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

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 consumption Czerny simplified to ~ exp(n) • nuclear spin P class • optical quantum computing 1996 Integers Energy and space Models: Clauser & Dowling factorization in ~ exp(n) P class • quantum gate model 2002 Gauss input pulses + quadratic nonlinear • cluster (or graph) states Bartlett optical interferometers can be • topological successfully modeled in classic P class • adiabatic 2010 Fock input states + photon number • quantum random walks Aaronson & Arkhipov discrimination Is atleast in classic NP calss • quantum Turing machine 2013 The same problem in LOQC • permutational Gard et al. implementation of random-walk • one-clean qubit model

Bozon sampling: 𝑒𝑓𝑕 𝐼 ~ 2 𝑜 because of exchange interaction 𝑄𝑓𝑠 𝑉 ≡ 𝑃(2 𝑜 𝑜) ≡ #𝑄 𝑑𝑚𝑏𝑡𝑡 FFT:  n N 2   n Classic : O ( N log N ) O ( 2 n )  2 2 Quantum : O ((log N ) ) O ( n ) Search among N elements: Classic : O ( N ) Quantum : O ( N ) Quantum systems simulation: N : ( ) Classic O e : ( ) Quantum O N

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.

Tunable single-photon sources

Tunable single-photon sources

Beamsplitters

Definitions −𝑓 𝑗𝜀 𝑇𝑗𝑜𝜄 𝐷𝑝𝑡𝜄 = 𝐶 −𝑓 𝑗𝜀 𝑇𝑗𝑜𝜄 𝐷𝑝𝑡𝜄 = 𝑓 𝑗𝑜 𝜒 𝑄

Step out with Hong-Ou-Mandel effect

Bozon sampling • single-photon sources • beamsplitters • single photon detectors

Problems 𝑜𝑣𝑛𝑐𝑓𝑠 𝑝𝑔 𝑏𝑚𝑚 𝑞𝑝𝑡𝑡𝑗𝑐𝑚𝑓 𝑝𝑣𝑢𝑑𝑝𝑛𝑓𝑡 𝑂 𝑏 = 𝑛 + 𝑜 − 1 𝑜 𝑜𝑣𝑛𝑐𝑓𝑠 𝑝𝑔 𝑡𝑗𝑜𝑕𝑚𝑓 − 𝑞ℎ𝑝𝑢𝑝𝑜 𝑝𝑣𝑢𝑑𝑝𝑛𝑓𝑡 𝑂 𝑡 = 𝑛 Sampling 𝑜 ~ 𝑜! (𝑗𝑔 𝑛 ~ 𝑜 2 ) 0, 0 < 𝑒 < 2 𝑂 𝑡 1 𝑛 ~ 𝑜 𝑒 lim = 𝑓 , 𝑒 = 2 𝑂 𝑏 𝑜→∞ 1, 𝑒 > 2 𝑞 − 𝑗𝑡 𝑢ℎ𝑓 𝑔𝑗𝑒𝑓𝑚𝑗𝑢𝑧 𝑝𝑔 |1 1| 𝑡𝑢𝑏𝑢𝑓 𝑞𝑠𝑓𝑞𝑏𝑠𝑏𝑢𝑗𝑝𝑜 𝑄 = 𝑞 𝑜 − 𝑞𝑠𝑝𝑞𝑏𝑐𝑗𝑚𝑗𝑢𝑧 𝑢𝑝 ℎ𝑏𝑤𝑓 𝑞𝑠𝑝𝑞𝑓𝑠 𝑗𝑜𝑞𝑣𝑢 𝑡𝑢𝑏𝑢𝑓 Fidelity Aaronson & Arkhipov: 1 𝑗𝑔 𝑄 > 𝑢ℎ𝑓 𝑠𝑓𝑡𝑣𝑚𝑢 𝑑𝑏𝑜 𝑐𝑓 𝑠𝑝𝑐𝑣𝑡𝑢 𝑢𝑝 𝑢ℎ𝑓 𝑓𝑠𝑠𝑝𝑠𝑡. 𝑞𝑝𝑚𝑧 𝑜, 1 𝜗

Lange coupler

Lange coupler

Current work

𝐸𝑓𝑢𝑓𝑑𝑢𝑝𝑠 𝑓𝑔𝑔𝑗𝑑𝑗𝑓𝑜𝑑𝑧: 𝑞 1 1 = 𝜃 2 = 0.88 𝐷𝑏𝑚𝑑𝑣𝑚𝑏𝑢𝑗𝑝𝑜 𝑠𝑓𝑡𝑣𝑚𝑢𝑡 𝜃 2 𝑂 С 1 0.88 0.65 4 0.84 0.65 ∞ 0.74 0.65

Bozon sampling • single-photon sources (SPDC) • beamsplitters • single photon detectors resolving photons number https://github.com/shamil777/BozonSampling