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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Generalized suppression law for validation of Boson Sampling

Niko Viggianiello, Fulvio Flamini, Marco Bentivegna, Nicolò Spagnolo, Andrea Crespi, Daniel J. Brod, Ernesto F. Galvão, Luca Innocenti, Roberto Osellame, Fabio Sciarrino

Published Jun 1, 2017• 0 citations
Publisher

Abstract

Summary form only given. Recently, interference of multi-particle states has raised a strong interest in the scientific community, since it is believed to be at the very heart of post-classical computation. In this context, Boson Sampling [1] devices exploit multi-photon interference effects to provide evidence of a superior quantum computational power with current state-of-the-art technology. Thus, the capability to correctly certify the presence of multi-particle interference and find optimal platforms, becomes a crucial task because is expected to find numerous applications in photonic quantum information as a diagnostic tool for quantum optical devices.We investigate different scenarios, namely, when the consider only a fixed set of input modes, but also for the situation where all input sets can be used. We find that, in certain cases, the best choice for this task consist of Hadamard [2,3] interferometers which we implemented with a novel architecture enabled by the 3D capabilities of femtosecond laser writing. We derive and experimentally demonstrate a novel zero-transmission law based on symmetric interferometers (Fig. 1) and we verifyied the optimality of these platforms by performing further Bayesian analysis and by maximizing the total variation distance between the probability distributions corresponding to indistinguishable and distinguishable particles. The results suggest an immediate application for scattershot Boson Sampling experiments [4], where an exponential advantage in terms of generation rate is obtained with respect to the fixed-input problem. The main advantage of this technique consists in the large fraction of input-output suppressed combinations when these trasformations are injected with indistinguishable photons. In summary, this work represents a further step for quantum interference analysis and it is worth noting that Hadamard matrices naturally appear as the optimal designs for identifying genuine photonic indistinguishability in multimode interferometers and a powerful tool to validate Boson Sampling experiments. We aknowledge QUCHIP and 3D-Quest for funding this work.

DOI
10.1109/cleoe-eqec.2017.8087431

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Summary form only given. Recently, interference of multi-particle states has raised a strong interest in the scientific community, since it is believed to be at the very heart of post-classical computation. In this context, Boson Sampling [1] devices exploit multi-photon interference effects to provide evidence of a superior quantum computational power with current state-of-the-art technology. Thus, the capability to correctly certify the presence of multi-particle interference and find optimal platforms, becomes a crucial task because is expected to find numerous applications in photonic quantum information as a diagnostic tool for quantum optical devices.We investigate different scenarios, namely, when the consider only a fixed set of input modes, but also for the situation where all input sets can be used. We find that, in certain cases, the best choice for this task consist of Hadamard [2,3] interferometers which we implemented with a novel architecture enabled by the 3D capabilities of femtosecond laser writing. We derive and experimentally demonstrate a novel zero-transmission law based on symmetric interferometers (Fig. 1) and we verifyied the optimality of these platforms by performing further Bayesian analysis and by maximizing the total variation distance between the probability distributions corresponding to indistinguishable and distinguishable particles. The results suggest an immediate application for scattershot Boson Sampling experiments [4], where an exponential advantage in terms of generation rate is obtained with respect to the fixed-input problem. The main advantage of this technique consists in the large fraction of input-output suppressed combinations when these trasformations are injected with indistinguishable photons. In summary, this work represents a further step for quantum interference analysis and it is worth noting that Hadamard matrices naturally appear as the optimal designs for identifying genuine photonic indistinguishability in multimode interferometers and a powerful tool to validate Boson Sampling experiments. We aknowledge QUCHIP and 3D-Quest for funding this work.
The Boson sampling problem consists in sampling from the output probability distribution of a bosonic Fock state, after it evolves through a linear interferometer. There is strong evidence that Boson sampling is computationally hard for classical computers, while it can be solved naturally by bosons. This has led it to draw increasing attention as a possible way to provide experimental evidence for the quantum computational supremacy. Nevertheless, the very complexity of the problem makes it hard to exclude the hypothesis that the experimental data are sampled from a different probability distribution. By exploiting integrated quantum photonics, we have carried out a set of three-photon Boson sampling experiments and analyzed the results using a Bayesian approach, showing that it represents a valid alternative to currently used methods. We adopt this approach to provide evidence that the experimental data correspond to genuine three-photon interference, validating the results against fully and partially-distinguishable photon hypotheses.
Photonic interference is a key quantum resource for optical quantum computation, and in particular for so-called boson sampling devices. In interferometers with certain symmetries, genuine multiphoton quantum interference effectively suppresses certain sets of events, as in the original Hong–Ou–Mandel effect. Recently, it was shown that some classical and semi-classical models could be ruled out by identifying such suppressions in Fourier interferometers. Here we propose a suppression law suitable for random-input experiments in multimode Sylvester interferometers, and verify it experimentally using 4- and 8-mode integrated interferometers. The observed suppression occurs for a much larger fraction of input–output combinations than what is observed in Fourier interferometers of the same size, and could be relevant to certification of boson sampling machines and other experiments relying on bosonic interference, such as quantum simulation and quantum metrology.
Particle indistinguishability is at the heart of quantum statistics that regulates fundamental phenomena such as the electronic band structure of solids, Bose-Einstein condensation and superconductivity. Moreover, it is necessary in practical applications such as linear optical quantum computation and simulation, in particular for Boson Sampling devices. It is thus crucial to develop tools to certify genuine multiphoton interference between multiple sources. Our approach employs the total variation distance to find those transformations that minimize the error probability in discriminating the behaviors of distinguishable and indistinguishable photons. In particular, we show that so-called Sylvester interferometers are near-optimal for this task. By using Bayesian tests and inference, we numerically show that Sylvester transformations largely outperform most Haar-random unitaries in terms of sample size required. Furthermore, we experimentally demonstrate the efficacy of the transformation using an efficient 3D integrated circuits in the single- and multiple-source cases. We then discuss the extension of this approach to a larger number of photons and modes. These results open the way to the application of Sylvester interferometers for optimal assessment of multiphoton interference experiments.
The investigation of multi-photon quantum interference in symmetric multi-port splitters has both fundamental and applicative interest. Destructive quantum interference in devices with specific symmetry leads to the suppression of a large number of possible output states, generalizing the Hong-Ou-Mandel effect; simple suppression laws have been developed for interferometers implementing the Fourier or the Hadamard transform over the modes. In fact, these enhanced interference features in the output distribution can be used to assess the indistinguishability of single-photon sources, and symmetric interferometers have been envisaged as benchmark or validation devices for Boson-Sampling machines. In this work we devise an innovative approach to implement symmetric multi-mode interferometers that realize the Fourier and Hadamard transform over the optical modes, exploiting integrated waveguide circuits. Our design is based on the optical implementations of the Fast-Fourier and Fast-Hadamard transform algorithms, and exploits a novel three-dimensional layout which is made possible by the unique capabilities of femtosecond laser waveguide writing. We fabricate devices with m = 4 and m = 8 modes and we let two identical photons evolve in the circuit. By characterizing the coincidence output distribution we are able to observe experimentally the known suppression laws for the output states. In particular, we characterize the robustness of this approach to assess the photons' indistinguishability and to rule out alternative non-quantum states of light. The reported results pave the way to the adoption of symmetric multiport interferometers as pivotal tools in the diagnostics and certification of quantum photonic platforms.
The progressive development of quantum technologies in many areas, ranging from investigation on foundamentals of quantum of mechanics to quantum information and computation, has increased the interest on those problems that can exhibit a quantum advantage. The Boson Sampling problem is a clear example where traditional computers fail in the task of sampling from the distribution of n indistinguishable photons after a propagation in a m-mode optical interferometer. In this context, in the absence of classical algorithms able to simulate efficiently multi-photon interference, the validation of Boson Sampling is still an open problem. Here we investigate a novel approach to Boson Sampling validation based on statistical properties of correlation functions. In particular we discuss its feasibility in actual proof-of-principle experiments. Furthermore we provide an extensive study of the physical resources required to validate experiments, investigating also the role of bosonic bunching in high-dimensional applications. Our investigation confirms the goodness of the validation protocol, paving the way to use this toolbox for the validation of Boson Sampling devices.
Quantum interference of correlated particles is a fundamental quantum phenomenon which carries signatures of the statistics properties of the particles, such as bunching or antibunching. In the presence of particular symmetries, interference effects take place with high visibility, one of the simplest cases being the suppression of coincident detection in the Hong-Ou-Mandel effect. Tichy et al., [Phys. Rev. Lett. 104, 220405 (2010)] recently demonstrated a simple sufficient criterion for the suppression of output events in the more general case of Fourier multiport beam splitters. Here we study the case in which 2q{2}^{q}2q particles (either bosonic or fermionic) are injected simultaneously in different ports of a Sylvester interferometer with ${2}^{p}\ensuremath{\ge}{2}^{q}$ modes. In particular, we prove a necessary and sufficient criterion for a significant fraction of output states to be suppressed, for specific input configurations. This may find application in assessing the indistinguishability of multiple single-photon sources and in the validation of boson sampling machines.