Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
PLDI '21論文読み会: Quantum Abstract Interpretation
Search
Idein
June 08, 2022
Research
0
1.5k
PLDI '21論文読み会: Quantum Abstract Interpretation
Idein
June 08, 2022
Tweet
Share
More Decks by Idein
See All by Idein
PLDI '21論文読み会: DNNFusion: Accelerating Deep Neural Networks Execution with Advanced Operator Fusion
ideininc
1
1.8k
PLDI '21論文読み会: AKG: Automatic Kernel Generation for Neural Processing Units using Polyhedral Transformations
ideininc
0
1.6k
PLDI '21論文読み会: Specification Synthesis with Constrainted Horn Clauses
ideininc
0
1.5k
PLDI '21論文読み会: Cyclic Program Synthesis
ideininc
0
1.5k
PLDI '21論文読み会: High Performance Correctly Rounded Math Libraries for 32-bit Floating Point Representations
ideininc
0
1.5k
PLDI '21論文読み会: Provable Repair of Deep Neural Networks
ideininc
2
1.7k
会社紹介資料/Idein株式会社
ideininc
0
41k
Other Decks in Research
See All in Research
生成的推薦の人気バイアスの分析:暗記の観点から / JSAI2025
upura
0
200
Mechanistic Interpretability:解釈可能性研究の新たな潮流
koshiro_aoki
1
310
SSII2025 [SS1] レンズレスカメラ
ssii
PRO
2
980
時系列データに対する解釈可能な 決定木クラスタリング
mickey_kubo
2
740
LLM-as-a-Judge: 文章をLLMで評価する@教育機関DXシンポ
k141303
3
830
90 分で学ぶ P 対 NP 問題
e869120
18
7.6k
ノンパラメトリック分布表現を用いた位置尤度場周辺化によるRTK-GNSSの整数アンビギュイティ推定
aoki_nosse
0
320
研究テーマのデザインと研究遂行の方法論
hisashiishihara
5
1.4k
CSP: Self-Supervised Contrastive Spatial Pre-Training for Geospatial-Visual Representations
satai
3
220
利用シーンを意識した推薦システム〜SpotifyとAmazonの事例から〜
kuri8ive
1
210
RapidPen: AIエージェントによるペネトレーションテスト 初期侵入全自動化の研究
laysakura
0
1.6k
rtrec@dbem6
myui
6
880
Featured
See All Featured
Embracing the Ebb and Flow
colly
86
4.7k
Faster Mobile Websites
deanohume
307
31k
The Power of CSS Pseudo Elements
geoffreycrofte
77
5.9k
Imperfection Machines: The Place of Print at Facebook
scottboms
267
13k
Build The Right Thing And Hit Your Dates
maggiecrowley
36
2.8k
What’s in a name? Adding method to the madness
productmarketing
PRO
23
3.5k
Improving Core Web Vitals using Speculation Rules API
sergeychernyshev
18
970
The Straight Up "How To Draw Better" Workshop
denniskardys
234
140k
RailsConf & Balkan Ruby 2019: The Past, Present, and Future of Rails at GitHub
eileencodes
138
34k
The Success of Rails: Ensuring Growth for the Next 100 Years
eileencodes
45
7.5k
A Tale of Four Properties
chriscoyier
160
23k
Building Adaptive Systems
keathley
43
2.7k
Transcript
தଜߊҰ 2VBOUVN"CTUSBDU*OUFSQSFUBUJPO 1-%*จಡΈձBU*EFJO
ಡΜͩจ w 2VBOUVN"CTUSBDU*OUFSQSFUBUJPO w ྔࢠϓϩάϥϜͷநղऍख๏ΛఏҊ͢Δจ /FOHLVO:VBOE+FOT1BMTCFSH2VBOUVNBCTUSBDUJOUFSQSFUBUJPO *O1SPDFFEJOHTPGUIFOE"$.4*(1-"/*OUFSOBUJPOBM$POGFSFODFPO1SPHSBNNJOH -BOHVBHF%FTJHOBOE*NQMFNFOUBUJPO 1-%*
"TTPDJBUJPOGPS$PNQVUJOH.BDIJOFSZ /FX:PSL /: 64" r %0*IUUQTEPJPSH
ΞδΣϯμ w நղऍͱ w ྔࢠܭࢉͱ w ຊจͷհ
w ϓϩάϥϜͷ੩తղੳͷϑϨʔϜϫʔΫͷҰͭ w ϓϩάϥϜΛԿΒ͔ͷநྖҬ BCTUSBDUEPNBJO ͷ্Ͱ࣮ߦ w நྖҬଋ MBUUJDF ͱͯ͠දݱ͞ΕΔ
நղऍ "CTUSBDU*OQUFSQSFUBUJPO \Y Z^ [Y Z \Y Z [^ நత ۩ମత
ྔࢠϏοτ 2VBOUVN#JU 2CJU w RVCJUೋ͕ͷෳૉͭͰදݱ w ͜ͷRVCJUΛ؍ଌ͢Δͱɺ֬ Ͱঢ়ଶ ɺ֬ Ͱঢ়ଶ
͕ಘΒΕΔ |α2 | |0⟩ |β2 | |1⟩ α|0⟩ + β|1⟩ = (α, β)T (α2 + β2 = 1) |0⟩ = (1,0)T, |1⟩ = (0,1)T
༧උࣝϒϥͱέοτ w Λέοτ LFU ϕΫτϧͱݺͿɻ w ͜ΕͷਵΛϒϥ CSB ϕΫτϧͱݺͼ ͱॻ͘
w ௨ৗͷੵʹͳΔ |ψ⟩ ⟨ψ| ⟨ψ|ϕ⟩ |ψ⟩ = ( α β), ⟨ψ| = (α* β*)
ྔࢠϏοτ 2VBOUVN#JU 2CJU w RVCJUෳૉ ݸͰද͞ΕΔ n 2n α|00⟩ +
β|01⟩ + γ|10⟩ + δ|11⟩ (α2 + β2 + γ2 + δ2 = 1) ྫRCJUঢ়ଶͷॏͶ߹Θͤ
ิෳ2VCJUͷܭࢉ |ϕ, ψ⟩ > = |ϕ⟩ ⊗ |ψ⟩ = (
α β) ⊗ ( γ δ) = αγ αδ βγ βδ
ྔࢠήʔτ 2VBOUVN-PHJD(BUF w ྔࢠϏοτͷঢ়ଶΛม͑Δૢ࡞ XJLJQFEJB2VBOUVNMPHJDHBUFΑΓҾ༻ |ψ⟩ |ψ′  ⟩
ྔࢠήʔτ 2VBOUVN-PHJD(BUF w ྔࢠϏοτͷঢ়ଶΛม͑Δૢ࡞ w ྫ)BEBNBSE(BUF XJLJQFEJB2VBOUVNMPHJDHBUFΑΓҾ༻ |0⟩ 1 2
|0⟩ + 1 2 |1⟩ H
ྔࢠճ࿏ 2VBOUVN$JSDVJU w ྔࢠήʔτΛΈ߹Θͤͯɺճ࿏Λߏͨ͠ͷ w ճ࿏Λతؒతʹදݱ͢Δͷ͕ྔࢠϓϩάϥϜ w ֤ԋࢉճ࿏શମϢχλϦߦྻ 6OJUBSZ.BUSJY
Λຬͨ͢ ͱͯ͠දݱ͞ΕΔ UU† = U†U = I U |ψ′  ⟩ = U|ψ⟩
ຊจͷऔΓΉ՝ w ྔࢠϓϩάϥϜͷ੩తղੳΛ͍ͨ͠ʂ w RVCJUΛදݱ͢Δͷʹ ݸͷෳૉ͕ඞཁɻετϨʔδɾԋࢉྔڞʹେɻ n 2n ܭࢉ݁ՌͲͷΑ͏ͳ ঢ়ଶϕΫτϧ
ࢀߟຊ࣌Ͱͷ ଟ ੈք࠷େͷྔࢠίϯϐϡʔλͷن w (PPHMFͷ#SJTUMFDPOF RVCJU w ݹయܭࢉػͰγϛϡϨʔτ͢Δʹ w
ঢ়ଶ ݸͷෳૉͰදݱ w ແཧͰ͢ 4.7 × 1021
ຊจͷߩݙ w ྔࢠϓϩάϥϜʹର͢Δநղऍख๏ΛఏҊ w RVCJUʹରͯ͠ଟ߲ࣜ࣌ؒͰ࣮ߦՄೳͰ͋Δ
ཧղ͢Δ্ͰͷϙΠϯτ w நྖҬ "CTUSBDU%PNBJO ΛͲ͏ఆΊΔ͔ʁ w ෦ઢܗۭࣹؒӨߦྻͷͳ͢ଋΛݩʹBCTUSBDUEPNBJOΛߏ͢Δ
ࣹӨߦྻ QSPKFDUJPONBUSJY w Λຬͨ͢ਖ਼ํߦྻ w ϕΫτϧΛ͋Δ෦ઢܗۭؒ ʹҠ͢ w ͱ ҰରҰʹରԠ
w ྫҎԼͷ ฏ໘ͱରԠ P = P† = P2 P SP P SP P xy P = 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
۩ମతঢ়ଶࣹӨߦྻͱͯ͠දݱ͞ΕΔ w ࣹӨߦྻͱͯ͠ͷੑ࣭Λຬͨ͢ ρ = |ψ⟩⟨ψ|
ࣹӨߦྻͷॱং P ⊆ Q J ff SP ⊆ SQ
நྖҬͷߏ w ORVCJUͷঢ়ଶʹରͯ͠ |ψ⟩⟨ψ| (Ps1 , ⋯, Psm ) ͷڊେߦྻ
2n × 2n Nݸͷখ͞ͳࣹӨ ߦྻͰۙࣅ
நྖҬͷఆٛ w ʹରͯ͠ ͱ͢Δɻͨͩ͠ w ORVCJUͷͷ͢ΔϏοτͷू߹Λදݱ w ͷॱংҎԼͰఆΊΔ 0
< m ≤ 2n S = (s1 , …, sm ) si ⊆ {0,…, n − 1} si P, Q ∈ AbsDom(S) AbsDom(S) = {(Ps1 , …, Psm ) ∣ Psi 2|si |ࣹ࣍Өߦྻ} P ⊑ Q J ff ∀i, Psi ⊆ Qsi
'JOFS"CTUSBDU%PNBJO AbsDom({0,1}, {1,2}) AbsDom({0,1,2}, {1,2}) AbsDom(S) ⊴ AbsDom(T) J ff
∀i si ⊆ ti
۩ମྖҬ $PODSFUF%PNBJO w நྖҬͷಛผͳ߹ɻ࠷ fi OFɻ ͱͯ͠ [n] = {0,…,
n − 1} AbsDom([n]m) = {2nࣹ࣍Өߦྻmݸͷ}
நԽࣸ૾ͱ۩ମԽࣸ૾ நԽ ۩ମԽ
ΨϩΞଓ (BMPJT$POOFDUJPO
ΨϩΞଓ (BMPJT$POOFDUJPO "CTUSBDU%PNBJOͰܭࢉͯ͠ಘͨॱংͱ $PODSFUF%PNBJOͰܭࢉͯ͠ಘͨॱংҰக
நԋࢉ RVCJUͷू߹'ʹର͢ΔϢχλϦߦྻ6ͰͷநԋࢉΛߦ͏ʹɺ 'ΛؚΉ fi OFͳEPNBJOʹҠͬͯ۩ମతʹܭࢉͯ͠ɺ"CTUSBDUEPNBJOʹΔ S = (s1 , …,
sm ) ⇒ T = (s1 ∪ sF , …, sm ∪ sF )
ओఆཧ நྖҬઢܗ෦ۭؒ ͷ ͷ-BUUJDFͩͬͨͷͰܭࢉ݁Ռͷ ͷ ʹؚ·ΕΔϏοτ෦ۭؒ ͷுΔۭؒʹؚ·ΕΔ ͱ͍ͬͨBTTFSUJPO͕ࣔͤΔ si Psi
ܭࢉྔ w ͭͷࣹӨߦྻͷαΠζΛLRVCJUͱͨ͠߹ w ۭؒܭࢉྔ w ࣌ؒܭࢉྔ ϓϩάϥϜͷήʔτ
O(|S| × (2k+3 × 2k+3)) O(|p| × 8k) |p|
ϕϯνϚʔΫ w #7G Y BY CͷB CΛݟ͚ͭΔ w ();શͯɺશ͕ͯॏͳͬͨঢ়ଶΛ࡞Δ w
(SPWFSG Y ͱͳΔYΛ୳ࡧ w .BD#PPL1SP $PSFJ()[ (#
݁ w ྔࢠܭࢉͷҝͷநղऍख๏ΛఏҊͨ͠ 4DBMBCMFͰ͋ΔRVCJUنͷγϛϡϨʔγϣϯग़དྷͨ 6TFGVMͰ͋ΔͭͷॏཁͳͰBTTFSUJPODIFDL͕ग़དྷͨ 'MFYJCMFͰ͋Δ"CTUSBDU%PNBJOͷઃܭࣗ༝͕ߴ͍