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QUantum advantage via non-linear BOSon Sampling

Periodic Reporting for period 2 - QU-BOSS (QUantum advantage via non-linear BOSon Sampling)

Reporting period: 2022-02-01 to 2023-07-31

After decades of progress in quantum information science, it is widely expected that in the next few years the field will start to yield practical applications in quantum chemistry, materials and pharmaceutical research, information security, and finance. For these applications to pan out, a crucial intermediate goal is to reach the quantum advantage regime, where quantum devices experimentally outperform classical computers in some computational tasks. The Boson Sampling problem is a specific computational task that is hard for classical computers, but which can be solved with a specialised quantum device using single photons interfering in a multimode linear interferometer. Pushing towards the quantum advantage regime will undoubtedly allow us to develop new algorithms which cannot be developed by our current technological capabilities. The aim of QU-BOSS project is to experimentally push towards the quantum advantage regime with integrated photonic technology. These integrated devices have several characteristics such as transportability, compactness, stability and reconfigurability thus representing a technology that will certainly fit in the future research and applications. The key innovative ingredient of QU-BOSS is the introduction of non-linearities acting at the single photon level embedded within the Boson Sampling interferometer. This new feature will be shown to boost the complexity of the corresponding classical simulation and will provide a new perspective to address several current problems and protocols. Furthermore, the QU-BOSS project aims at establishing further connections between Boson Sampling with non-linearities and machine learning approaches.
The activities of project QU-BOSS are divided into three main Workpackages. WP1 is dedicated to the development of the Non-linear Boson Sampling approach for quantum advantage. WP2 then focuses on the photonics architectures necessary for the implementation of such a novel paradigm. Finally, WP3 is dedicated to the development of quantum machine learning approaches via the non-linear Boson Sampling approach. Since the beginning of the project several work has been performed in all three workpackages, leading to results ranging from scientific publications in high-impact journals, the construction of a dedicated laboratory and the hiring of a researcher devoted to the project. Dissemination activities have been carried out also for the general public, such as the Italian quantum week initiative that has involved around 750 people only at the University of Rome.

Let us highlight the main scientific results.

- The new laboratory facility dedicated to the QU-BOSS activities has been completed: two quantum dots are installed and have been characterised to their exploitation for the research activities. This achievement allows not only to progress in the scientific direction but also to train new Master and PhD students.

- A theoretical publication entitled “Non-linear Boson Sampling” connected to the main argument of the project has been published by the journal npj Quantum Information. This paper has established a novel framework through a newly defined variant of the original Boson Sampling problem, that can open new perspectives both for lowering the quantum advantage threshold and for defining novel applications of this computational model.
[Spag23] N. Spagnolo, et al., npj Quantum Information 9, 3 (2023)

- In the manuscript “Deep reinforcement learning for quantum multiparameter estimation”, Advanced Photonics, 5, Issue 1, 016005 (2023)” We have implemented a fully-automated procedure based on a machine-learning approach for the calibration and operation of a generic quantum sensor, without requiring an a-priori complete modelling of the system. This paper has been highlighted by SPIE (link: https://spie.org/news/deep-learning-for-quantum-sensing?SSO=1).
[Cimi23] V. Cimini et al., Advanced Photonics 5, 016005 (2023).

- Two review papers on integrated quantum photonics in the different fields of quantum technologies have been published:
[Pelu22] E. Pelucchi, et al., Nature Reviews Physics 4, 194-208 (2022)
[Gior23] T. Giordani et al., La Rivista del Nuovo Cimento 46, 71-103 (2023).

Other work has been carried out towards the final objective of the project. Besides the definition of the non-linear Boson Sampling as a new route to achieve quantum advantage, a fundamental requirement is to develop appropriate methods for the certification of quantum operation in devices solving such a class of problems. We have performed several work in this direction [Gior21a,Gior22,Flam20], by establishing and testing new validation methods based on the connections between sampling problems and graph theory, and by devising a novel family of coherence and indistinguishability witness tests for multiphoton inputs. Indeed, testing photon indistinguishability is at the basis of any validation protocol designed to rely on multiphoton interference as the fundamental resources. Further work have been also carried out to apply machine learning approaches for the generation and detection of d-dimensional states via quantum walk architectures [Gior21,Supr21,Zia23], and to test architectures for quantum networks [Pode22,Poli23a,Poli23b,Supr22].

Other main publications are:
[Flam20] F. Flamini, et al., Quantum Science and Technology 5, 045005 (2020).
[Gior21] T. Giordani et al., New Journal of Physics 23 023012 (2021).
[Gior21a] T. Giordani, et al., Physical Review Research 3, 023031 (2021).
[Gior22] T. Giordani, et al., Quantum Science and Technology 8, 015005 (2022)
[Pode22] D. Poderini et al.,. Physical Review Research 4, 013159 (2022).
[Poli23a] E. Polino et al., Nature Communications 14, 909 (2023).
[Poli23b] E. Polino et al., Europhysics News 54/1, 28–31 (2023).
[Supr22] A. Suprano et al., PRX Quantum 3, 030342 (2022).
[Supr21] A. Suprano et al., Advanced Photonics 3, 066002 (2021).
[Zia23] D. Zia et al., Physical Review Research 5, 013142 (2023).
The activities detailed above have led to several progress beyond the state-of-the-art.
On a first note, the work carried out for the formal definition of the non-linear Boson Sampling paradigm, provided a first outline of the effect of the introduction of non-linear photon-photon interactions on the complexity of Boson Sampling. In particular, we have identified the cost involved in simulating on-linear Boson Sampling using linear optics and postselection, and we constructively use linear-optical simulation techniques to perform such a simulation. This result provides constructive support to the complexity of the non-linear Boson Sampling problem. Such a model provides a novel route towards achievement of the quantum advantage regime in photonic systems. Furthermore, given the more general functionalities that can be implemented by a quantum device solving such a problem, with respect to those tackling the original Boson Sampling problem, we also expect that further connections with machine learning approaches can be identified in the future project development.

Results on validation of Boson Sampling have also been obtained. More specifically, we have investigated the certification of the Gaussian Boson Sampling variant via connections with graph theory, and also assessed validation of Boson Sampling in the finite sample regime. Furthermore, we have demonstrated a class of coherence witnesses for multiphoton indistinguishability, an essential ingredient in all sampling problems that require genuine quantum interference between multiple photon inputs. These results will be part of the verification toolbox for the non-linear Boson Sampling problem, and may be the basis for future demonstrations using the devices developed in the QU-BOSS project.

Within this project, improvement of the technological photonic platform has been achieved, by developing new processes and approaches, as well as by designing new nonlinear waveguides that will be exploited for on-chip sources. In synthesis, we have significantly improved the propagation losses, the number of modes and the reconfigurability of multimode integrated photonic processors employed within the project.
Finally, important steps towards hybrid quantum computing enhanced by non-linear Boson Sampling and photonics architectures for quantum machine learning have been obtained. In particular, we have contributed with a theoretical study and an experimental proposal to attain entangled states of d-dimensional systems through a quantum walk, providing general conditions for the accumulation and retrieval of entanglement. Furthermore, we have investigated machine learning approaches for classification of such kinds of d-dimensional systems. Moreover, it has been possible to experimentally implement a fully automated approach based on deep reinforcement learning for multiphase estimation, enabling both calibration of the sensor and application of adaptive protocols without the need of an apriori system modelling. This latter results represents an important step towards efficient adoption of practical quantum sensors for quantum metrology in noisy conditions and in the finite resource regime.

Finally, important steps towards hybrid quantum computing enhanced by non-linear Boson Sampling and photonics architectures for quantum machine learning have been obtained. In particular, we have contributed with a theoretical study and an experimental proposal to attain entangled states of d-dimensional systems through a quantum walk, providing general conditions for the accumulation and retrieval of entanglement. Furthermore, we have investigated machine learning approaches for classification of such kinds of d-dimensional systems. Moreover, it has been possible to experimentally implement a fully automated approach based on deep reinforcement learning for multiphase estimation, enabling both calibration of the sensor and application of adaptive protocols without the need of an apriori system modelling. This latter results represents an important step towards efficient adoption of practical quantum sensors for quantum metrology in noisy conditions and in the finite resource regime.