This is an archive of what I found useful, interesting, or simply enjoyable from March and April 2019.
Research
Stabilizer quantum mechanics
 Unbiased Simulation of NearClifford Quantum Circuits, Bennink et al. 2017
 Simulation of Qubit Quantum Circuits via Pauli Propagation, Rall, Liang, Cook and Kretschmer 1901.09070
Efficient classical simulation of Clifford circuits with nonstabilizer input states, Bu and Koh 1902.11257
Let \(\mathcal{C}_3\) be a circuit composed of gates from the third level of Clifford hierarchy.
Theorem 1. The output probabilities of a circuit \(\mathcal{C}_3\) on \(n+m\) qubits with input state \(\ketbra{0}{0}^{\otimes n} \otimes^m_{j=1} \rho_j\) and computational basis measurement can be approximated up to \(l_1\) norm \(\delta\) in \[(n+m)^{\mathcal{O}(1)} m^{\mathcal{O}\left[ \log \left( \sqrt{\alpha} /\delta \right)/\lambda \right]}.\] \(\lambda\) measures the mixedness of the most pure \(\rho_j\), namely the \(\lambda = \epsilon\) for every qubit state of the form \((1\epsilon)\ketbra{\psi}{\psi} + \epsilon\id/2\). The \(12/\alpha\) comes from using the Markov inequality on the average of the \(l_1\) norm of the Fourier coefficients of the output probabilities over the uniform distribution of Cliffords (a unitary 2design). Since qudit (\(d \ge 3\)) Cliffords also form a 2design, the latter technique should generalize. (The set of qubit Cliffords is not just a 2design but also a 3design.)
When every input state is pure, the exponent blows up. For that, we have
Theorem 2 The output probabilities of a circuit \(\mathcal{C}_3\) on \(n+m\) qubits with input state \(\ket{0}^{\otimes n} \otimes^m_{j=1} \ket{\psi_j}\) and computational basis measurement on \(k\) qubits, the number of of unmeasured qubits being greater than the log of the Pauli rank \[ n+mk \ge \sum^m_{j=1} \log \left( \frac{\chi(\psi_j)}{2} \right), \] can be approximated up to \(l_1\) norm \(\delta\) in \[ (n+m)^{\mathcal{O}(1)} m^{\mathcal{O}\left[ \log \left( \sqrt{\alpha} /\delta \right)/\mu \right]}, \] where now \[ \mu(\psi) := 2(1\max_{\phi \in \mathrm{stab}} \av{\phi\psi}^2). \] The fidelity to the closest stabilizer state is the stabilizer rank. Curiously, the more “stabilizerness” the worse the runtime!
The method is inspired by “Efficient classical simulation of noisy quantum computation” by Gao and Duan, and much like that paper, Bu and Koh’s paper is about averagecase difficulty. Notably Gao and Duan’s paper gives a classical simulation of a random quantum circuit with constant noise, seemingly contradicting the threshold theorem, but a faulttolerant circuit is hardly a random circuit.
Having talked to Kaifeng Bu, I should read his “Classical simulation of quantum circuits by half Gauss sums”. Interestingly, the paper also has something to say about the “Holant function”, related to perfect matchings on weighted graphs (“matchgate tensors”).
Representation theory
 Applications of commutative harmonic analysis, Sanders (Convolutions in analysis, random walks, combinatorics, and number theory)
 An introduction to Tannaka duality and quantum groups, Joyal and Street
Algebraic geometry
 Linear Algebraic Groups, Humphreys 1998
John Baez on Geometric quantization [Nautilus article on how algebraic geometry (“Hartshorne”), or rather algebraic topology finally clicked for him]
According to some school of thought, quantization is a process of taking a symplectic manifold \(M\) and turn it into a complex Hilbert space (and smooth functions–classical observables–to linear operators). But that is really just a “prequantization”. Baez points out. We need much more than that; we need a line bundle \(L\) over \(M\) and various structures (even if \(M\) is already Kähler) that make \(L\) compatible with the symplectic, complex, and Riemannian structure on \(M\). (This shows you how it works for 2spheres.)
The world is quantum so perhaps it makes little sense to expect that just the symplectic structure can take us all the way to the complex Hilbert space. Instead, Baez proposing, let us start with a complex projective variety \(\C P^n \subset \C^{n+1}\), then take the smallest subspace in \(V \subset \C^{n+1}\) whose projectivized space \(\mathbb{P}V\) contains \(M\) to be its quantization \(Q(M) = V\). Projectivization then gives back \(P(V) = M\). In this way, we have poset categories
Class
of classical state spaces andQuant
of quantum state spaces and a pair of adjoint functors between them. You can make them monoidal (essentially having the tensor product structure—Segre embedding for varieties) and clone the system with symmetrized product (Veronese embedding for varieties). The latter is actually how you take a classical limit of generalized coherent states (equivalently, scaling up the symplectic structure).
\(HV\)varieties
 On a class of quasihomogeneous affine varieties, Popov and Vinberg 1972 [English translation: Math USSR Izvestija 6 74358]
 Symmetry, Representations, and Invariants, Goodman and Wallach 2009 (Exercise 12.2.5.2)
 “\(HV\)varieties of small codimensions” in Tangents and Secants of Algebraic Varieties, Zak 1993
 On Spherical Double Cones, Littelmann 1994
 Complexity and rank of actions in invariant theory, Panyushev 1999
 Homogeneous Spaces and Equivalent Embeddings, Timashev 2011
Linear programming
Why are optimization problems called “programs”?, MO
The military refer to their various plans or proposed schedules of training, logistical supply and deployment of combat units as a program. When I first analyzed the Air Force planning problem and saw that it could be formulated as a system of linear inequalities, I called my paper Programming in a Linear Structure. Note that the term ‘program’ was used for linear programs long before it was used as the set of instructions used by a computer. In the early days, these instructions were called codes.
 Eigenvalue optimization [paywalled], Lewis and Overton 1996
 Minimizing the largest eigenvalue (minimizing the \(l_{\infty}\)norm) can be written as a linear program.
 Finding the sparsest solution (minimizing the \(l_0\)“norm”) is NPhard. The standard trick is to instead optimize for the \(l_1\)norm. But for the problem I’m concerning, I’m optimizing over probability vectors so that is out of the question.
 Mathematical Programming Methods for Minimizing the Zeronorm over Polyhedral Sets, Francesco Rinaldi, University of Rome thesis
 The example pages for
cvxpy
has a code for the iterative logarithm heuristic to find a sparse solution. ^{1}
Media
Links

his wish to overcome gravity dated from the childhood drowning of his sister. “She was unable to fight gravity, which came up and seized her like a dragon and brought her to the bottom,” he wrote.
 Dopamine: fast and slow (Fast spike or inhibition of dopamine signals the (emotionally positive or negative) error between prediction and reality, not reward. Slow dopamine is for wanting, motivation to work, not happiness.)
The Scientists Who Make Apps Addictive (B.J. Fogg’s students went on to found Instagram and write books like Hooked: How to Build HabitForming Products.)
“I look at some of my former students and I wonder if they’re really trying to make the world better, or just make money,” said Fogg. “What I always wanted to do was unenslave people from technology.”
Harris was Mike Krieger’s collaborator on Send the Sunshine in Fogg’s class of 2006. Like Krieger, Harris went on to create a realworld app, Apture, which was designed to give instant explanations of complex concepts to online readers […] Harris believed in his mission to explain, yet he could not persuade publishers that incorporating his app would lead to people spending more time on their sites. He came to believe that the internet’s potential to inform and enlighten was at loggerheads with the commercial imperative to seize and hold the attention of users by any means possible.
After working for Google for a year or so, Harris resigned […] Before leaving, he gave a farewell presentation to Google’s staff in which he argued that they needed to see themselves as moral stewards of the attention of billions of people. Unexpectedly, the slides from his talk became a viral hit inside the company, travelling all the way to the boardroom. Harris was persuaded to stay on and pursue his research at Google, which created a new job title for him: design ethicist and product philosopher. After a while, Harris realised that although his colleagues were listening politely, they would never take his message seriously without pressure from the outside. He left Google for good earlier this year […]
 Human Contact is Now a Luxury Good, NY Times
 The bad PowerPoint slide that contributes to the Space Shuttle Columbia disaster
 If you think you’re in a bad place, your life could be worse if you are Facebook moderators
 What happened to 90s environmentalism?, SSC (Do environmental problems fall out of public consciousness because they have been solved successfully or because they were just a fad all along?)
 Insect biomass declines by 75% [SA] [NYT] [HuffPost] [Guardian] (Not sure what to conclude from all these.)
 Kimura & Crow: Infinite Alleles (Wanting to “do something in genetics like what the theoretical physicists were doing in physics,” Kimura ended up writing a heat equation obeyed by neutrallyevolved genes.)
 Why should we care about neutral evolution? (Neutral evolution provides a “null hypothesis”, the background noise to be compared and subtracted to get the signal.)
 An estimate of how much of the human genome undergoes neutral selection, Quanta (<5% and not all neutral alleles evolve following Kimura’s theory, for example, those that are transmitted through physical mechanism such as linkage.)
 Natural selection on weighted graphs, Quanta
 The grandmother hypothesis, Quanta
 Mutations render a woman unable to feel pain or anxiety. The mutations shut down the gene controlling FAAH which breaks down anandamide, a natural cannabislike substance.
 Karen Uhlenback is the first woman to win the Abel Prize. (Uhlenback of the OrnsteinUhlenback process is her fatherinlaw.)
 The 1993 article, The Death of Proof doesn’t age well, and the author knows it: [The Horgan Surface and the Death of Proof] [Okay, Maybe Proofs Aren’t Dying After All]
 Corn production is estimated to account for 4,300 premature deaths related to air pollution in the US per year. Ammonia from fertilizer application was by far the largest contributor to corn’s air pollution footprint. 86% of PM2.5 emissions happen on farm
 The 2019 Winter smog in Thailand seems to correlate most with fire from as far as 720 km away (Myanmar, Laos and Cambodia)
The Day the Dinosaurs Died, New Yorker
One day sixtysix million years ago, life on Earth almost came to a shattering end. The world that emerged after the impact was a much simpler place. When sunlight finally broke through the haze, it illuminated a hellish landscape. The oceans were empty. The land was covered with drifting ash. The forests were charred stumps. The cold gave way to extreme heat as a greenhouse effect kicked in. Life mostly consisted of mats of algae and growths of fungus: for years after the impact, the Earth was covered with little other than ferns. Furtive, ratlike mammals lived in the gloomy understory. But eventually life emerged and blossomed again, in new forms.
tl;dr version:
“3 metre problem”: almost no dinosaur remains have before been found 3 metres below the socalled “KT boundary”, a layer of sediment that preserves the asteroid’s debris and ash from the extinction event.
In the 70’s, Walter (geologist) and Luis Alvarez (nuclear physicist) discovered a KT layer laced with iridium, conjectured to be from the asteroid impact. The impact crater (named Chicxulub) was found in 1991. The debate was considered largely settled in 2010 (wow!) that the asteroid caused the extinction.
The new paper is a result from the discovery dated back to 2012 by a grad student Robert DePalma of the KT site “Tanis” (a RaidersoftheLostArk reference) at Hell Creek in North Dakota. Among the things found are preserved microtektites, a sort of glass beads or spindles that formed from molten rock ejected during the impact and solidified while reentering the atmosphere. This suggests that the site recorded the first hours or so of the extinction event.
Geophysics problem: there was not enough time for the flood that would preserve the microtektites to reach the site from the source of impact. They conjectured that the flood was caused by seiches that can happen far away from the source, and estimated the time all kinds of different seismic waves would arrive at the site to cause such seiches (6, 10, and 13 minutes).
 Skepticism greet fossils claimed to record dinosaurkilling asteroid impact, ScienceMag
 Tax preparation companies lobby Congress to ban IRS from creating their own free tax preparation software.
 Weighted average of opinions based on prediction track records is at least as accurate as prediction markets (n=535)
Anime
 A documentary on the CGI animation industry (1/n)
Physics/quantum/machine learning
 Chameleons change their colors by adjusting the osmotic pressure to change the spacing of Guanine crystals in a lattice. See also animal reflectors.
 Das Sarma on how the scale of unifications in the present day physics is not so grand anymore, Physics Today
 The 2016 Nobel laureate David Thouless passes away at 84.
 Advanced LIGO+ will have frequencydependent squeezing. (“LIGO is already able to spot black holes billions of parsecs away. By 2022, it should detect about one such event per day, and the subsequent ALIGO+ upgrade should push that to one event every few hours.”)
What It Took to Capture a Black Hole, Physics Todays
the team was able to resolve superheated plasma streaking just outside the photon orbit radius, the distance from the center of a black hole at which any inwardmoving photon no longer has a chance to escape (as opposed to the event horizon, where nothing, regardless of its motion, can escape).
The data were from the observing runs all in April 2017. The research team dedicated to imaging was divided into four groups, crunching the data in four different ways. The final image is essential a composite of the four group images “update with higherquality data”.
The next observing run in Spring next year should give us the spin of M87*. Meanwhile, the data that we have from observing Sagittarius A*, the black hole at the center of our galaxy, should already be enough to create a similar image. The only things required are “further advances in computational analysis” due to time variation.
 How Katie Bouman Accidentally Became the Face of the Black Hole Project, NY Times
 Alán AspuruGuzik now has a quantum computing startup Zapata Computing. (He left Harvard for Toronto last year.)
 Michael Nielsen’s spacedrepetition based pedagogical article on Grover’s search algorithm
 Machine learning in manybody quantum physics and quantum ML algorithms, recommended.
 Machine learning and the physical sciences 1903.10563 (review article)
 Geoffrey Hinton, Yann LeCun and Yoshua Bengio won the Turing Award.
 The Book of Why, Pearl and Mackenzie 2018 [A critical review on Goodreads]
Meditation
 Meditation as predictive processing, a comment on Meditative States as Mental Feedback Loops, SSC
 An approach through the lookingglass, Hershberger 1986
 The Neuroscience of Meditation: Four Models (Buddhism, Predictive coding (“freeenergy principle”), Connectomespecific harmonic waves, Neural annealing)
 Sequence introduction: nonagent and multiagent models of mind
Musics
 Great covers of almost every Mega Man X5 and X6 theme by Lenny Lederman
Touhou
 2+1 hours of Touhou trance remixes by D514
 邪な炎 (Solar Sect of Mystic Wisdom ~ Nuclear Fusion), Abyss (C95), BUTAOTOME
 TickTock Anthology (Kid’s Festival ~ Innocent Treasures & Gensokyo The Gods Loved), Baby Little City (C90), Fuling Cat Mark (Genre: ShibuyaKei)
Manga
 Kimetsu no Yaiba (Chapter 20  58), Gotouge Koyoharu (One of the manga recommended by Togashi Yoshihiro, the other two being Gunjou no Magmel and EXARM
Anime
 Hyouka (22 Episodes), Kyoto Animation {Honezawa Yonobu} [Novel] 2012 (Notable episodes: 17, 21)
 Mob Psycho 100 II (13 Episodes), Bones {ONE} [Webmanga] 2019
 Bakemonogatari (15 Episodes), Shaft {Nisio Isin} [Light novels] 2009, 2010 (Rewatch)
Video games
Touhou Luna Nights, Team Ladybug
Pros: Great pixel art and attentions to details. A number of objects interacts with time manipulation. (Yes, you play as Sakuya.) The water physics is especially cool. Cons: Snail Time and the grace mechanics makes the game really easy, in addition to the short length and the map not sprawling enough for a Metroidvania, which reminds me that I haven’t finished RabiRibi. That one has a wondrous, sprawling map (and in a sense a funny comparison because it is a bullet hell game while Luna Nights is not.)
cvxpy
needs Microsoft Visual C++ 14.0. Go and download Visual Studio 2019 (16.0) (Community). Open the installer and check “Desktop Development with C++”. To be safe, also upgrade thesetuptools
withpip install upgrade setuptools
↩