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BOSON SAMPLING

BOSON SAMPLING

VALIDATION

BOSON SAMPLING

VALIDATION

EFFICIENCY

CONVERTIBLE

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

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).



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

Uniform Distinguishable Mean Field Ideal

?

|ψ𝑀𝐹 =1

𝑛 𝑒𝑖𝜃𝑝 𝑎𝑗𝑝

†

𝑛

𝑃=1

|0

Uniform Distinguishable Mean Field Ideal

!

|ψ𝑀𝐹 =1

𝑛 𝑒𝑖𝜃𝑝 𝑎𝑗𝑝

†

𝑛

𝑃=1

|0

𝑉𝐻𝑂𝑀 = 1 −𝐶𝑖𝑛𝑑

𝐶𝑑𝑖𝑠𝑡

𝐶𝑑𝑖𝑠𝑡

𝐶𝑖𝑛𝑑

mod 𝑘𝑙

𝑛

𝑙=1

, 𝑛 ≠ 0

per 𝐴 = 𝑎𝑖,𝜎(𝑖)

𝑚

𝑖=1𝜎∈𝑆𝑚

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


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, 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

Perspectives

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).



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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