Implementation of integrated photonics experiments towards scalable quantum technologies

Candidate: Fulvio Flamini

Supervisor: Prof. Fabio SciarrinoDipartimento di Fisica, Sapienza Universita di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy

I. INTRODUCTION

Nowadays society deeply relies on the power of telecommunication and computing technologies. In the last decades, a funda-mental improvement has been offered by the introduction of optical fibers, exhibiting low transfer losses, flexibility, reliabilityand no electromagnetic interference crucial for long-haul communications. At the same time, the increasing interest towards thepotentialities hidden in quantum phenomena gave birth to several fields of research [1, 2], falling under the name of quantuminformation theory, aiming to take advantage of the possibilities offered by the quantum framework to recreate new quantumnetworks for managing the transfer of information [3]. Nonetheless, their implementation would still rely on the use of opticalfibers to transfer photons, on whose quantum states the information can be encoded [7]. This constraint has led to choose asoptimal windows for the transmission wavelength those undergoing the lowest attenuation throughout silica fibers, the mostcommon ones, namely around 1310 nm and 1550 nm. The latter, especially, is now widely used for lower losses, tunable disper-sion and the availability of very efficient erbium-doped fiber amplifiers [4–6].In general, besides an efficient and reliable transfer of signals, projecting optical quantum networks requires the possibility ofsetting up any unitary transformation using optical elements. Furthermore, the importance of linear optics potentialities has beenhighlighted also in the context of quantum computing, where it has been proved that efficient quantum computation is possibleusing only beam splitters, phase shifters, single photon sources and photo-detectors [8]. In this direction, it has been shownalso that unitary transformations can be indeed decomposed into the actions of the fundamental linear-optical elements, that isthe very beam splitters and phase shifters, arranged in a network properly designed [9]. Unfortunately, interferometers set upwith this scheme can heavily suffer from mechanical instabilities, undermining the goodness of the whole apparatus, as well asfrom difficulties in scaling up the experiments. For all these reasons, the need for both stability and scalability in telecommu-nication implementations has prompted a progressive miniaturization of such optical devices. In addition to lithography, usingsilica-on-silicon [10] and LiNbO3 substrates [11], a powerful approach to transfer linear optics elements on an integrated pho-tonic platform is that of using femtosecond laser micromachining fabrication [12, 13]. With this technique, waveguides are builtexploiting nonlinear absorption of focused femtosecond pulses in a transparent material, inducing a localized permanent refrac-tive index increase in the medium. Indeed this approach allows the unique engineering of complex three-dimensional circuitalstructures [14], by translating the sample along the desired path at constant velocity with respect to the laser beam. Waveguidescan also be realized either polarization sensitive or insensitive, due to the low birefringence, efficiently enabling polarizationentanglement experiments [15, 16]. The absence of necessity of using masks and various steps of fabrication, together with itspeculiar versatile potentialities, make this technique faster and often more convenient than conventional lithography for manyapplications.

II. PH.D. RESEARCH LINE

The operational framework of my Ph.D. studies is closely related to this research line in integrated photonics, for quantumcomputing and quantum communication applications. In particular, my research project aims to explore the potentialities ofthis advanced technology by directly applying it to some applications of interest, so as to prove the feasibility of new, quantumdevices that will play a role in the development of different areas of quantum information theory. Ultimately, the main goal of myPh.D. research is to carry out telecom wavelength multi-photon experiments, that exploit the integrated photonics potentialitiesto achieve innovative and stronger results in the field of quantum communication.More in detail, in the following I will briefly outline the path planned for the whole course of study.

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A. Quantum simulation on integrated photonics circuits

1. Experimental implementation of the BOSON SAMPLING problem

A quantum computer composed of only linear-optical elements and able to manage adaptive measurements becomes a uni-versal quantum computer, promising to solve problems that are intractable for a classical one [1, 8]. In spite of the strongtheoretical framework behind its designing, its actual implementation remains still far from currently available implementations.The first theoretical platform on which it has been possible to device an experiment both feasible for current technology andyielding evidence of the superior computational power of a quantum (simulator) machine has been offered by the so-calledBOSON SAMPLING problem [17]. In this model, a classical computer is required to simulate the outputs of an interferometricdevice implementing an unitary transformation on the input bosonic Fock state, with a probability distribution close to the oneobtained experimentally. The classical complexity arises from the fact that a system of non-interacting indistinguishable bosonsevolves according to the permanent of a proper submatrix of the unitary transformation. Specifically, defining the input state ofthe interferometer as S = |s1s2...sm〉 = a†s11 a†s22 ...a†smm |0〉, where a†sii is the creation operator applied si times to the vacuumstate in the i-th mode and si is the number of bosons in the input mode i of the m-mode interferometer, it can be shown that theprobability amplitude of finding a certain configuration of photons in the output, given one in the input, follows the rule

〈T |U |S〉 =Per (UST )√

s1!...sm! t1!...tm!

where UST is a proper submatrix of the complete matrix describing the action of the interferometer. Therefore, while for aquantum simulator it is possible to solve this problem simply running the experiment, for the classical counterpart it would benecessary to deal with the permanent function, which has been definitely proved to be #P-hard to calculate [18].

As a first step in my Ph.D. research project, I am going to experimentally realize instances of the BOSON SAMPLING problemwith up to three photons at increasing scale of the size of the interferometer and, hence, of the hardness of the problem. Everyinterferometer has been fabricated using femtosecond laser writing techique on a glass substrate, implementing on an integratedplatform all beam splitters and phase shifters required to reproduce the desidered U transformation after applying Reck’s de-composition [9]. Photons are generated through spontaneous parametric downconversion (SPDC) in a nonlinear crystal andcollected in optical fibers inserted in the input of the integrated device. Ultimately, such experiments would indeed represent astrong evidence against the Church-Turing conjecture, stating that any physical process can be efficiently simulated by a prob-abilistic Turing machine, and would constitute a proof of principle that future, quantum computers can be exponentially moreefficient than classical ones [19].

Fig. 1 Scheme of the integrated BOSON SAMPLING photonic circuit, fabricated on a glass substrate with femtosecond laser writing technique.Arbitrary unitary transformations are implemented through directional couplers (beam splitter’s integrated equivalent) and phase shifters (redcircles) properly tuned and arranged in this structure.

2. Scattershot approach to BOSON SAMPLING

Though current technology in the quantum optics domain already allows the implementation of BOSON SAMPLING, theschemes adopted so far are still insufficient to give a strong evidence of the superiority of quantum over classical computation.For this reason a new approach to the problem has recently been proposed, capable of yelding an exponential improvement withrespect to the possibilities of the former scheme [20, 21]. One of the main limitations met in scaling up the power of BOSON

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SAMPLING was indeed the requirement of a reliable and efficient source of many indistinguishable photons. Despite recentadvances in photon generation, in fact, currently the most widely used platform remains spontaneous parametric downconversion,already used in the first realization of the experimental BOSON SAMPLING [22, 23]. This technique requires pumping a nonlinearcrystal with an intense laser to generate pairs of highly indistinguishable photons. Nevertheless, SPDC technique suffers fromthe drawbacks of being a nondeterministic process, though heralded, and of requiring to keep the brilliance low to avoid higher-order terms in the generation process. To overcome these difficulties, a new scheme has been proposed to enhance the rate ofn-photon events, making the best use of these sources for photonic BOSON SAMPLING. The so-called Scattershot approach toBOSON SAMPLING involves connecting k>n SPDC heralded single-photon sources to different input ports of the interferometer.The underlying idea exploits the observation that, if each source yields a single photon with probability ε per pulse, by pumpingall k crystals with simultaneous laser pulses n photons will be simultaneously generated in a random, but heralded, set of inputports with probability

(kn

)εn. Thus, for k�n this scheme offers an exponential improvement in generation rate with respect to

the standard implementation with fixed input. The Scattershot BOSON SAMPLING problem is then to sample from the outputdistribution of a given, random interferometer for random sets of input modes.

Such approach clearly yields two advantages: the enhancement of the photon generation rate and of the complexity of theexperiment to be simulated classically, due to the random input combinations used. For all these reasons the Scattershot approachis thought to be decisive in future experiments deviced to reach the regime in which quantum computers can no longer besimulated efficiently by classical ones. Along this direction, after the realization of standard BOSON SAMPLING experiments, inthe research project I am going to upgrade the scheme setting up the new Scattershot implementation, to scale up the complexityof the system to be simulated to strengthen the platform as a test of the quantum computational power. For this aim, I am goingto set up an apparatus with six SPDC photon sources to generate up to three single photons, to be injected in a new 13-modeintegrated photonic chip fabricated with femtosecond laser writing technique.

Fig. 2 Scheme of the six sources used to realize Scattershot BOSON SAMPLING photonic experiment. Each crystal generates two pairs ofphotons via type-II SPDC processes, which are then selected using the orthogonal polarizations, HV and VH respectively. The selection process,in which photons are sent or in the trigger channel (V) or in the input mode (H), occurs in six polarizing beam splitters and is depicted for thesake of clarity in the picture with a two-level scheme.

3. BOSON SAMPLING and the validation of quantum simulators

The positive results obtained with the experimental realizations of both the BOSON SAMPLING problem and its more advancedScattershot variation apparently suffice to claim the superior potentialities of the quantum domain over the classical one, for bothcomputing and philosophical scopes [24]. Nevertheless, it has been actually observed that in the hard-to-simulate regime, whereclassical computers cannot verify the goodness of the quantum simulator outcomes, it becomes of fundamental importance theproblem of how to certify the correct functioning of quantum devices [25]. Hence, a step forward in the investigation of thequantum computation potentialities was represented by the study of the eventual limits of this approach. Such obstacle willbe taken into account by using a scalable statistical test [26], proposed by the same authors of the BOSON SAMPLING, to

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discriminate sets of experimental data against the hypothesis that they are sampled from a fake, uniform distribution. Assumingthat, for each event, the n input photons occupy the set of modes S = {s1, s2, ..., sn} of the m-mode interferometer, describedby a m×m unitary matrix U , and leave the interferometer in the set of modes T = {t1, t2, ..., tn}, defining Ai,j = Usi,tj it hasbeen shown that the estimator

P =

n∏i=1

n∑j=1

|Ai,j |2

is correlated with the Boson Sampler probability associated with that event [26]. Intuitively, one expects to observe more high-probability than low-probability events, so the idea is to compare each event’s probability (or its efficiently computable estimatorP ) with what would be expected if the output distribution was uniform. The test decides the outcome is more likely to arisefrom Boson Sampling if P >

(nm

)n, otherwise the outcome is assigned to the uniform distribution. Further investigation will

be carried on to demonstrate the feasibility of discriminating experimental data taken with indistinguishable or distinguishableinput photons [27].

B. Reconfigurable Mach-Zehnder interferometer for photonic applications at telecom wavelength

BOSON SAMPLING problem promises to be a milestone in the development of quantum computation, showing that smallinstances of quantum simulators can solve problems that are hard for classical platforms. The inherent advantages of a quan-tum framework [2, 17] and the convenience of using photons to encode information [4, 7] have therefore recently drawn in-creasing attention to the field of quantum optics for the implementation of future quantum computers and networks [3]. Tofully take advantage of such capabilities, it is necessary to have available proper infrastructures supporting future quantum de-vices’functioning [3]. Ultimately, in order to design versatile and practical implementations, an essential feature of componentsof these networks would be also the capability of finely, dynamically controlling their functioning, so as to realize a tunabledevice for dynamic protocols and measurements [28–30]. However, currently available photonic components are still mainlyrestricted to wavelength windows different from the telecom one, for which optimal transfering is achieved.

For this purpose, in the second part of my research project I will experimentally work with the first realization of a reconfig-urable integrated Mach-Zehnder interferometer, designed for the very telecom wavelength 1550 nm, fabricated with femtosecondlaser writing technique.

Fig. 3 Schematic picture of the reconfigurable integrated Mach-Zehnder interferometer. Yellow wires bring current to the resistive heater for atunable phase modulation on the waveguide.

The output of a Mach-Zehnder interferometer depends on the difference between the phase delays accumulated in the twoarms (φ = ϕ1 − ϕ2). For coherent light injected in one input, interference fringes will be observed monitoring the intensity ofeither one of the two outputs, following:

Iout =Itot2

[1 + V cos (Φ0 + αP)]

where Itot is the sum of the intensities on the two outputs, V is the fringe visibility, Φ0 is a phase term present in the interfer-ometer when no power P is applied to the heater and α is a constant which depends on all the geometric, thermal and opticalproperties of the interferometers. In our case, with of ohmic resistive heaters, we can write P = ∆V 2/R, where ∆V is the im-posed voltage on the resistor and R the resistance value. The control over the phase inside the integrated device is thus obtainedthrough thermo-optic effect, by changing the current flowing in resistive heaters placed close to the waveguides.

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A complete characterization of this reconfigurable device will require single-photon and two-photon measurements to demon-strate its correct functioning. The tomography of the corresponding unitary transformation will be performed for different valuesof the phases φ, by applying recently proposed methods. Starting from single-photon probability measurements, or equivalentlyintensity measurements with classical light, and from two-photon interference Hong-Ou-Mandel experiments, the action of theunitary linear transformations can be retrieved by applying a suitable numerical [31], analytical [32] or hybrid [33] algorithm.

0 0.1 0.2 0.3 0.40.0

0.2

0.4

0.6

0.8

1.0

Dissipated power HWL

Norm

aliz

edco

inci

den

ces

Fig. 3 Experimental fringe pattern for a two-photon input |1, 1〉 as a function of the dissipated power. Blue points: normalized coincidencesof the output |1, 1〉, with one photon for each output port. Green points: normalized coincidences of the output |0, 2〉, with two photons in theoutput port 2. Both fringes show twice the periodicity of those for single photons (dashed red curve). Horizontal blue and green lines showestimated contributions of accidental coincidences.

C. New single-photon sources for experiments at telecom wavelength

Further developments are planned along this line. I am going to design and set up a new apparatus for more advancedexperiments of photonics at telecom wavelength. This apparatus will comprehend a single-photon source at 1550 nm, based onType-II spontaneous parametric down-conversion process in a nonlinear crystal, a bulk optics system for manipulating the stateof the photons, a new photonic integrated circuit and a system of detection. To enhance the efficiency in the SPDC generationprocess, a new choice in the nonlinear crystal employed is thought to be decisive. For this aim, periodically-poled nonlinearcrystals can offer better performances than the BiBO crystal used, thanks to their large values in the nonlinear tensor. Indeed,the final goal would be to exploit the higher efficiency in the generation rate to set up single-photon type-II SPDC sources fornew experiments with up to four photons. Ultimately, advanced researches are planned involving an improved version of thereconfigurable photonic integrated circuit for multi-photon quantum walk experiments, paving the way for broader, concreteapplications in several areas of quantum information theory.

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III. SCHOOLS AND CONFERENCES

Winter School on Quantum Physics and Quantum Information, Olomouc, 27-30 January 2014:Poster - ”Experimental realization of photonic Boson Sampling and efficient validation against uniform distribution”

PICQUE Scientific School in Integrated Photonic manipulation for Quantum applications, Varenna, 26-29 May 2014:Poster - ”Non-monotonic trend of bosonic coalescence within Boson Sampling architecture”

Italian Quantum Information Science Conference (IQIS2014), Salerno, 15-19 September 2014:Poster ”Efficient experimental validation of photonic Boson Sampling”

100o Congresso Nazionale SIF, Pisa, 22-26 September 2014:Talk - ”Experimental validation of photonic Boson Sampling”

PICQUE Scientific School in Integrated Quantum Photonics applications, from simulation to sensing:Talk - planned for 6-10 July 2015 in Rome.

QUTE-EUROPE Summer School 2015, Quantum Simulation and Computation:Poster - planned for 21-27 June, 2015 in Gothenburg, Sweden.

IV. PUBLICATIONS

• 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. Galvao, and F. Sciarrino, ”Experimental validation of photonic boson sampling”,Nature Photonics 8, 615 - 620 (2014).

• M. Bentivegna, N. Spagnolo, C. Vitelli, D. J. Brod, A. Crespi, F. Flamini, R. Ramponi, P. Mataloni, R. Osellame, E. F.Galvo, and F. Sciarrino, ”Bayesian approach to Boson sampling validation”, International Journal of Quantum Information12 (2015).

• M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D.J. Brod, E. F. Galvao,A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, ”Experimental Scattershot Boson Sampling”, to be published inScience Advances (2015).

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[10] A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. OBrien, Silica-on-Silicon Waveguide Quantum Circuits, Science 320, 646649 (2008).[11] D. Bonneau, M. Lobino, P. Jiang, C. Natarajan, M. Tanner, R. Hadfield, S. Dorenbos, V. Zwiller, M. Thompson, and J. OBrien, ”Fast

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[14] A. Crespi, R. Osellame, R. Ramponi, D. J. Brod, E. F. Galvao, N. Spagnolo, C. Vitelli, E. Maiorino, P. Mataloni, and F. Sciarrino,”Integrated multimode interferometers with arbitrary designs for photonic boson sampling,” Nature Photonics 7, 545-549 (2013).

[15] L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, R. Osellame, ”Two-particle bosonic-fermionic quantum walkvia integrated photonics,” Physical Review Letters 108, 010502 (2012).

[16] L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, R. Osellame, ”Polarization entangled states measurement on achip”, Phys. Rev. Lett. 105 (20), 200503 (2010).

[17] S. Aaronson and A. Arkhipov,”The computational complexity of linear optics”, Proceedings of the 43rd annual ACM symposium onTheory of computing 333, (2011).

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84 (1970).[23] K. R. Motes, J. P. Dowling, P. P. Rohde, ”Spontaneous parametric down-conversion photon sources are scalable in the asymptotic limit

for boson-sampling”, ArXiv:1307.8238 (2014).[24] A. Crespi, R. Osellame, R. Ramponi, D. J. Brod, E. F. Galvao, N. Spagnolo, C. Vitelli, E. Maiorino, P. Mataloni, F. Sciarrino, ”Integrated

multimode interferometers with arbitrary designs for photonic boson sampling”, Nature Photonics 7, 545 (2013).[25] C. Gogolin, M. Kliesch, L. Aolita, J. Eisert, ”Boson-Sampling in the light of sample complexity”, ArXiv:1306.3995 (2013).[26] S. Aaronson and A. Arkhipov, ”Boson Sampling is far from uniform,” ArXiv:1309.7460 (2013).[27] N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame,

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