Algorithmic Assertions - Craig Gidney's Computer Science BlogA blog about computer science, software engineering, quantum computing, mathematical puzzles, and so forth.
http://algassert.com
Why care about circuit width?<p>I've been thinking about circuit constructions lately, and the question occurred to me: if circuit $A$ uses $O(N)$ gates and circuit $B$ uses $O(N^2)$ gates, but in parallel and with a better constant factor so that $B$'s depth is a bit better than $A$'s, would you ever use $A$ instead...Mon, 13 Mar 2017 01:10:10 -0400
http://algassert.com/post/1704
http://algassert.com/post/1704Bugs from the Future: Hadamard Coins and Implicit Measurement<p>Suppose it's fifty years from now, and everyone considers manipulating quantum information to be routine. You're new to the quantum programming profession, still trying stuff out, and you've come up with (well, rediscovered) a <em>clever idea</em> for generating random data.</p> <p>You call it the Hadamard coin. You'll use the fact...Sat, 04 Mar 2017 00:10:10 -0500
http://algassert.com/post/1703
http://algassert.com/post/1703[Meta] Joining Google's Quantum AI Team<p>I have really exciting news. This month I'm moving from New York to Santa Barbara, to become part of the <a href="https://research.google.com/pubs/QuantumAI.html">quantum ai team at Google</a>!</p> <p>If you've been following news or <a href="https://www.youtube.com/watch?v=kgMWommXxU8">talks</a> about quantum stuff at Google, then you already know why I'm excited. I don't know if...Wed, 01 Mar 2017 00:10:10 -0500
http://algassert.com/post/1702
http://algassert.com/post/1702Trouble Adding Constants into Qubit Registers<p>I had a bit of a surprise this week. Despite never publishing a paper, I've been cited in one! The preprint <a href="https://arxiv.org/abs/1611.07995">"Factoring using 2n+2 qubits with Toffoli based modular multiplication"</a>, by HÃ¤ner et al., cited <a href="http://cs.stackexchange.com/a/44292/535">this answer on cs.stackexchange</a>. The answer is me summarizing a few of the...Sun, 26 Feb 2017 00:10:10 -0500
http://algassert.com/post/1701
http://algassert.com/post/1701Quantum Bomb Detector Detectors<p>The <a href="https://en.wikipedia.org/wiki/Elitzur%E2%80%93Vaidman_bomb_tester">Elitzur-Vaidman bomb tester</a> is one of the funnest quantum devices to teach people about. It uses the <a href="https://en.wikipedia.org/wiki/Quantum_Zeno_effect">quantum Zeno effect</a> to safely separate dud bombs from live bombs, even when the only way to "test" a bomb is by triggering it! The main caveat is that the...Sat, 11 Feb 2017 00:10:10 -0500
http://algassert.com/post/1700
http://algassert.com/post/1700Quantum Data Locking vs Recognizable Data<p>Quantum information theory differs from classical information theory in many interesting ways. The ability to perform "data locking", where the amount of classical information that you have access to can go up dramatically as you receive clarifying information, is one of those differences.</p> <p>The <a href="https://arxiv.org/abs/quant-ph/0303088">original quantum data locking paper,...Sun, 18 Dec 2016 00:10:10 -0500
http://algassert.com/post/1632
http://algassert.com/post/1632Turning Detection into Correction with Quantum Teleportation<p>Suppose we were in a world with good quantum computers, but not-so-good quantum networks. Where qubits lived long malleable lives in the cool safety of dilution refrigerators, interspersed with torrid journeys through noisy fiber optic cable.</p> <p>In that world, what kinds of strategies would be used to make sending qubits...Mon, 12 Dec 2016 00:10:10 -0500
http://algassert.com/post/1631
http://algassert.com/post/1631Improper Priors<p>Here is the basic process for Bayesian reasoning:</p> <ol> <li><p>Start with a <a href="https://en.wikipedia.org/wiki/Prior_probability">prior</a>. A probability distribution over hypothesis space that represents your starting beliefs.</p></li> <li><p>Make an observation $B$.</p></li> <li><p>Scale the prior pointwise by each hypothesis' predicted probability of $B$.</p></li> <li><p>Normalize the prior so it adds up to 100%. This...Sun, 04 Dec 2016 00:10:10 -0500
http://algassert.com/post/1630
http://algassert.com/post/1630Bra-Ket Notation Trivializes Matrix Multiplication<p>One of the first things you notice, when learning quantum things, is people surrounding all their symbols with a strange angular notation. Instead of writing "let $a$ be the state", they keep writing "let $|a\rangle$ be the state". And the natural reaction is: "Why do they do that? It seems...Sun, 27 Nov 2016 00:10:10 -0500
http://algassert.com/post/1629
http://algassert.com/post/1629From Swapping to Teleporting with Simple Circuit Moves<p>There are many ways to prove that a quantum circuit does what you say it does. In this post, we're going to do that kind of proof in a somewhat unusual way.</p> <p>We're going to prove that quantum teleportation works. Not by carefully considering how it affects input states, but...Sun, 20 Nov 2016 00:10:10 -0500
http://algassert.com/post/1628
http://algassert.com/post/1628