is one of the earliest quantum algorithms that
+demonstrates the potential of quantum computing. It solves a specific problem
+exponentially faster than any classical algorithm.</p>
<h3 id="problem-statement">Problem Statement</h3>
-<p>Given a function ( f: {0,1}^n \rightarrow {0,1} ), determine whether the
function is <strong>constant</strong> (returns the same value for all inputs)
or <strong>balanced</strong> (returns 0 for half of the inputs and 1 for the
other half).</p>
+<p>Given a function $ f: {0,1}^n \rightarrow {0,1} $, determine whether the
+function is <strong>constant</strong> (returns the same value for all inputs)
or <strong>balanced</strong>
+(returns 0 for half of the inputs and 1 for the other half).</p>
<h3 id="quantum-solution">Quantum Solution</h3>
-<p>The Deutsch-Jozsa algorithm uses quantum parallelism to evaluate the
function over all possible inputs simultaneously. It requires only <strong>one
query</strong> to the function, whereas a classical algorithm would need (
2^{n-1} + 1 ) queries in the worst case.</p>
+<p>The Deutsch-Jozsa algorithm uses quantum parallelism to evaluate the
function
+over all possible inputs simultaneously. It requires only <strong>one
query</strong> to the
+function, whereas a classical algorithm would need $ 2^{n-1} + 1 $ queries in
+the worst case.</p>
<h3 id="implementation-with-qumat">Implementation with <code
class="language-plaintext highlighter-rouge">qumat</code></h3>
<p>Here’s how you can implement the Deutsch-Jozsa algorithm using <code
class="language-plaintext highlighter-rouge">qumat</code>:</p>
@@ -269,10 +276,12 @@
<h2 id="72-grovers-algorithm">7.2 Grover’s Algorithm</h2>
-<p>Grover’s algorithm is a quantum search algorithm that can search an
unsorted database of ( N ) items in ( O(\sqrt{N}) ) time, compared to ( O(N) )
for classical algorithms.</p>
+<p>Grover’s algorithm is a quantum search algorithm that can search an
unsorted
+database of $ N $ items in $ O(\sqrt{N}) $ time, compared to $ O(N) $ for
+classical algorithms.</p>
<h3 id="problem-statement-1">Problem Statement</h3>
-<p>Given an unsorted database of ( N ) items, find a specific item (marked by
an oracle) with as few queries as possible.</p>
+<p>Given an unsorted database of $ N $ items, find a specific item (marked by
an oracle) with as few queries as possible.</p>
<h3 id="quantum-solution-1">Quantum Solution</h3>
<p>Grover’s algorithm uses amplitude amplification to increase the probability
of measuring the marked item. It consists of two main steps:</p>
@@ -325,7 +334,16 @@
<h3 id="explanation-1">Explanation</h3>
<ul>
- <li>The oracle marks the desired state (e.g., <code
class="language-plaintext highlighter-rouge">|110></code>).</li>
+ <li>
+ <table>
+ <tbody>
+ <tr>
+ <td>The oracle marks the desired state (e.g., $</td>
+ <td>110\rangle$).</td>
+ </tr>
+ </tbody>
+ </table>
+ </li>
<li>The diffusion operator amplifies the probability of measuring the marked
state.</li>
<li>After running the algorithm, the marked state will have a higher
probability of being measured.</li>
</ul>
diff --git a/quantum-computing-primer/10_advanced_topics/index.html
b/quantum-computing-primer/10_advanced_topics/index.html
index 3fa8be313..8948f5fe2 100644
--- a/quantum-computing-primer/10_advanced_topics/index.html
+++ b/quantum-computing-primer/10_advanced_topics/index.html
@@ -237,11 +237,11 @@
<span class="c1"># Apply the Quantum Fourier Transform
</span><span class="k">def</span> <span class="nf">apply_qft</span><span
class="p">(</span><span class="n">qc</span><span class="p">,</span> <span
class="n">n_qubits</span><span class="p">):</span>
-<span class="k">for</span> <span class="n">qubit</span> <span
class="ow">in</span> <span class="nf">range</span><span class="p">(</span><span
class="n">n_qubits</span><span class="p">):</span>
-<span class="n">qc</span><span class="p">.</span><span
class="nf">apply_hadamard_gate</span><span class="p">(</span><span
class="n">qubit</span><span class="p">)</span>
-<span class="k">for</span> <span class="n">next_qubit</span> <span
class="ow">in</span> <span class="nf">range</span><span class="p">(</span><span
class="n">qubit</span> <span class="o">+</span> <span class="mi">1</span><span
class="p">,</span> <span class="n">n_qubits</span><span class="p">):</span>
-<span class="n">angle</span> <span class="o">=</span> <span
class="mi">2</span> <span class="o">*</span> <span class="mf">3.14159</span>
<span class="o">/</span> <span class="p">(</span><span class="mi">2</span>
<span class="o">**</span> <span class="p">(</span><span
class="n">next_qubit</span> <span class="o">-</span> <span
class="n">qubit</span> <span class="o">+</span> <span class="mi">1</span><span
class="p">))</span>
-<span class="n">qc</span><span class="p">.</span><span
class="nf">apply_cu_gate</span><span class="p">(</span><span
class="n">next_qubit</span><span class="p">,</span> <span
class="n">qubit</span><span class="p">,</span> <span
class="n">angle</span><span class="p">)</span>
+ <span class="k">for</span> <span class="n">qubit</span> <span
class="ow">in</span> <span class="nf">range</span><span class="p">(</span><span
class="n">n_qubits</span><span class="p">):</span>
+ <span class="n">qc</span><span class="p">.</span><span
class="nf">apply_hadamard_gate</span><span class="p">(</span><span
class="n">qubit</span><span class="p">)</span>
+ <span class="k">for</span> <span class="n">next_qubit</span> <span
class="ow">in</span> <span class="nf">range</span><span class="p">(</span><span
class="n">qubit</span> <span class="o">+</span> <span class="mi">1</span><span
class="p">,</span> <span class="n">n_qubits</span><span class="p">):</span>
+ <span class="n">angle</span> <span class="o">=</span> <span
class="mi">2</span> <span class="o">*</span> <span class="mf">3.14159</span>
<span class="o">/</span> <span class="p">(</span><span class="mi">2</span>
<span class="o">**</span> <span class="p">(</span><span
class="n">next_qubit</span> <span class="o">-</span> <span
class="n">qubit</span> <span class="o">+</span> <span class="mi">1</span><span
class="p">))</span>
+ <span class="n">qc</span><span class="p">.</span><span
class="nf">apply_cu_gate</span><span class="p">(</span><span
class="n">next_qubit</span><span class="p">,</span> <span
class="n">qubit</span><span class="p">,</span> <span
class="n">angle</span><span class="p">)</span>
<span class="nf">apply_qft</span><span class="p">(</span><span
class="n">qc</span><span class="p">,</span> <span class="mi">3</span><span
class="p">)</span>
@@ -267,11 +267,11 @@
<span class="c1"># Apply the Quantum Phase Estimation
</span><span class="k">def</span> <span class="nf">apply_qpe</span><span
class="p">(</span><span class="n">qc</span><span class="p">,</span> <span
class="n">n_qubits</span><span class="p">):</span>
-<span class="k">for</span> <span class="n">qubit</span> <span
class="ow">in</span> <span class="nf">range</span><span class="p">(</span><span
class="n">n_qubits</span><span class="p">):</span>
-<span class="n">qc</span><span class="p">.</span><span
class="nf">apply_hadamard_gate</span><span class="p">(</span><span
class="n">qubit</span><span class="p">)</span>
-<span class="c1"># Apply controlled unitary operations (simplified example)
-</span><span class="n">qc</span><span class="p">.</span><span
class="nf">apply_cu_gate</span><span class="p">(</span><span
class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span
class="p">,</span> <span class="mf">3.14159</span> <span class="o">/</span>
<span class="mi">2</span><span class="p">)</span>
-<span class="n">qc</span><span class="p">.</span><span
class="nf">apply_cu_gate</span><span class="p">(</span><span
class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span
class="p">,</span> <span class="mf">3.14159</span> <span class="o">/</span>
<span class="mi">4</span><span class="p">)</span>
+ <span class="k">for</span> <span class="n">qubit</span> <span
class="ow">in</span> <span class="nf">range</span><span class="p">(</span><span
class="n">n_qubits</span><span class="p">):</span>
+ <span class="n">qc</span><span class="p">.</span><span
class="nf">apply_hadamard_gate</span><span class="p">(</span><span
class="n">qubit</span><span class="p">)</span>
+ <span class="c1"># Apply controlled unitary operations (simplified
example)
+</span> <span class="n">qc</span><span class="p">.</span><span
class="nf">apply_cu_gate</span><span class="p">(</span><span
class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span
class="p">,</span> <span class="mf">3.14159</span> <span class="o">/</span>
<span class="mi">2</span><span class="p">)</span>
+ <span class="n">qc</span><span class="p">.</span><span
class="nf">apply_cu_gate</span><span class="p">(</span><span
class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span
class="p">,</span> <span class="mf">3.14159</span> <span class="o">/</span>
<span class="mi">4</span><span class="p">)</span>
<span class="c1"># Inverse QFT
</span><span class="nf">apply_qft</span><span class="p">(</span><span
class="n">qc</span><span class="p">,</span> <span
class="n">n_qubits</span><span class="p">)</span>
@@ -299,13 +299,13 @@
<span class="c1"># Apply the Quantum Annealing process
</span><span class="k">def</span> <span
class="nf">apply_quantum_annealing</span><span class="p">(</span><span
class="n">qc</span><span class="p">,</span> <span
class="n">n_qubits</span><span class="p">):</span>
-<span class="k">for</span> <span class="n">qubit</span> <span
class="ow">in</span> <span class="nf">range</span><span class="p">(</span><span
class="n">n_qubits</span><span class="p">):</span>
-<span class="n">qc</span><span class="p">.</span><span
class="nf">apply_hadamard_gate</span><span class="p">(</span><span
class="n">qubit</span><span class="p">)</span>
-<span class="c1"># Apply a simple Hamiltonian (simplified example)
-</span><span class="n">qc</span><span class="p">.</span><span
class="nf">apply_rx_gate</span><span class="p">(</span><span
class="mi">0</span><span class="p">,</span> <span class="mf">3.14159</span>
<span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
-<span class="n">qc</span><span class="p">.</span><span
class="nf">apply_ry_gate</span><span class="p">(</span><span
class="mi">1</span><span class="p">,</span> <span class="mf">3.14159</span>
<span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
-<span class="c1"># Measure the qubits
-</span><span class="n">qc</span><span class="p">.</span><span
class="nf">execute_circuit</span><span class="p">()</span>
+ <span class="k">for</span> <span class="n">qubit</span> <span
class="ow">in</span> <span class="nf">range</span><span class="p">(</span><span
class="n">n_qubits</span><span class="p">):</span>
+ <span class="n">qc</span><span class="p">.</span><span
class="nf">apply_hadamard_gate</span><span class="p">(</span><span
class="n">qubit</span><span class="p">)</span>
+ <span class="c1"># Apply a simple Hamiltonian (simplified example)
+</span> <span class="n">qc</span><span class="p">.</span><span
class="nf">apply_rx_gate</span><span class="p">(</span><span
class="mi">0</span><span class="p">,</span> <span class="mf">3.14159</span>
<span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
+ <span class="n">qc</span><span class="p">.</span><span
class="nf">apply_ry_gate</span><span class="p">(</span><span
class="mi">1</span><span class="p">,</span> <span class="mf">3.14159</span>
<span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
+ <span class="c1"># Measure the qubits
+</span> <span class="n">qc</span><span class="p">.</span><span
class="nf">execute_circuit</span><span class="p">()</span>
<span class="nf">apply_quantum_annealing</span><span class="p">(</span><span
class="n">qc</span><span class="p">,</span> <span class="mi">2</span><span
class="p">)</span>
