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arXiv:2407.06026 · Optica Quantum

Variational quantum cloning machine on an integrated photonic interferometer

Francesco Hoch, Giovanni Rodari, Eugenio Caruccio, Beatrice Polacchi, Gonzalo Carvacho, Taira Giordani, Mina Doosti, Sebastià Nicolau, Ciro Pentangelo, Simone Piacentini, Andrea Crespi, Francesco Ceccarelli, Roberto Osellame, Ernesto F. Galvão, Nicolò Spagnolo, Fabio Sciarrino

Published Jun 9, 2025• 3 citations

Abstract

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.

DOI: 10.1364/opticaq.553762

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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.

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In several quantum information (QI) phenomena of large technological importance the information is carried by the phase of the quantum superposition states, or qubits. The phase-covariant cloning machine (PQCM) addresses precisely the problem of optimally copying these qubits with the largest attainable ``fidelity.'' We present a general scheme which realizes the $1\ensuremath{\rightarrow}3$ phase covariant cloning process by a combination of three different QI processes: the universal cloning, the NOT gate, and the projection over the symmetric subspace of the output qubits. The experimental implementation of a PQCM for polarization encoded qubits, the first ever realized with photons, is reported.

The optimal phase-covariant quantum cloning machine (PQCM) broadcasts the information associated to an input qubit into a multiqubit system, exploiting a partial a priori knowledge of the input state. This additional a priori information leads to a higher fidelity than for the universal cloning. The present article first analyzes different innovative schemes to implement the $1\ensuremath{\rightarrow}3$ PQCM. The method is then generalized to any $1\ensuremath{\rightarrow}M$ machine for an odd value of

M

by a theoretical approach based on the general angular momentum formalism. Finally different experimental schemes based either on linear or nonlinear methods and valid for single photon polarization encoded qubits are discussed.

Abstract Variational quantum metrology represents a powerful tool to optimize estimation strategies, resulting particularly beneficial for multiparameter estimation problems that often suffer from limitations due to the curse of dimensionality and computational complexity. To overcome these challenges, we develop a variational approach able to efficiently optimize a quantum multiphase sensor. Leveraging the reconfigurability of an integrated photonic device, we implement a hybrid quantum-classical feedback loop able to enhance the estimation performances. The quantum circuit evaluations are used to compute the system partial derivatives by applying the parameter-shift rule, and thus reconstruct experimentally the Fisher information matrix. This in turn is adopted as the cost function of a classical learning algorithm run to optimize the measurement settings. Our experimental results showcase significant improvements in estimation accuracy and noise robustness, highlighting the potential of variational techniques for practical applications in quantum sensing and more generally in quantum information processing using photonic circuits.

While exact cloning of an unknown quantum state is prohibited by the linearity of quantum mechanics, approximate cloning is possible and has been used, e.g., to derive limits on the security of quantum communication protocols. In the case of asymmetric cloning, the information from the input state is distributed asymmetrically between the different output states. Here, we consider asymmetric phase-covariant cloning, where the goal is to optimally transfer the phase information from a single input qubit to different output qubits. We construct an optimal quantum cloning machine for two qubits that does not require ancilla qubits and implement it on an NMR quantum information processor.

We experimentally realize the $1\ensuremath{\rightarrow}2$ optimal universal quantum cloning machine for arbitrary qubits and the ancilla-free $1\ensuremath{\rightarrow}3$ optimal phase-covariant quantum cloning machine for $x\text{\ensuremath{-}}y$ equatorial qubits, which were constructed by Zou et al. [Phys. Lett. A 366, 36 (2007)]. The qubits are represented by the polarization states of photons prepared from the process of spontaneous parametric down-conversion. The copies of each machine are shown to have almost equal fidelities conditioned on fourfold coincidences.