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Moving-boundary work, also called pressure-volume work or expansion work, is perhaps the main form of work discussed in introductory courses about Thermodynamics. Here, we take a particular definition of this kind of thermodynamic work. On this basis, we show with simple reasoning that significant phenomena involving dissipation of mechanical energy, often mentioned as well in those courses but with a vague formalization, can be traced back right to moving-boundary processes. We refer in particular to the conversion of external work into internal energy in paddle-wheel experiments such as the one conducted by J.P.Joule in 1850, and to other processes involving friction.

In the current era of noisy intermediate-scale quantum computers, variational quantum algorithms represent one of the most viable approaches for their application to solve tasks of interest. These algorithms train a parameterized quantum circuit to execute a specific task encoded in a cost function that needs to be minimized using a classical optimizer. In this context, photonic platforms based on reconfigurable integrated optics appear as one of the prominent platforms for the implementation of variational algorithms. In the circuital model of quantum computation based on qubits, to train variational circuits, the parameter shift rule came into being, which allows for the exact calculation of the derivatives of many functions at the output of a quantum circuit, opening up the possibility of using classical optimisation algorithms based on gradient descent. In this paper, we derive a formulation of the parameter shift rule for reconfigurable optical linear circuits based on the Boson Sampling paradigm. This allows us to naturally embed the common types of experimental noise, such as partial distinguishability, and mixedness of the states, thus obtaining a resilient approach. We also present similar rules for the computations of integrals over the variational parameters. Finally, we employ the developed approach to experimentally test variational algorithms with single-photon states processed in a reconfigurable 6-mode universal integrated interferometer. Specifically, we apply the photonic parameter shift rules to the variational implementation, on a photonic platform, of both an eigensolver and a Universal-Not gate., Comment: 10 pages, 4 figures

Generation and manipulation of randomness is a relevant task for several applications of information technology. It has been shown that quantum mechanics offers some advantages for this type of task. A promising model for randomness manipulation is provided by the Bernoulli factories, protocols capable of changing the bias of Bernoulli random processes in a controlled way. At first, this framework was proposed and investigated in a fully classical regime. Recent extensions of this model to the quantum case showed the possibility of implementing a wider class of randomness manipulation functions. We propose a Bernoulli factory scheme with quantum states as input and output, using a photonic path-encoding approach. Our scheme is modular, universal, and its functioning is truly oblivious of the input bias, characteristics that were missing in earlier work. We report on experimental implementations using an integrated and fully programmable photonic platform, thus demonstrating the viability of our approach. These results open new paths for randomness manipulation with integrated quantum technologies.

Quantum computing has brought a paradigm change in computer science, where non-classical technologies have promised to outperform their classical counterpart. Such an advantage was only demonstrated for tasks without practical applications, still out of reach for the state-of-art quantum technologies. In this context, a promising strategy to find practical use of quantum computers is to exploit hybrid quantum-classical models, where a quantum device estimates a hard-to-compute quantity, while a classical optimizer trains the parameters of the model. In this work, we demonstrate that single photons and linear optical networks are sufficient for implementing Variational Quantum Algorithms, when the problem specification, or ansatz, is tailored to this specific platform. We show this by a proof-of-principle demonstration of a variational approach to tackle an instance of a factorization task, whose solution is encoded in the ground state of a suitable Hamiltonian. This work which combines Variational Quantum Algorithms with hardware efficient ansatzes for linear-optics networks showcases a promising pathway towards practical applications for photonic quantum platforms.

Recently, machine learning had a remarkable impact, from scientific to everyday-life applications. However, complex tasks often imply unfeasible energy and computational power consumption. Quantum computation might lower such requirements, although it is unclear whether enhancements are reachable by current technologies. Here, we demonstrate a kernel method on a photonic integrated processor to perform a binary classification. We show that our protocol outperforms state-of-the-art kernel methods including gaussian and neural tangent kernels, exploiting quantum interference, and brings a smaller improvement also by single photon coherence. Our scheme does not require entangling gates and can modify the system dimension through additional modes and injected photons. This result opens to more efficient algorithms and to formulating tasks where quantum effects improve standard methods.

A seminal task in quantum information theory is to realize a device able to produce copies of a generic input state with the highest possible output fidelity, thus realizing an \textit{optimal} quantum cloning machine. Recently, the concept of variational quantum cloning was introduced: a quantum machine learning algorithm through which, by exploiting a classical feedback loop informed by the output of a quantum processing unit, the system can self-learn the programming required for an optimal quantum cloning strategy. In this work, we experimentally implement a $1 \rightarrow 2$ variational cloning machine of dual-rail encoded photonic qubits, both for phase-covariant and state-dependent cloning. We exploit a fully programmable 6-mode universal integrated device and classical feedback to reach near-optimal cloning performances. Our results demonstrate the potential of programmable integrated photonic platforms for variational self-learning of quantum algorithms., Comment: 9 pages, 4 figures

Waveguide-based interferometric circuits are widely employed in optical communications, sensing and computing applications. In particular, glass-based devices are appealing due to the transparency and bio-compatibility of this substrate, or where low-loss interfacing with fiber networks is required. However, fast electro-optic phase modulation is hard to achieve in glass materials. Here, we demonstrate an optical phase and intensity modulator in glass, working in the megahertz range. This modulator exploits the elasto-optic effect inside a mechanical microstructure, brought to oscillation at resonance, and is entirely realized by femtosecond laser micromachining. In detail, we demonstrate 23-dB optical intensity modulation at 1.17 MHz, with an internal optical loss of the phase-modulator component as low as 0.04 dB., Comment: Raw data of the graphs reported in the figures are publicly available on Zenodo (https://doi.org/10.5281/zenodo.11354220)

Quantum superposition of high-dimensional states enables both computational speed-up and security in cryptographic protocols. However, the exponential complexity of tomographic processes makes certification of these properties a challenging task. In this work, we experimentally certify coherence witnesses tailored for quantum systems of increasing dimension, using pairwise overlap measurements enabled by a six-mode universal photonic processor fabricated with a femtosecond laser writing technology. In particular, we show the effectiveness of the proposed coherence and dimension witnesses for qudits of dimensions up to 5. We also demonstrate advantage in a quantum interrogation task, and show it is fueled by quantum contextuality. Our experimental results testify to the efficiency of this novel approach for the certification of quantum properties in programmable integrated photonic platforms, Comment: 9 pages, 5 figures + Supplementary Information

Universal photonic processors (UPPs) are fully programmable photonic integrated circuits that are key components in quantum photonics. With this work, we present a novel platform for the realization of low-loss, low-power and high-fidelity UPPs based on femtosecond laser writing (FLW) and compatible with a large wavelength spectrum. In fact, we demonstrate different UPPs, tailored for operation at 785 nm and 1550 nm, providing similar high-level performances. Moreover, we show that standard calibration techniques applied to FLW-UPPs result in Haar random polarization independent photonic transformations implemented with average amplitude fidelity as high as 0.9979 at 785 nm (0.9970 at 1550 nm), with the possibility of increasing the fidelity over 0.9990 thanks to novel optimization algorithms. Besides being the first demonstrations of polarization-transparent UPPs, these devices show the highest level of control and reconfigurability ever reported for a FLW circuit. These qualities will be greatly beneficial to applications in quantum information processing.

Multi-mode optical interferometers represent the most viable platforms for the successful implementation of several quantum information schemes that take advantage of optical processing. Examples range from quantum communication, sensing and computation, including optical neural networks, optical reservoir computing or simulation of complex physical systems. The realization of such routines requires high levels of control and tunability of the parameters that define the operations carried out by the device. This requirement becomes particularly crucial in light of recent technological improvements in integrated photonic technologies, which enable the implementation of progressively larger circuits embedding a considerable amount of tunable parameters. In this work, we formulate efficient procedures for the characterization of optical circuits in the presence of imperfections that typically occur in physical experiments, such as unbalanced losses and phase instabilities in the input and output collection stages. The algorithm aims at reconstructing the transfer matrix that represents the optical interferometer without making any strong assumptions about its internal structure and encoding. We show the viability of this approach in an experimentally relevant scenario, defined by a tunable integrated photonic circuit, and we demonstrate the effectiveness and robustness of our method. Our findings can find application in a wide range of optical setups, based both on bulk and integrated configurations., Comment: 18 pages, 5 figures

Quantum parameter estimation offers solid conceptual grounds for the design of sensors enjoying quantum advantage. This is realised not only by means of hardware supporting and exploiting quantum properties, but data analysis has its impact and relevance, too. In this respect, Bayesian methods have emerged as an effective and elegant solution, with the perk of incorporating naturally the availability of a priori information. In this article we present an evaluation of Bayesian methods for multiple phase estimation, assessed based on bounds that work beyond the usual limit of large samples assumed in parameter estimation. Importantly, such methods are applied to experimental data generated from the output statistics of a three-arm interferometer seeded by single photons. Our studies provide a blueprint for a more comprehensive data analysis in quantum metrology., Comment: 8 pages, 6 figures

Quantum key distribution (QKD) is nowadays a well established method for generating secret keys at a distance in an information-theoretic secure way, as the secrecy of QKD relies on the laws of quantum physics and not computational complexity. In order to industrialize QKD, low-cost, mass-manufactured and practical QKD setups are required. Hence, photonic and electronic integration of the sender's and receiver's respective components is currently in the spotlight. Here we present a high-speed (2.5 GHz) integrated QKD setup featuring a transmitter chip in silicon photonics allowing for high-speed modulation and accurate state preparation, as well as a polarization-independent low-loss receiver chip in aluminum borosilicate glass fabricated by the femtosecond laser micromachining technique. Our system achieves raw bit error rates, quantum bit error rates and secret key rates equivalent to a much more complex state-of-the-art setup based on discrete components.

We report on a universal method to measure the genuine indistinguishability of n-photons - a crucial parameter that determines the accuracy of optical quantum computing. Our approach relies on a low-depth cyclic multiport interferometer with N = 2n modes, leading to a quantum interference fringe whose visibility is a direct measurement of the genuine n-photon indistinguishability. We experimentally demonstrate this technique for a 8-mode integrated interferometer fabricated using femtosecond laser micromachining and four photons from a quantum dot single-photon source. We measure a four-photon indistinguishability up to 0.81$\pm$0.03. This value decreases as we intentionally alter the photon pairwise indistinguishability. The low-depth and low-loss multiport interferometer design provides an efficient and scalable path to evaluate the genuine indistinguishability of resource states of increasing photon number.

Integrated quantum photonics, i.e. the generation, manipulation and detection of quantum states of light in integrated photonic chips, is revolutionizing the field of quantum information in all applications, from communications to computing. Although many different platforms are being currently developed, from silicon photonics to lithium niobate photonic circuits, none of them has shown the versatility of femtosecond laser micromachining (FLM) in producing all the components of a complete quantum system, encompassing quantum sources, reconfigurable state manipulation, quantum memories and detection. It is in fact evident that FLM has been a key enabling tool in the first-time demonstration of many quantum devices and functionalities. Although FLM cannot achieve the same level of miniaturization of other platforms, it still has many unique advantages for integrated quantum photonics. In particular, in the last five years, FLM has greatly expanded its range of quantum applications with several scientific breakthroughs achieved. For these reasons, we believe that a review article on this topic is very timely and could further promote the development of this field by convincing end-users of the great potentials of this technological platform and by stimulating more research groups in FLM to direct their efforts to the exciting field of quantum technologies., Comment: 23 pages, 6 figures, to be published in Nanophotonics, De Gruyter

Boson Sampling is a computational paradigm representing one of the most viable and pursued approaches to demonstrate the regime of quantum advantage. Recent results have demonstrated significant technological leaps in single-photon generation and detection, leading to progressively larger experimental instances of Boson Sampling experiments in different photonic systems. However, a crucial requirement for a fully-fledged platform solving this problem is the capability of implementing large-scale interferometers, that must simultaneously exhibit low losses, high degree of reconfigurability and the realization of arbitrary transformations. In this work, we move a step forward in this direction by demonstrating the adoption of a compact and reconfigurable 3D-integrated platform for photonic Boson Sampling. We perform 3- and 4-photon experiments by using such platform, showing the possibility of programming the circuit to implement a large number of unitary transformations. These results show that such compact and highly-reconfigurable layout can be scaled up to experiments with larger number of photons and modes, and can provide a viable direction for hybrid computing with photonic processors., Comment: 17 pages, 15 figures

Quantum computer technology harnesses the features of quantum physics for revolutionizing information processing and computing. As such, quantum computers use physical quantum gates that process information unitarily, even though the final computing steps might be measurement-based or non-unitary. The applications of quantum computers cover diverse areas, reaching from well-known quantum algorithms to quantum machine learning and quantum neural networks. The last of these is of particular interest by belonging to the promising field of artificial intelligence. However, quantum neural networks are technologically challenging as the underlying computation requires non-unitary operations for mimicking the behavior of neurons. A landmark development for classical neural networks was the realization of memory-resistors, or "memristors". These are passive circuit elements that keep a memory of their past states in the form of a resistive hysteresis and thus provide access to nonlinear gate operations. The quest for realising a quantum memristor led to a few proposals, all of which face limited technological practicality. Here we introduce and experimentally demonstrate a novel quantum-optical memristor that is based on integrated photonics and acts on single photons. We characterize its memristive behavior and underline the practical potential of our device by numerically simulating instances of quantum reservoir computing, where we predict an advantage in the use of our quantum memristor over classical architectures. Given recent progress in the realization of photonic circuits for neural networks applications, our device could become a building block of immediate and near-term quantum neuromorphic architectures., Comment: First revision

Multi-particle interference is an essential ingredient for fundamental quantum mechanics phenomena and for quantum information processing to provide a computational advantage, as recently emphasized by Boson Sampling experiments. Hence, developing a reliable and efficient technique to witness its presence is pivotal towards the practical implementation of quantum technologies. Here we experimentally identify genuine many-body quantum interference via a recent efficient protocol, which exploits statistical signatures at the output of a multimode quantum device. We successfully apply the test to validate three-photon experiments in an integrated photonic circuit, providing an extensive analysis on the resources required to perform it. Moreover, drawing upon established techniques of machine learning, we show how such tools help to identify the - a priori unknown - optimal features to witness these signatures. Our results provide evidence on the efficacy and feasibility of the method, paving the way for its adoption in large-scale implementations., Comment: 15 pages, 12 figures

Calibration of sensors is a fundamental step to validate their operation. This can be a demanding task, as it relies on acquiring a detailed modelling of the device, aggravated by its possible dependence upon multiple parameters. Machine learning provides a handy solution to this issue, operating a mapping between the parameters and the device response, without needing additional specific information on its functioning. Here we demonstrate the application of a Neural Network based algorithm for the calibration of integrated photonic devices depending on two parameters. We show that a reliable characterization is achievable by carefully selecting an appropriate network training strategy. These results show the viability of this approach as an effective tool for the multiparameter calibration of sensors characterized by complex transduction functions.

Achieving ultimate bounds in estimation processes is the main objective of quantum metrology. In this context, several problems require measurement of multiple parameters by employing only a limited amount of resources. To this end, adaptive protocols, exploiting additional control parameters, provide a tool to optimize the performance of a quantum sensor to work in such limited data regime. Finding the optimal strategies to tune the control parameters during the estimation process is a non-trivial problem, and machine learning techniques are a natural solution to address such task. Here, we investigate and implement experimentally for the first time an adaptive Bayesian multiparameter estimation technique tailored to reach optimal performances with very limited data. We employ a compact and flexible integrated photonic circuit, fabricated by femtosecond laser writing, which allows to implement different strategies with high degree of control. The obtained results show that adaptive strategies can become a viable approach for realistic sensors working with a limited amount of resources., Comment: 10+4 pages, 6+2 figures

Femtosecond laser writing is a powerful technique that allows rapid and cost-effective fabrication of photonic integrated circuits with unique three-dimensional geometries. In particular, the possibility to reconfigure such devices by thermo-optic phase shifters represents a paramount feature, exploited to produce adaptive and programmable circuits. However, the scalability is strongly limited by the flaws of current thermal phase shifters, which require hundreds of milliwatts to operate and exhibit large thermal crosstalk. In this work, thermally-insulating three-dimensional microstructures are exploited to decrease the power needed to induce a 2{\pi} phase shift down to 37 mW and to reduce the crosstalk to a few percent. Further improvement is demonstrated when operating in vacuum, with sub-milliwatt power dissipation and negligible crosstalk. These results pave the way towards the demonstration of complex programmable integrated photonic circuits fabricated by femtosecond laser writing, thus opening exciting perspectives in integrated quantum photonics.

Multiparameter estimation is a general problem that aims at measuring unknown physical quantities, obtaining high precision in the process. In this context, the adoption of quantum resources promises a substantial boost in the achievable performances with respect to the classical case. However, several open problems remain to be addressed in the multiparameter scenario. A crucial requirement is the identification of suitable platforms to develop and experimentally test novel efficient methodologies that can be employed in this general framework. We report the experimental implementation of a reconfigurable integrated multimode interferometer designed for the simultaneous estimation of two optical phases. We verify the high-fidelity operation of the implemented device, and demonstrate quantum-enhanced performances in two-phase estimation with respect to the best classical case, post-selected to the number of detected coincidences. This device can be employed to test general adaptive multiphase protocols due to its high reconfigurability level, and represents a powerful platform to investigate the multiparameter estimation scenario., Comment: 10+7 pages, 7+4 figures

Topological insulators are materials that have a gapped bulk energy spectrum, but contain protected in-gap states appearing at their surface. These states exhibit remarkable properties such as unidirectional propagation and robustness to noise that offer an opportunity to improve the performance and scalability of quantum technologies. For quantum applications, it is essential that the topological states are indistinguishable. Here we report high-visibility quantum interference of single photon topological states in an integrated photonic circuit. Two topological boundary-states, initially at opposite edges of a coupled waveguide array, are brought into proximity, where they interfere and undergo a beamsplitter operation. We observe $93.1\pm2.8\%$ visibility Hong-Ou-Mandel (HOM) interference, a hallmark non-classical effect that is at the heart of linear optics-based quantum computation. Our work shows that it is feasible to generate and control highly indistinguishable single photon topological states, opening pathways to enhanced photonic quantum technology with topological properties, and to study quantum effects in topological materials.

The decay of an unstable system is usually described by an exponential law. Quantum mechanics predicts strong deviations of the survival probability from the exponential: indeed, the decay is initially quadratic, while at very large times it follows a power law, with superimposed oscillations. The latter regime is particularly elusive and difficult to observe. Here we employ arrays of single-mode optical waveguides, fabricated by femtosecond laser direct inscription, to implement quantum systems where a discrete state is coupled and can decay into a continuum. The optical modes correspond to distinct quantum states of the photon and the temporal evolution of the quantum system is mapped into the spatial propagation coordinate. By injecting coherent light states in the fabricated photonic structures and by measuring light with an unprecedented dynamic range, we are able to experimentally observe not only the exponential decay regime, but also the quadratic Zeno region and the power-law decay at long evolution times.

We study analytically the polarization behaviour of directional couplers composed of birefringent waveguides, showing that they can induce polarization transformations that depend on the specific input-output path considered. On the basis of this study, we propose and demonstrate experimentally, by femtosecond laser writing, directional couplers that are free from this problem and also yield a polarization independent power-splitting ratio. More in detail, we devise two different approaches to realize such devices: the first one is based on local birefringence engineering, while the second one exploits ultra-low birefringence waveguides obtained by thermal annealing.

The difficulty of validating large-scale quantum devices, such as Boson Samplers, poses a major challenge for any research program that aims to show quantum advantages over classical hardware. To address this problem, we propose a novel data-driven approach wherein models are trained to identify common pathologies using unsupervised machine learning methods. We illustrate this idea by training a classifier that exploits K-means clustering to distinguish between Boson Samplers that use indistinguishable photons from those that do not. We train the model on numerical simulations of small-scale Boson Samplers and then validate the pattern recognition technique on larger numerical simulations as well as on photonic chips in both traditional Boson Sampling and scattershot experiments. The effectiveness of such method relies on particle-type-dependent internal correlations present in the output distributions. This approach performs substantially better on the test data than previous methods and underscores the ability to further generalize its operation beyond the scope of the examples that it was trained on., Comment: 11+5 pages, 5+4 figures

Photon entanglement is an important state of light that is at the basis of many protocols in photonic quantum technologies, from quantum computing, to simulation and sensing. The capability to generate entangled photons in integrated waveguide sources is particularly advantageous due to the enhanced stability and more efficient light-crystal interaction. Here we realize an integrated optical source of entangled degenerate photons at telecom wavelength, based on the hybrid interfacing of photonic circuits in different materials, all inscribed by femtosecond laser pulses. We show that our source, based on spontaneous parametric down-conversion, gives access to different classes of output states, allowing to switch from path-entangled to polarization-entangled states with net visibilities above 0.92 for all selected combinations of integrated devices.

We design and demonstrate on-chip homodyne detection operating in the quantum regime, i.e. able to detect genuine nonclassical features. Our setup exploits a glass-integrated homodyne analyzer (IHA) entirely fabricated by femtosecond laser micromachining. The IHA incorporates on the same chip a balanced waveguide beam splitter and a thermo-optic phase shifter, allowing us to record homodyne traces at different phases and to perform reliable quantum state tomography. In particular, we show that the IHA allows for the detection of nonclassical features of continuous-variable quantum states, such as squeezed states., Comment: 5+2 pages, 5+1 figures

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. Here we show that so-called Sylvester interferometers are near-optimal for the task of discriminating the behaviors of distinguishable and indistinguishable photons. We report the first implementations of integrated Sylvester interferometers with 4 and 8 modes with an efficient, scalable and reliable 3D-architecture. We perform two-photon interference experiments capable of identifying indistinguishable photon behaviour with a Bayesian approach using very small data sets. Furthermore, we employ experimentally this new device for the assessment of scattershot Boson Sampling. These results open the way to the application of Sylvester interferometers for the optimal assessment of multiphoton interference experiments., Comment: 9+10 pages, 6+6 figures, added supplementary material, completed and updated bibliography

Photonic platforms represent a promising technology for the realization of several quantum communication protocols and for experiments of quantum simulation. Moreover, large-scale integrated interferometers have recently gained a relevant role for restricted models of quantum computing, specifically with Boson Sampling devices. Indeed, various linear optical schemes have been proposed for the implementation of unitary transformations, each one suitable for a specific task. Notwithstanding, so far a comprehensive analysis of the state of the art under broader and realistic conditions is still lacking. In the present work we address this gap, providing in a unified framework a quantitative comparison of the three main photonic architectures, namely the ones with triangular and square designs and the so-called fast transformations. All layouts have been analyzed in presence of losses and imperfect control over the reflectivities and phases of the inner structure. Our results represent a further step ahead towards the implementation of quantum information protocols on large-scale integrated photonic devices., Comment: 10 pages, 6 figures + 2 pages Supplementary Information

Photonic interference is a key quantum resource for optical quantum computation, and in particular for so-called boson sampling machines. 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 is stronger 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., Comment: 5 pages, 3 figures + 11 pages, 3 figures Supplementary Information

The polarisation of light is a powerful and widely used degree of freedom to encode information, both in classical and quantum applications. In particular, quantum information technologies based on photons are being revolutionised by the use of integrated photonic circuits. It is therefore very important to be able to manipulate the polarisation of photons in such circuits. We experimentally demonstrate the fabrication by femtosecond laser micromachining of components such as polarisation insensitive or polarising directional couplers, operating at 1550 nm wavelength, where the two opposite behaviours are achieved just by controlling the geometric layout of the photonic circuits, being the waveguides fabricated with the same irradiation recipe. We expect to employ this approach in complex integrated photonic devices, capable of a full control of the photons polarisation for quantum cryptography, quantum computation and quantum teleportation experiments., Comment: 9 pages, 7 figures

In classical physics, properties of the objects exist independently on the context, i.e. whether and how measurements are performed. Quantum physics showed this assumption to be wrong and that Nature is indeed "contextual". Contextuality has been observed in the simplest physical systems such as single particles, and plays fundamental roles in quantum computation advantage. Here, we demonstrate for the first time quantum contextuality in an integrated photonic chip. The chip implements different combinations of measurements on a single photon delocalized on four distinct spatial modes. We show violations of a CHSH-like non-contextuality inequality by 14 standard deviations. This paves the way to compact and portable devices for contextuality-based quantum-powered protocols.

Recent developments in integrated photonics technology are opening the way to the fabrication of complex linear optical interferometers. The application of this platform is ubiquitous in quantum information science, from quantum simulation to quantum metrology, including the quest for quantum supremacy via the boson sampling problem. Within these contexts, the capability to learn efficiently the unitary operation of the implemented interferometers becomes a crucial requirement. In this letter we develop a reconstruction algorithm based on a genetic approach, which can be adopted as a tool to characterize an unknown linear optical network. We report an experimental test of the described method by performing the reconstruction of a 7-mode interferometer implemented via the femtosecond laser writing technique. Further applications of genetic approaches can be found in other contexts, such as quantum metrology or learning unknown general Hamiltonian evolutions., Comment: 5 pages, 3 figures + 3 pages, 1 figure Supplementary Information

Quantum networks of growing complexity play a key role as resources for quantum computation; the ability to identify the quality of their internal correlations will play a crucial role in addressing the buiding stage of such states. We introduce a novel diagnostic scheme for multipartite networks of entangled particles, aimed at assessing the quality of the gates used for the engineering of their state. Using the information gathered from a set of suitably chosen multiparticle Bell tests, we identify conditions bounding the quality of the entangled bonds among the elements of a register. We demonstrate the effectiveness, flexibility, and diagnostic power of the proposed methodology by characterizing a quantum resource engineered combining two-photon hyperentanglement and photonic-chip technology. Our approach is feasible for medium-sized networks due to the intrinsically modular nature of cluster states, and paves the way to section-by-section analysis of large photonics resources., Comment: 5 pages, 3 figures, RevTex4-1

Free-space light beams with complex intensity patterns, or non-trivial phase structure, are demanded in diverse fields, ranging from classical and quantum optical communications, to manipulation and imaging of microparticles and cells. Static or dynamic spatial light modulators, acting on phase or intensity of an incoming light wave, are the conventional choices to produce beams with such non-trivial characteristics. However, interfacing these devices with optical fibers or integrated optical circuits often requires difficult alignment or cumbersome optical setups. Here we explore theoretically and with numerical simulations the potentialities of directly using the output of engineered three-dimensional waveguide arrays, illuminated with linearly polarized light, to project light beams with peculiar structures. We investigate through a collection of illustrative configurations the far field distribution, showing the possibility to achieve orbital angular momentum, or to produce elaborate intensity or phase patterns with several singularity points. We also simulate the propagation of the projected beam, showing the possibility to concentrate light. We note that these devices should be at reach of current technology, thus perspectives are open for the generation of complex free-space optical beams from integrated waveguide circuits.

The Majorization Principle is a fundamental statement governing the dynamics of information processing in optimal and efficient quantum algorithms. While quantum computation can be modeled to be reversible, due to the unitary evolution undergone by the system, these quantum algorithms are conjectured to obey a quantum arrow of time dictated by the Majorization Principle: the probability distribution associated to the outcomes gets ordered step-by-step until achieving the result of the computation. Here we report on the experimental observation of the effects of the Majorization Principle for two quantum algorithms, namely the quantum fast Fourier transform and a recently introduced validation protocol for the certification of genuine many-boson interference. The demonstration has been performed by employing integrated 3-D photonic circuits fabricated via femtosecond laser writing technique, which allows to monitor unambiguously the effects of majorization along the execution of the algorithms. The measured observables provide a strong indication that the Majorization Principle holds true for this wide class of quantum algorithms, thus paving the way for a general tool to design new optimal algorithms with a quantum speedup., Comment: 6 pages, 4 figures + 2 pages Supplementary Information

The time evolution of quantum many-body systems is one of the least understood frontiers of physics. The most curious feature of such dynamics is, generically, the growth of quantum entanglement with time to an amount proportional to the system size (volume law) even when the interactions are local. This phenomenon, unobserved to date, has great ramifications for fundamental issues such as thermalisation and black-hole formation, while its optimisation clearly has an impact on technology (e.g., for on-chip quantum networking). Here we use an integrated photonic chip to simulate the dynamics of a spin chain, a canonical many-body system. A digital approach is used to engineer the evolution so as to maximise the generation of entanglement. The resulting volume law growth of entanglement is certified by constructing a second chip, which simultaneously measures the entanglement between multiple distant pairs of simulated spins. This is the first experimental verification of the volume law and opens up the use of photonic circuits as a unique tool for the optimisation of quantum devices., Comment: 8+14 pages, 4+9 figures

The transfer of data is a fundamental task in information systems. Microprocessors contain dedicated data buses that transmit bits across different locations and implement sophisticated routing protocols. Transferring quantum information with high fidelity is a challenging task, due to the intrinsic fragility of quantum states. We report on the implementation of the perfect state transfer protocol applied to a photonic qubit entangled with another qubit at a different location. On a single device we perform three routing procedures on entangled states with an average fidelity of 97.1%. Our protocol extends the regular perfect state transfer by maintaining quantum information encoded in the polarisation state of the photonic qubit. Our results demonstrate the key principle of perfect state transfer, opening a route toward data transfer for quantum computing systems.

Encoding many qubits in different degrees of freedom (DOFs) of single photons is one of the routes towards enlarging the Hilbert space spanned by a photonic quantum state. Hyperentangled photon states (i.e. states showing entanglement in multiple DOFs) have demonstrated significant implications for both fundamental physics tests and quantum communication and computation. Increasing the number of qubits of photonic experiments requires miniaturization and integration of the basic elements and functions to guarantee the set-up stability. This motivates the development of technologies allowing the precise control of different photonic DOFs on a chip. We demonstrate the contextual use of path and polarization qubits propagating within an integrated quantum circuit. We tested the properties of four-qubit linear cluster states built on both DOFs. Our results pave the way towards the full integration on a chip of hybrid multiqubit multiphoton states., Comment: 7 pages, 7 figures, RevTex4-1, Light: Science & Applications AAP:http://aap.nature-lsa.cn:8080/cms/accessory/files/AAP-lsa201664.pdf

The importance of integrated quantum photonics in the telecom band resides on the possibility of interfacing with the optical network infrastructure developed for classical communications. In this framework, femtosecond laser written integrated photonic circuits, already assessed for quantum information experiments in the 800 nm wavelength range, have great potentials. In fact these circuits, written in glass, can be perfectly mode-matched at telecom wavelength to the in/out coupling fibers, which is a key requirement for a low-loss processing node in future quantum optical networks. In addition, for several applications quantum photonic devices will also need to be dynamically reconfigurable. Here we experimentally demonstrate the high performance of femtosecond laser written photonic circuits for quantum experiments in the telecom band and we show the use of thermal shifters, also fabricated by the same femtosecond laser, to accurately tune them. State-of-the-art manipulation of single and two-photon states is demonstrated, with fringe visibilities greater than 95%. This opens the way to the realization of reconfigurable quantum photonic circuits on this technological platform.

The identification of phenomena able to pinpoint quantum interference is attracting large interest. Indeed, a generalization of the Hong-Ou-Mandel effect valid for any number of photons and optical modes would represent an important leap ahead both from a fundamental perspective and for practical applications, such as certification of photonic quantum devices, whose computational speedup is expected to depend critically on multiparticle interference. Quantum distinctive features have been predicted for many particles injected into multimode interferometers implementing the Fourier transformation in the Fock space. In this work we develop a scalable approach for the implementation of quantum fast Fourier transform using 3-D photonic integrated interferometers, fabricated via femtosecond laser writing technique. We observe the quantum suppression of a large number of output states with 4- and 8-mode optical circuits: the experimental results demonstrate genuine quantum interference between the injected photons, thus offering a powerful tool for diagnostic of photonic platforms., Comment: 10+4 pages, 6 figures

Boson Sampling is a computational task strongly believed to be hard for classical computers, but efficiently solvable by orchestrated bosonic interference in a specialised quantum computer. Current experimental schemes, however, are still insufficient for a convincing demonstration of the advantage of quantum over classical computation. A new variation of this task, Scattershot Boson Sampling, leads to an exponential increase in speed of the quantum device, using a larger number of photon sources based on parametric downconversion. This is achieved by having multiple heralded single photons being sent, shot by shot, into different random input ports of the interferometer. Here we report the first Scattershot Boson Sampling experiments, where six different photon-pair sources are coupled to integrated photonic circuits. We employ recently proposed statistical tools to analyse our experimental data, providing strong evidence that our photonic quantum simulator works as expected. This approach represents an important leap toward a convincing experimental demonstration of the quantum computational supremacy., Comment: 8 pages, 5 figures (plus Supplementary Materials, 14 pages, 8 figures)

Quantum interference of correlated particles is a fundamental quantum phenomenon which carries signatures of the statistics properties of the particles, such as bunching or anti-bunching. In 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. recently demonstrated a simple sufficient criterion for the suppression of output events in the more general case of Fourier multi-port beam splitters. Here we study the case in which $2^q$ particles (either bosonic or fermionic) are injected simultaneously in different ports of a Sylvester interferometer with $2^p \geq 2^q$ 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.

Escaping from a complex maze, by exploring different paths with several decision-making branches in order to reach the exit, has always been a very challenging and fascinating task. Wave field and quantum objects may explore a complex structure in parallel by interference effects, but without necessarily leading to more efficient transport. Here, inspired by recent observations in biological energy transport phenomena, we demonstrate how a quantum walker can efficiently reach the output of a maze by partially suppressing the presence of interference. In particular, we show theoretically an unprecedented improvement in transport efficiency for increasing maze size with respect to purely quantum and classical approaches. In addition, we investigate experimentally these hybrid transport phenomena, by mapping the maze problem in an integrated waveguide array, probed by coherent light, hence successfully testing our theoretical results. These achievements may lead towards future bio-inspired photonics technologies for more efficient transport and computation., Comment: 13 pages, 10 figures