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Prob 𝑆 → 𝑇 = 𝑇 𝑈 𝑆 2 ∝ per 𝑈𝑆𝑇2
per 𝐴 = 𝑎𝑖,𝜎(𝑖)
𝑚
𝑖=1𝜎∈𝑆𝑚
Study of bosonic dynamics with multi-mode interferometers
Single photon source via spontaneous Parametric Down-Conversion
𝜔𝑃 𝜔𝐼
𝜔𝑆
𝜔𝑆, 𝒌𝑠
𝜔𝐼 , 𝒌𝐼
𝜔𝑃 , 𝒌𝑃
𝒌𝑃
𝒌𝐼 𝒌𝑆
𝝌(2)
PDC
Evolution through interferometric architectures fabricated via Femtosecond Laser Writing technique
U
U
Evolution through interferometric architectures fabricated via Femtosecond Laser Writing technique
••••
Single photon source via spontaneous Parametric Down-Conversion
𝜔𝑃 𝜔𝐼
𝜔𝑆
𝜔𝑆, 𝒌𝑠
𝜔𝐼 , 𝒌𝐼
𝜔𝑃 , 𝒌𝑃
𝒌𝑃
𝒌𝐼 𝒌𝑆
𝝌(2)
PDC
Scattershot
Sources
M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, F. Sciarrino,
Experimental Scattershot Boson Sampling, Science Advances 1 (3), e1400255 (2015).
Measured distributions and predictions: Output distributions for 7-, 9-, 13- mode Boson Sampling experiments
N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini,
S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvão, F. Sciarrino, Experimental validation of photonic boson sampling, Nature Photonics 8, 615 (2014).
N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini,
S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvão, F. Sciarrino, Experimental validation of photonic boson sampling, Nature Photonics 8, 615 (2014).
Validation against: - Uniform distribution
- Distribution obtained from distinguishable input photons
LR test RNE test
M. Bentivegna, N. Spagnolo, C. Vitelli, D.J. Brod, A. Crespi, F. Flamini, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvao, and F. Sciarrino,
Bayesian approach to boson sampling validation, Int. J. Quant. Inf. 12, 1560028 (2015).
Bayesian
𝐷 =𝑁𝑓𝑜𝑟𝑏𝑖𝑑𝑑𝑒𝑛
𝑁𝑒𝑣𝑒𝑛𝑡𝑠= 𝑃𝑐𝑜𝑚𝑏
𝑄
𝑐𝑜𝑚𝑏 𝑓𝑜𝑟𝑏𝑖𝑑𝑑𝑒𝑛
= 𝑃𝑐𝑜𝑚𝑏𝐷
𝑐𝑜𝑚𝑏 𝑓𝑜𝑟𝑏𝑖𝑑𝑑𝑒𝑛
(1 − 𝑉𝑐𝑜𝑚𝑏𝐻𝑂𝑀)
A. Crespi, R. Osellame, R. Ramponi, M. Bentivegna, F. Flamini, N. Spagnolo, N. Viggianiello, L. Innocenti, P. Mataloni, F. Sciarrino,
Suppression law of quantum states in a 3D photonic fast Fourier transform chip, Nature Commun. 7: 10469 (2016).
Experimental demonstration
𝐷𝐷𝑖𝑠𝑡 > 0.5 𝐷𝑀𝐹 > 0.25
𝑫𝑭𝒐𝒄𝒌 = 𝟎
Measurable!
Cyclic input (1,0,1,0)
mod 𝑘𝑙
𝑛
𝑙=1
, 𝑛 ≠ 0
1 + 2 ≠ 0(mod 2)
1 + 4 ≠ 0(mod 2)
2 + 3 ≠ 0(mod 2)
3 + 4 ≠ 0(mod 2)
Cyclic input (0,1,0,1)
Experimental demonstration
FLW integrated circuits for QFT via Barak and Ben-Aryeh decomposition
Traditional general scheme: 𝑂 𝑚2 elements Barak & Ben-Aryeh scheme optimized for QFT: 𝑂 𝑚 log𝑚 elements
FLW integrated circuits for QFT via Barak and Ben-Aryeh decomposition
F. Flamini, N. Viggianiello, T. Giordani, M. Bentivegna, N. Spagnolo, A. Crespi, R. Osellame, M.A. Martin-Delgado, F. Sciarrino, Observation of Majorization Principle for quantum algorithms via 3-D integrated photonic circuits, arXiv:1608.01141 (2016).
FLW integrated circuits for QFT via Barak and Ben-Aryeh decomposition
F. Flamini, N. Viggianiello, M. Bentivegna, N. Spagnolo, P. Mataloni, A. Crespi, R. Ramponi, R. Osellame, F. Sciarrino, Generalized quantum fast transformations via femtosecond laser writing technique,
preprint at Interdisciplinary Information Sciences (2016).
Changing τ and ϕ we can span a whole class of quantum fast transformations
FLW integrated circuits for QFT
F. Flamini, L. Magrini, A. S. Rab, N. Spagnolo, V. D’Ambrosio, P. Mataloni, F. Sciarrino, T. Zandrini, A. Crespi, R. Ramponi, and R. Osellame,
Thermally reconfigurable quantum photonic circuits at telecom wavelength by femtosecond laser micromachining, Light: Science & Applications 4, e354 (2015).
𝜑 = 𝜑0 + 𝛼 𝑃 𝑃 =∆𝑉2
𝑅
𝜑
Tunable circuits at telecom wavelength are enabled by thermal shifters, fabricated with FLW.
Resistor
Arm1
Arm2
FLW integrated circuits for QFT
𝐼𝑜𝑢𝑡 =𝐼𝑡𝑜𝑡
2[1 + 𝑉 cos(𝜑0+𝛼 𝑃)]
𝜑
|ψ ∝ |0, 2 + 𝑒𝑖2𝜑 |2,0
Resistor
Arm1
Arm2
F. Flamini, N. Viggianiello, T. Giordani, M. Bentivegna, N. Spagnolo, A. Crespi, R. Osellame, M.A. Martin-Delgado, F. Sciarrino, Observation of Majorization Principle for quantum algorithms via 3-D integrated photonic circuits, arXiv:1608.01141 (2016).
F. Flamini, L. Magrini, A. S. Rab, N. Spagnolo, V. D’Ambrosio, P. Mataloni, F. Sciarrino, T. Zandrini, A. Crespi, R. Ramponi, and R. Osellame,
Thermally reconfigurable quantum photonic circuits at telecom wavelength by femtosecond laser micromachining, Light: Science & Applications 4, e354 (2015).
F. Flamini, N. Viggianiello, M. Bentivegna, N. Spagnolo, P. Mataloni, A. Crespi, R. Ramponi, R. Osellame, F. Sciarrino,
Generalized quantum fast transformations via femtosecond laser writing technique, preprint at Interdisciplinary Information Sciences (2016).
A. Crespi, R. Osellame, R. Ramponi, M. Bentivegna, F. Flamini, N. Spagnolo, N. Viggianiello, L. Innocenti, P. Mataloni, F. Sciarrino,
Suppression law of quantum states in a 3D photonic fast Fourier transform chip, Nature Communications 7, 10469 (2016).
M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, F. Sciarrino,
Experimental Scattershot Boson Sampling, Science Advances 1 (3), e1400255 (2015).
N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini,
S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvão, F. Sciarrino, Experimental validation of photonic boson sampling, Nature Photonics 8, 615 (2014).
M. Bentivegna, N. Spagnolo, C. Vitelli, D.J. Brod, A. Crespi, F. Flamini, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvão, and F. Sciarrino,
Bayesian approach to boson sampling validation, Int. J. Quant. Inf. 12, 1560028 (2015).
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