July 2020 Archive-draft

Writings

Blog post

• Representations: morphisms and induction functor

Research papers

• Quantum supremacy in driven quantum many-body systems, 2002.11946
• Expressibility and trainability of parameterized analog quantum systems for machine learning applications, 2005.11222
• Optimal verification of stabilizer states, 2007.09713

Research

• Epsilon-nets, unitary designs and random quantum circuits, Oszmaniec, Sawicki and Horodecki 2007.10885
  • Random walks in compact groups Varjú 2013
• Dual pairing of symmetry groups and dynamical groups in physics, Rowe, Carvalho and Repka 2012

Quantum computational supremacy

Continuing from the previous log, we examine more closely nuances about the quantum supremacy argument.

• Adaptive Quantum Computation, Constant Depth Quantum Circuits and Arthur-Merlin Games, Terhal and DiVincenzo 2004
• Simulating quantum computers with probabilistic methods, Nest 2011
• From estimation of quantum probabilities to simulation of quantum circuits, Pashayan, Bartlett and Gross 2020
  • $\epsilon$-simulation is operational

  • Poly-box is not enough for $\epsilon$-simulation

    Define a family of “obfustication” quantum circuits that output ${x\oplus \mathrm{Parity}({\bf{y}}),{\bf{y}}$ where ${\bf{y}} \in {0,1}^n$ is a uniformly random bit string and $x$ is the measurement outcome of the first qubit of a quantum circuit drawn from a universal set. This family of circuits can’t be classically simulated unless $\mathrm{BQP \subseteq BPP}$. However it admits a deterministic poly-box (with exponential precision!): for $\epsilon < 1/2^n$, compute the Born probability. For $\epsilon \ge 1/2^n$, just guess $1/2^{n+1}$. Computing the Born probability takes exponential time but that’s ok because the time is still inverse polynomial in $\epsilon$.

  • Supremacy circuits may admit poly-box

    $\mathcal{C}{\mathrm{Prod}}$ admits a poly-box: if $z=0$ (resp. $z=1$), sample from $\id$ and $+Z$ (resp. $-Z$) with equal probability. Evolve the sampled Pauli string back to the beginning of the circuit by Gottesman-Knill. The Born probability factorizes into a product of $n$ terms which can be calculated efficiently. \(\Pr\left[\bigotimes_{j=1}^{n} \rho_j \bigotimes_{j=1}^{n} P_j\right] = \prod_{j=1}^n \Pr(\rho_jP_j)\) However, $\mathcal{C}{\mathrm{Prod}}$ with adaptive measurement (or post-selection ) is universal therefore $\mathcal{C}_{\mathrm{Prod}}$ is believed to be hard to classically simulated.

• Quantum Supremacy and the Complexity of Random Circuit Sampling, Bouland, Fefferman, Nirkhe, and Vazirani 2018 [Nat Phys supplementary (pdf)]
• Cayley path and quantum computational supremacy: A proof of average-case #P−hardness of Random Circuit Sampling with quantified robustness, Movassagh 1909.06210
  • The Random Matrix Theory of the Classical Compact Groups, Elizabeth Mecke 2019

Given a #P-function $f:{0,1}^n\to{0,1}$. Define a GapP-function $f’:{0,1}^n \to {-1,1}$ and note that the value of the sum $\sum_{x\in{0,1}^n} f’(x)$ is in one-to-one correspondence to the value of $\sum_{x\in{0,1}^n} f(x)$. In particular, \(\begin{align} \sum_{x\in\{0,1\}^n} f(x) = \frac{1}{2}\left(\sum_{x\in\{0,1\}^n} f'(x) + 2^n\right). \end{align}\) Now append an ancilla bit and define a new GapP-function $g$ such that $g(x,0) = f’(x)$ and $g(x,1)$ takes on value +1 \(\begin{align} g(x,0) &= f'(x) \\ g(x,1) &= \begin{cases} +1\: \textrm{for $\alpha$ bitstrings}\\ -1\: \textrm{for $\beta$ bitstrings} \end{cases} \end{align}\) We have that \(\begin{align} \sum_{x\in\{0,1\}^n} g(x) = \sum_{x\in\{0,1\}^n} f'(x) + \alpha - \beta. \end{align}\) That is, the effect is to shift the sum of $f’(x)$ by an even number.

Classical simulation of boson sampling

• Classical boson sampling algorithms with superior performance to near-term experiments, Neville et al Nat Phys 2017 (Exactly calculate for fully distinguishable photons and then approximate. Previously with the punny title “No imminent quantum supremacy by boson sampling”.)
• The Classical Complexity of Boson Sampling, Clifford and Clifford 2018 (Exact algorithm by sample each photon, then sample conditioned on previous photons. Have to calculate only 2 permanents in the worst case!)
• Efficient algorithm for boson sampling with partially distinguishable photons, Renema et al PRL 2018 (Calculate $O(n^{2k})$ permanents of $k\times k$ matrices. Constant error in $n$ the number of photons. What is $k$?)
  • Sampling of partially distinguishable bosons and the relation to the multidimensional permanent, Tichy PRA 2015
  • Boson-sampling with photons of arbitrary spectral structure, Rhodes PRA 2015
• Classical simulation of photonic linear optics with lost particles, Oszmaniec and Brod NJP 2018
• Classical simulability of noisy boson sampling, Renema, Shchesnovich and García-Patrón 1809.01953

• Classical simulation of linear optics subject to nonuniform losses, Oszmaniec and Brod 1906.06696 (Generalizes Clifford and Clifford 2018 to allow $n$ photons in one mode. (1) The convex hull of the orbit of $\ket{n,0,\dots,0}$ (2) The convex hull of the orbit of $

  n-r,\underbrace{1,\dots,1}_{r},0,\dots,0\rangle$)

• Classically simulating near-term partially-distinguishable and lossy boson sampling, Moylett, García-Patrón, Renema and Turner QST 2020 (Combine Renema and Clifford. Calculate 2 permanents of $k\times k$ matrices. Exponential error in $n$.)
• Faster classical Boson sampling, Clifford and Clifford 2005.04214

Media

Musics

• Frequency analysis of Monogatari OST
• Chain, Back-On, Air Gear (OP)
• Winding Road, Man with a Mission, Golden Kamuy (OP)
• Chiisana Hibi, flumpool, Kakushigoto (OP)
• Megaman X arranges, Lenny Lederman
  • Armored Armadillo (X1) Setsuo Yamamoto [X1 OST credit]
  • Flame Stag (X2), Yuki Iwai
  • Opening stage / Blast Hornet (X3), Toshihiko Horiyama [X3 OST credit]
  • Neon Tiger / Toxic Seahorse (X3), Shusaku Uchiyama
  • Jakob orbital elevator (X8), Yuko Komiyama
• Pokemon Sword & Shield arranges, RichaadEB
  • Marnie theme (JP: Mary)
  • Gym leader battle
• Covers, Tokoyami Towa
  • brilliant / ERROR, niki
• Cover, Nekomata Okayu
  • Otome Kaibou, DECO*27

Touhou

• TOUHOU PIANO lullaby medley / 1hour, TAMUSIC
• Far-East El Dorado, Touhou Shinjutou ~ Hollow Song of Birds (fangame)
• Arranges, RichaadEB
  • Satori Maiden ~ 3rd Eye
  • Pierrot of the Star-Spangled Banner
  • Emotional Skyscraper ~ Cosmic Mind
  • Kobito of the Shining Needle ~ Little Princess, ft. YaboiMatoi
  • Entrusting This World to Idols ~ Idolatrize World (1:54!)

Hoshimachi Suisei

MV

• Next Color Planet (My current preference: NCP > Tenkyuu > Pieces > Comet)

• Hanamuke no Tori w/ Tokino Sora, THE IDOLM@STER: Million Live!
• Saga Jihen w/ Hololive Fantasy, Zombieland Saga

Karaoke

All karaoke songs are listed on Hoshiyomi Studio maintained by Kamaboko ¹.

• 2020-05-28 【歌枠】復活の歌祭！！【ホロライブ / 星街すいせい】
  • 43:30 Kane wo Narashite, Bonnie Pink, Tales of Vesperia
  • 52:44 Yume de aru You ni, DEEN, Tales of Destiny
• 2020-06-29 ショート歌枠🎶【ホロライブ / 星街すいせい】
  • 29:10 Hanamuke no Tori, THE IDOLM@STER: Million Live!
• 2020-07-24 【B限】B站出道一周年纪念歌回！ (bilibili)
  • 48:48 Platinum, Sakamoto Maya, Cardcaptor Sakura (OP3)
• 2020-07-21 【歌枠】【ホロライブ / 星街すいせい】
  • 07:02 Gurenge, LiSA, Kimetsu no Yaiba (OP)
  • 13:19 Namae no Nai Kaibutsu, EGOIST, Psycho-Pass (ED1)
  • 18:57 Kyouran Hey Kids!, The Oral Cigarettes, Noragami Aragoto (OP)
• 2020-08-04 ゲリラ！！！40万人突破するまで歌うのを止めるな！！！！🎶【ホロライブ / 星街すいせい】
  • 20:27 Karma, Bump of Chicken, Tales of the Abyss (I requested the song in this utawaku)
  • 33:38 Hikari, Utada Hikaru

Manga

• Vinland Saga, Vol. 15-22 (Chapter 101-161), Yukimura Makoto
• Tengoku Daimakyou, Ishiguro Masakazu

Anime

Pre-pandemic

• Zoku Owarimonogatari, Shaft {Nisio Isin} [Light novels] 2018
• Yuru Camp△ (12), C-Station {Afro} [Manga] 2018 (Notable episodes: 9,12; Notable moment: くぁwせdrftgyふじこlp)
• Serial Experiments Lain, Triangle Staff 1998 (Notable episodes: 5, 9-10) [TV Tropes shoutout] [reddit]
• Shouwa Genroku Rakugo Shinjuu, Studio DEEN {Haruko Kumota} [Manga] 2016
• Vinland Saga, Wit Studio {Makoto Yukimura} [Manga] 2019 (Notable episodes: 1-4 and 24 are movie quality. Episode 14 stands out in term of directing.)

Intra-pandemic AKA stuck at home with Netflix

• Violet Evergarden, Kyoto Animation {Kana Akatsuki} [Light novel] 2018 (Notable episode: 10)
• Psycho-Pass. Production I.G. (Urobuchi Gen) 2012-2013 (Notable episodes: 11,17)
• Yojouhan shinwa taikei (The Tatami Galaxy) , Madhouse (Masaaki Yuasa) {Tomihiko Morimi} [novel] 2010 (Notable episode: 11)
• Kobayashi-san chi no Maid Dragon, Kyoto Animation {Coolkyousinnjya} [Manga] 2017 (Notable episode 12)
• Eizouken ni wa te wo dasu na!, Science SARU (Masaaki Yuasa) {Sumito Ouwara} [Manga] 2020 (Notable episode: 7)
• Seishun buta yarou wa Bunny Girl senpai no yume wo minai, CloverWorks 2018 {Kamoshida Hajime} [Light novel] (Same author as Sakurasou; I’m not a fan of leaving arguably the most important plot point to a movie.)

1. Most older videos are not available due to the Great Hololive Purge. Check HoloTools for the recovery status, Playboard for information of missing videos. ↩