Traditional quantum metrology assesses precision using the figures of merit of continuous-valued parameter estimation. Recently, quantum digital estimation was introduced: it evaluates the performance information-theoretically by quantifying the number of significant bits of the parameter, redefining key benchmarks like the Heisenberg bound. Here, we report the first experimental realization of a Quantum Analog-to-Digital Converter for quantum metrology, that takes an input continuous parameter and outputs a bit string, using an advanced photonic platform, comprising a fully reconfigurable integrated circuit and a quantum dot source of highly indistinguishable photons. We implement a protocol for digital phase estimation that is capable of surpassing the standard quantum limit, through the simultaneous use of different entangled state resources. We tackle experimental imperfections by employing machine learning techniques for noise deconvolution and estimation process refinement. Our protocol is experimentally benchmarked against classical strategies via the number of recoverable bits of the unknown parameter. Our results open new perspectives for future implementation of quantum digital estimation strategies.

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 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 -> 2 variational cloning machine of dual-rail encoded photonic qubits, both for phase-covariant and state-dependent cloning. We exploit a fully programmable six-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. (c) 2025 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

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.

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 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 the input and output, using a photonic-path-encoding approach. Our scheme is modular and 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, thereby demonstrating the viability of our approach. These results open new paths for randomness manipulation with integrated quantum technologies. A quantum-to-quantum Bernoulli factory is demonstrated by using a reconfigurable Clements's squared unitary circuit in an integrated quantum photonic platform. Three interferometer designs are proposed for the basic operations of a field on qubit states.

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.

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.

Universal photonic processors (UPPs) are programmable photonic integrated circuits (PICs) that are attracting increasing attention from both the industry and the academic world in applications as diverse as quantum information processing, neuromorphic computing and 3D imaging [1]. Differently from application-specific PICs, UPPs can implement any arbitrary linear optical transformation, providing the possibility of reconfiguring the circuit operation even at run-time. Today the most common UPP architectures rely on interferometric meshes, whose operation is set through thermo-optic phase shifters. UPPs have been demonstrated in different waveguide fabrication platforms and materials, but the state of the art in terms of complexity is currently set by the silicon nitride. The best in class device operates at 1550 nm wavelength and features 20 photonic modes, insertion losses around 2.9 dB and an average fidelity of 97.4%, at the cost of a large power budget of hundreds of mW per shifter that hinders a further scaling [2].

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 approach for the certification of quantum properties in programmable integrated photonic platforms.

Universal photonic processors are enabling novel experiments in quantum in-formation science. A femtosecond-laser-written 6-mode processor shows an unprecedented performance. The perspective of a remarkably higher complexity is discussed in light of the most recent results.

Programmability in femtosecond-laser-written integrated circuits is commonly achieved with the implementation of thermal phase shifters. Recent work has shown how such phase shifters display significantly reduced power dissipation and thermal crosstalk with the implementation of thermal isolation structures. However, the aforementioned phase shifter technology is based on a single gold film, which poses severe limitations on integration density and circuit complexity due to intrinsic geometrical constraints. To increase the compactness, we propose two improvements to this technology. Firstly, we fabricated thermal phase shifters with a photolithography process based on two different metal films, namely (1) chromium for microheaters and (2) copper for contact pads and interconnections. Secondly, we developed a novel curved isolation trench design that, along with a state-of-the-art curvature radius, allows for a significant reduction in the optical length of integrated circuits. As a result, curved Cr-Cu phase shifters provide a compact footprint with low parasitic series resistance and no significant increase in power dissipation (∼38 mW) and thermal crosstalk (∼20%). These results pave the way toward the fabrication of femtosecond-laser-written photonic circuits with a steep increase in terms of layout complexity.

Femtosecond laser writing (FLW) can open new perspectives on universal photonic processors (UPPs). We propose here two building blocks for the realization of FLW-UPPs and we show the preliminary results obtained on a 6-mode device.

Thermo-optic phase shifters are widely adopted to achieve dynamical reconfiguration of integrated waveguide circuits [1] , with applications encompassing diverse fields, ranging from free-space beam steering and shaping [2] to quantum information experiments [3] .

Thermo-optic phase shifters allow one to dynamically tune and control the operation of integrated-optics interferometers. They have been demonstrated nowadays in different waveguide platforms, and their reliable functioning has enabled the realization of reconfigurable circuits of notable complexity. The design approach to such devices is often based on finite-element numerical simulations, which provide accurate descriptions of the underlying thermal phenomena, at the price of long computational times. Here, on the contrary, we devise an analytical model for the heat diffusion in a simplified geometrical configuration. The model describes both static and dynamic regimes, and can be conveniently applied both to three-dimensional waveguide devices inscribed by femtosecond laser pulses and to planar lithographic circuits. The accuracy of the predictions of the model is validated with experimental measurements on Mach-Zehnder interferometers with different geometries, realized in both kinds of platforms.

Photonic Integrated Circuits (PICs) are today both pervading our life and enabling several novel experiments in research applications by tackling the issues of complex bulk optical setups. Their development is closely following what already witnessed for the microelectronics industry, with two main design approaches: on the one hand, application-specific PICs guarantee optimal performance by purposely tailoring the design for a given application, while, on the other hand, programmable PICs based on a mesh of reconfigurable Mach-Zehnder Interferometers (MZIs) provide a flexible solution to implement an arbitrary unitary transformation that can be modified at run-time. Such devices are usually referred to as programmable photonic processors [1] . To date, the most common technique to reconfigure large MZI meshes is thermo-optic phase shifting.

Femtosecond laser writing is a powerful technique that allows rapid and cost‐effective fabrication of photonic integrated circuits with unique 3D 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 3D microstructures are exploited to decrease the power needed to induce a 2π 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 toward the demonstration of complex programmable integrated photonic circuits fabricated by femtosecond laser writing, thus opening exciting perspectives in integrated quantum photonics.