Exploring Quantum Computing: From Essential Mathematical Equations to Python Scripts and…
<p>We’re back to explore more of the quantum computing world, and guess what? Math is still our best buddy on this journey. In Part 1, we familiarized with complex numbers, matrix math, and even did some fun with Python. Now, in Part 2, we’re going deeper into quantum computing.</p>
<p><strong>TL;DR:</strong></p>
<p><strong>In this chapter I will only cover:</strong></p>
<p><strong>- Eigenvectors and Eigenvalues<br />
- Traces<br />
- Inner and Outer Products<br />
- Norm and Unit Vectors<br />
- Orthogonality<br />
- Adjoint<br />
- Tensor and Kronecker Products</strong></p>
<p>So, in this part of our quantum adventure, we are not just visualizing vectors with python, we will create computations with the help of the <code>NumPy</code> library which will guide us to a better understanding of Quantum Computing.</p>
<p>Lets clear out in the beginning, what is the difference between row and column vectors by introducing two types of vectors:<br />
The row vector has dimensions <code>1×n</code> and looks like the following:</p>
<p><img alt="" src="https://miro.medium.com/v2/resize:fit:522/1*YikX9HuW8sbOAk4oTOzYjQ.png" style="height:83px; width:580px" /></p>
<p>Figure [2]: row vector</p>
<p>The column vector has dimensions <code>m×1</code> and looks like the following:</p>
<p><img alt="" src="https://miro.medium.com/v2/resize:fit:522/1*hJ39k_n1buz-lF8zjNO4lA.png" style="height:137px; width:580px" /></p>
<p>Figure [3]: column vector</p>
<p>Quantum mechanics usually favors the column vector representation. The actual orientation is arbitrary for representing the actual values contained but for certain operations it becomes something one must be aware of as will be explained later.</p>
<p><a href="https://medium.com/@marcell.ujlaki/exploring-quantum-computing-from-essential-mathematical-equations-to-python-scripts-and-821008019cb7">Read More</a></p>