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古典プログラマが量子プログラミングをさわろうとした話 / FFTT #383
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Masaya Nakamura
January 24, 2020
Programming
170
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古典プログラマが量子プログラミングをさわろうとした話 / FFTT #383
社内勉強会 FFTT で発表した内容です。
Masaya Nakamura
January 24, 2020
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Transcript
ݹయϓϩάϥϚ͕ ྔࢠϓϩάϥϛϯάΛ ͞ΘΖ͏ͱͨ͠ ݄ !NBTIBCPX
งғؾͱ͔ײ৮͙Β͍͍͑ͨ ͜Μʹͪ w !NBTIBCPX w ιʔγϟϧ1-64ϑϩϯτΤϯυΤϯδχΞ w લճϕδΤۂઢʹ͍ͭͯޠͬͨΜͰ͕͢ w ࠓճྔࢠίϯϐϡʔλͷΛ͠·͢
ࡢ݄͡Ί w ʻ͋ʔɺϑϩϯτΤϯυ.5(ͷωλ୳ͯ͠͠ͳ͍ʜ w ͯϒͰVTFST͙Β͍৳ͼ͍ͯͨ w શવΘ͔ΒΜ͚Ͳհ͠ͱ͜ w ͳΜ͔͔͍͍ͬ͜͠
ղܾ✅ ྔࢠྗֶΘ͔Βͳ͍ w ಈؔɺγϡϨσΟϯΨʔํఔࣜɺεϐϯɺʜ w w ྔࢠྗֶʹཱͪೖΒͳ͍͜ͱʹͨ͠
දݱྗ͕ߴ͍ ྔࢠϏοτ w ݹయϏοτͷঢ়ଶ͔ͩͬͨ w ྔࢠϏοτͷঢ়ଶɺϒϩοϗٿ্ͷͰද͞ΕΔΒ͍͠
ͳΔ΄Ͳʁ ೖྗͷྔࢠήʔτ w ೖྗͷݹయήʔτɺ/05ήʔτ͚ͩʢˠ ˠʣ w ྔࢠήʔτͰ9 : ; )ͳͲͳͲɺ͍Ζ͍Ζ͋Δ
w ྔࢠϏοτΛೖΕΔͱɺྔࢠϏοτ͕͙Δ͙ΔճΔ
্͖͔Լ͖͔↕ ྔࢠϏοτͷଌఆ w ྔࢠϏοτΛଌఆ͢Δͱɺ͔͕֬తʹग़ͯ͘Δ w ग़ͯ͘Δׂ߹ྔࢠϏοτͷঢ়ଶʹΑܾͬͯ·Δ ͕ ͕ ͕
͕
શʹཧղͨ͠ جຊͷϧʔϧ w ྔࢠϏοτٿΈ͍ͨͳΠϝʔδ w ྔࢠήʔτʹ௨͢ͱ͙Δ͙ΔճΔ w ଌఆ͢Δͱ͔͕֬తʹग़ͯ͘Δ
ཧܥֶ෦ੜ͙Β͍ͷֶඞཁͩͬͨ ߦྻ͕ग़ͯ͘Δ w ྔࢠϏοτcʫ ͱcʫ ͷॏͶ߹ΘͤͰදݱ͞ΕΔ w ྔࢠήʔτϢχλϦߦྻͰදݱ͞ΕΔ |ψ⟩
= ( α β) = α ( 1 0) + β ( 0 1) = α|0⟩ + β|1⟩ (α, β ∈ ℂ, |α|2 + |β|2 = 1) X = ( 0 1 1 0) X|0⟩ = ( 0 1 1 0) ( 1 0) = ( 0 1) = |1⟩ ͳͷͰɺ
ྔࢠϏοτ్தͰ૿͑ͨΓݮͬͨΓ͠ͳ͍☝ ೖྗͷྔࢠήʔτ w $/05ήʔτ͕͍ͪΜ༗໊ͬΆ͍ w ੍ޚϏοτ͕cʫ ͷͱ͖͚ͩɺඪతϏοτΛస ੍ޚϏοτ ඪతϏοτ
CNOT |00⟩ = |00⟩ CNOT |01⟩ = |01⟩ CNOT |10⟩ = |11⟩ CNOT |11⟩ = |10⟩ 903తͳ CNOT = 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0
͜ΕΛͬͯ͏·͍͜ͱ͍ͬͯ͘Β͍͠ ͭΕ w ྔࢠϏοτؒʹ૬ؔؔΛ࡞Δ͜ͱ͕Ͱ͖Δ w ยํͷྔࢠϏοτΛଌఆ͢Δͱɺ͏ยํͷྔࢠϏοτͷ͕ܾ·Δɺͱ͔ 1 2 (|00⟩
+ |11⟩) ग़ྗɿ ยํ͕ͩͬͨΒ͏ยํ ยํ͕ͩͬͨΒ͏ยํ
None
͚ͬ͜͏ϨΠϠ ։ൃڥ w ઐ༻ͷݴޠͩͬͨΓɺ1ZUIPOͷϥΠϒϥϦͩͬͨΓɺ͍Ζ͍Ζ͋Δ w γϛϡϨʔλʔ͕͍͍ͭͯΔͷͰɺݹయίϯϐϡʔλ্Ͱ࣮ߦͰ͖Δ w ن͕େ͖͘ͳΔͱܭࢉ͕͍͔ͭͳ͍ w جຊతʹɺྔࢠήʔτΛฒͯྔࢠճ࿏Λ࡞͍͚ͬͯͩ͘
2VBOUVN,BUBT w .JDSPTPGUͷྔࢠϓϩάϥϛϯάݴޠ2Λͬͨ࿅श w ʹ࠷ॳͷํ͚ͩղ͍ͯΈͨɻύζϧͬΆ͍ ݴޠʹ׳ΕΔ·Ͱ͕ʜ
*#.ͷ$JSDVJU$PNQPTFS w (6*Ͱϙνϙν͢Δͱྔࢠճ࿏͕ΊΔ w ࣮ߦͰ͖Δ Ϋϥυ্ͷ࣮ػͰ࣮ߦͰ͖Δ
σϞ *#.ͷ2JTLJU/PUFCPPL w 1ZUIPOϥΠϒϥϦ2JTLJU +VQZUFS/PUFCPPL w ͪ͜Βϒϥβ্͔Β͙͢ʹಈ͔ͤΔ
ྔࢠϓϩάϥϜͷ͍ํ w ྔࢠϓϩάϥϜྔࢠճ࿏ʹίϯύΠϧ͞ΕΔ w ͦͷճ࿏ΛԿճ࣮ߦͯ͠ɺଌఆ݁ՌͷΛݟΔ w ·ͩྔࢠϝϞϦͳ͍ɻྔࢠ௨৴Ͱ͖ͳ͍ w ݹయϓϩάϥϜʹΈ߹ΘͤͯཁॴͰ͏Πϝʔδ
࠷ॳͷΠϝʔδͱҧͬͨ ճͱ͔܁Γฦ͢
؊৺ͳͱ͜Ζ͕ ੵΈ͠ w ͲΜͳྔࢠΞϧΰϦζϜ͕͋Δͷʁ w ྔࢠίϯϐϡʔλԿ͕ಘҙͳͷʁ w ྔࢠήʔτܕͱྔࢠΞχʔϦϯάܕͬͯʁ w Ͳ͜·Ͱ࣮༻తͳͷʁ
͓͠·͍