Algorithmic Assertions - Craig Gidney's Computer Science BlogA blog about computer science, software engineering, quantum computing, mathematical puzzles, and so forth.
http://algassert.com
Reversible Computation isn't Free<p><a href="https://en.wikipedia.org/wiki/Landauer%27s_principle">Landauer's principle</a> puts a lower limit on the cost of irreversible computations. Basically: clearing a bit requires a minimum amount of energy (that depends on the ambient temperature), so a computation must consume an amount of energy proportional to how many bits it clears. (The energy efficiency of current...Sun, 23 Jul 2017 13:10:20 -0700
http://algassert.com/post/1714
http://algassert.com/post/1714Impractical Experiments #4: High Powered Phase Estimation<p>In <a href="/post/1710">a previous post</a>, I explained how using quantum phase estimation on an operation can provide a mechanism for applying fractional powers of that operation. The basic idea being that the register containing the phase estimation acts as an index into the eigenspaces of the operation, allowing you phase...Sun, 09 Jul 2017 13:10:20 -0700
http://algassert.com/post/1713
http://algassert.com/post/1713My First Paper: Dirty Period Finding<p>A couple years ago, I was stuck on a question from <a href="https://www.amazon.com/Quantum-Computation-Information-10th-Anniversary/dp/1107002176">Mike & Ike</a>. This was partially because I knew nothing about how to make circuits, and partially because as soon as I had the question figured out I made it harder:</p> <p><img style="max-width:100%; border:1px solid gray; padding: 5px;"...Wed, 28 Jun 2017 13:10:10 -0700
http://algassert.com/post/1712
http://algassert.com/post/1712[Meta] Who Owns Quirk?<p>When I first started making Quirk, the toy drag-and-drop quantum circuit simulator at <a href="http://algassert.com/quirk">algassert.com/quirk</a>, it was clearly separate from my day job at Google. After I joined the quantum computing team, that separation wasn't so obvious. So I decided it was worth going through the internal process to get...Sun, 18 Jun 2017 13:10:10 -0700
http://algassert.com/post/1711
http://algassert.com/post/1711Computing Fractional Fourier Transforms<p>Recently, I was side-tracked by a stumble into the <a href="https://en.wikipedia.org/wiki/Fractional_Fourier_transform">Wikipedia article on fractional Fourier transforms</a>. I found it interesting, because normally I think of the Fourier transform as an all-or-nothing proposition. I'm either thinking in the frequency domain or in the time domain, not some combination both. What would...Sun, 11 Jun 2017 12:11:11 -0700
http://algassert.com/post/1710
http://algassert.com/post/1710Simple Algorithm for Multiplicative Inverses mod 2ⁿ<p>Lately, as part of writing a paper, I've been thinking about quantum circuits for doing multiplication while using very little workspace. Surprisingly, this stumbled me into a nice way to compute multiplicative-inverses.</p> <p>Consider that multiplying by 3 is equivalent to adding a register into itself, left-shifted:</p> <div class="highlight"><pre><code class="language-python" data-lang="python"><span></span><span...Tue, 06 Jun 2017 10:10:10 -0700
http://algassert.com/post/1709
http://algassert.com/post/1709Efficient Controlled Phase Gradients<p>The phase gradient is a useful, but under-appreciated, quantum operation. When you apply a phase gradient to a register, each computational basis state $|k\rangle$ is phased by an amount proportional to $k$:</p> <p>$$\text{Grad}^t = \sum_{k=0}^{N-1} |k\rangle \langle k| \exp(i \tau t k / N)$$</p> <p>Phase gradients are the frequency-space equivalent...Wed, 24 May 2017 10:10:10 -0700
http://algassert.com/post/1708
http://algassert.com/post/1708Quirk v2.0 - Bowing to Convention<p>Last week I released version 2.0 of my <a href="https://github.com/Strilanc/Quirk">open-source</a> drag-and-drop <a href="/quirk">quantum circuit simulator Quirk</a>.</p> <p><a href="/quirk"><img style="max-width:100%;" src="/assets/2017-05-02-quirk-v2/empty-circuit-full-ui.png"/></a></p> <p>In this post, in addition to the breaking changes that prompted bumping the major version, I want to talk about events and improvements in the year since the <a href="/2016/05/22/quirk.html">previous...Tue, 02 May 2017 13:10:10 -0700
http://algassert.com/post/1707
http://algassert.com/post/1707Thinking of Operations as Controls<p>Controlled operations are a core part of quantum computation. Not <em>strictly</em> necessary, since any two-qubit gate tends to be sufficient for universal quantum computation, but certainly common.</p> <p>For example, the core of both Grover's and Shor's algorithms are defined by controlled operations. Shor's algorithm uses controlled multiplication operations as part...Sun, 09 Apr 2017 13:10:10 -0700
http://algassert.com/post/1706
http://algassert.com/post/1706Difficulty of Classical Control<p>Historically speaking, I think it's fair to say that quantum computing papers have often assumed that, when it comes to conditionally applying an operation, it's better for the conditionion to be classical. It makes intuitive sense, after all. Instead of having to do some complicated multi-qubit interaction, you just either...Sun, 02 Apr 2017 13:10:10 -0700
http://algassert.com/post/1705
http://algassert.com/post/1705