Bozon Sampling Kadyrmetov Shamil, DGAP 325 MIPT, 2016 History - - PowerPoint PPT Presentation

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Aug 29, 2023 391 likes •633 views

Bozon Sampling Kadyrmetov Shamil, DGAP 325 MIPT, 2016 History Implementations : Year/author Succeed in Disadvantages ion trap quantum computing superconducting qbits NMR (nuclear magnetic resonance) 1993 NP class Energy

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Bozon Sampling

Kadyrmetov Shamil, DGAP 325

MIPT, 2016

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History

Implementations:

ion trap quantum computing
superconducting qbits
NMR (nuclear magnetic resonance)
nuclear spin
optical quantum computing

Models:

quantum gate model
cluster (or graph) states
topological
adiabatic
quantum random walks
quantum Turing machine
permutational
one-clean qubit model

Year/author Succeed in Disadvantages 1993 Czerny NP class simplified to P class Energy consumption ~ exp(n) 1996 Clauser & Dowling Integers factorization in P class Energy and space ~ exp(n) 2002 Bartlett Gauss input pulses + quadratic nonlinear

ptical interferometers can be

successfully modeled in classic P class 2010 Aaronson & Arkhipov Fock input states + photon number discrimination Is atleast in classic NP calss 2013 Gard et al. The same problem in LOQC implementation of random-walk

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FFT:

) ( ) ) ((log : ) 2 ( ) log ( : 2

2 2

n O N O Quantum n O N N O Classic N

n n

   

Search among N elements:

) ( : ) ( : N O Quantum N O Classic

Quantum systems simulation:

) ( : ) ( : N O Quantum e O Classic

𝑒𝑓𝑕 𝐼 ~ 2𝑜 because of exchange interaction 𝑄𝑓𝑠 𝑉 ≡ 𝑃(2𝑜𝑜) ≡ #𝑄 𝑑𝑚𝑏𝑡𝑡

Bozon sampling:

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Requirements of full LOQC

synchronization of pulses
mode-matching
quickly controllable delay lines
tunable beamsplitters and phase-shifters
single-photon sources
accurate, fast, single photon detectors.

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Tunable single-photon sources

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Tunable single-photon sources

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Beamsplitters

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Definitions

𝑄 = 𝑓𝑗𝑜

𝜒

𝐶 = 𝐷𝑝𝑡𝜄 −𝑓𝑗𝜀𝑇𝑗𝑜𝜄 −𝑓𝑗𝜀𝑇𝑗𝑜𝜄 𝐷𝑝𝑡𝜄

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Step out with Hong-Ou-Mandel effect

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Bozon sampling

single-photon sources
beamsplitters
single photon detectors

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Problems

𝑜𝑣𝑛𝑐𝑓𝑠 𝑝𝑔 𝑏𝑚𝑚 𝑞𝑝𝑡𝑡𝑗𝑐𝑚𝑓 𝑝𝑣𝑢𝑑𝑝𝑛𝑓𝑡 𝑂𝑏 = 𝑛 + 𝑜 − 1 𝑜 𝑜𝑣𝑛𝑐𝑓𝑠 𝑝𝑔 𝑡𝑗𝑜𝑕𝑚𝑓 − 𝑞ℎ𝑝𝑢𝑝𝑜 𝑝𝑣𝑢𝑑𝑝𝑛𝑓𝑡 𝑂𝑡 = 𝑛 𝑜 ~ 𝑜! (𝑗𝑔 𝑛 ~ 𝑜2) 𝑛 ~ 𝑜𝑒 lim

𝑜→∞

𝑂𝑡 𝑂𝑏 = 0, 0 < 𝑒 < 2 1 𝑓 , 𝑒 = 2 1, 𝑒 > 2

𝑞 − 𝑗𝑡 𝑢ℎ𝑓 𝑔𝑗𝑒𝑓𝑚𝑗𝑢𝑧 𝑝𝑔 |1 1| 𝑡𝑢𝑏𝑢𝑓 𝑞𝑠𝑓𝑞𝑏𝑠𝑏𝑢𝑗𝑝𝑜 𝑄 = 𝑞𝑜 − 𝑞𝑠𝑝𝑞𝑏𝑐𝑗𝑚𝑗𝑢𝑧 𝑢𝑝 ℎ𝑏𝑤𝑓 𝑞𝑠𝑝𝑞𝑓𝑠 𝑗𝑜𝑞𝑣𝑢 𝑡𝑢𝑏𝑢𝑓 Aaronson & Arkhipov: 𝑗𝑔 𝑄 >

1 𝑞𝑝𝑚𝑧 𝑜,1

𝜗

𝑢ℎ𝑓 𝑠𝑓𝑡𝑣𝑚𝑢 𝑑𝑏𝑜 𝑐𝑓 𝑠𝑝𝑐𝑣𝑡𝑢 𝑢𝑝 𝑢ℎ𝑓 𝑓𝑠𝑠𝑝𝑠𝑡.

Sampling Fidelity

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Lange coupler

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Lange coupler

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Current work

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𝐸𝑓𝑢𝑓𝑑𝑢𝑝𝑠 𝑓𝑔𝑔𝑗𝑑𝑗𝑓𝑜𝑑𝑧: 𝑞 1 1 = 𝜃2 = 0.88

𝑂 𝜃2 С 1 0.88 0.65 4 0.84 0.65 ∞ 0.74 0.65 𝐷𝑏𝑚𝑑𝑣𝑚𝑏𝑢𝑗𝑝𝑜 𝑠𝑓𝑡𝑣𝑚𝑢𝑡

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Bozon sampling

single-photon sources (SPDC)
beamsplitters
single photon detectors

resolving photons number

https://github.com/shamil777/BozonSampling