arXiv subjects

A. Mandilara

Publications and source records attributed to A. Mandilara.

At least 19 recordsLinked to original sources

arXiv2026

Let the Qudit Do the Jacobi: A Structured Quantum Algorithm for Spectral Decomposition

Jacobi diagonalization is a long-established numerical algorithm for the spectral decomposition of Hermitian and, more generally, normal matrices. In this work, we develop a qudit-native quantum realization of the Jacobi diagonalization algorithm for unknown unitary operators. The proposed framework avoids explicit reconstruction of the operator and controlled-unitary operations. Each elementary two-parameter Givens rotation is implemented through two sequential single-parameter quantum variational optimizations that are directly accessible experimentally. An interferometric protocol is further introduced for extracting the eigenvalues of the diagonalized unitary, up to an overall global phase. Numerical simulations on ensembles of Haar-random unitary matrices demonstrate that the proposed algorithm preserves the characteristic convergence behavior of the classical Jacobi method and exhibits the expected quadratic scaling in the number of elementary operations with the dimension $d$, comparable to its classical counterpart. The results establish the proposed algorithm as a structured quantum numerical linear algebra algorithm naturally suited to qudit architectures and provide a bridge between classical iterative matrix algorithms and their quantum realizations.

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arXiv2025

Learning kernels with quantum optical circuits

Support Vector Machines (SVMs) are a cornerstone of supervised learning, widely used for data classification. A central component of their success lies in kernel functions, which enable efficient computation of inner products in high-dimensional feature spaces. Recent years have seen growing interest in leveraging quantum circuits -- both qubit-based and quantum optical -- for computing kernel matrices, with ongoing research exploring potential quantum advantages. In this work, we investigate two classical techniques for enhancing SVM performance through kernel learning -- the Fisher criterion and quasi-conformal transformations -- and translate them into the framework of quantum optical circuits. Conversely, using the example of the displaced squeezed vacuum state, we demonstrate how established concepts from quantum optics can inspire novel perspectives and enhancements in SVM methodology. This cross-disciplinary approach highlights the potential of quantum optics to both inform and benefit from advances in machine learning.

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arXiv2025

Applications of Hybrid Machine Learning Methods to Large Datasets: A Case Study

We combine classical and quantum Machine Learning (ML) techniques to effectively analyze long time-series data acquired during experiments. Specifically, we demonstrate that replacing a deep classical neural network with a thoughtfully designed Variational Quantum Circuit (VQC) in an ML pipeline for multiclass classification of time-series data yields the same classification performance, while significantly reducing the number of trainable parameters. To achieve this, we use a VQC based on a single qudit, and encode the classical data into the VQC via a trainable hybrid autoencoder which has been recently proposed as embedding technique. Our results highlight the importance of tailored data pre-processing for the circuit and show the potential of qudit-based VQCs.

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arXiv2025

A Measurement Device Independent Quantum Key Distribution protocol in the service of three users

Quantum Key Distribution (QKD) is the only theoretically proven method for secure key distribution between two users. In this work, we propose and analyze a Measurement Device Independent (MDI) protocol designed to distribute keys among three users in a pairwise manner. Each user randomly selects a basis, encodes bit values in the phase of coherent states, and sends the resulting pulses to a central measurement unit (MU) composed of three beam splitters and three photon detectors. When the three pulses arrive simultaneously at the MU and under the condition of successful detection of photons, a key bit is distributed to at least one pair of users. This protocol extends the foundational phase-encoding MDI protocol introduced by [K. Tamaki, et al., Phys. Rev. A 85, 042307 (2012)] to three users, but this comes at the cost of introducing a systematic error in the implementation of the honest protocol.

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arXiv2024

Enhancing the performance of Variational Quantum Classifiers with hybrid autoencoders

Variational Quantum Circuits (VQC) lie at the forefront of quantum machine learning research. Still, the use of quantum networks for real data processing remains challenging as the number of available qubits cannot accommodate a large dimensionality of data --if the usual angle encoding scenario is used. To achieve dimensionality reduction, Principal Component Analysis is routinely applied as a pre-processing method before the embedding of the classical features on qubits. In this work, we propose an alternative method which reduces the dimensionality of a given dataset by taking into account the specific quantum embedding that comes after. This method aspires to make quantum machine learning with VQCs more versatile and effective on datasets of high dimension. At a second step, we propose a quantum inspired classical autoencoder model which can be used to encode information in low latent spaces. The power of our proposed models is exhibited via numerical tests. We show that our targeted dimensionality reduction method considerably boosts VQC's performance and we also identify cases for which the second model outperforms classical linear autoencoders in terms of reconstruction loss.

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arXiv2024

Real-time diagnostics on a QKD link via QBER Time Series Analysis

The integration of QKD systems in Metro optical networks raises challenges which cannot be completely resolved with the current technological status. In this work we devise a methodology for identifying different kind of impairments which may occur on the quantum channel during its transmission in an operational network. The methodology is built around a supervised ML pipeline which is using as input QBER and SKR time-series and requires no further interventions on the QKD system. The identification of impairments happens in real time and even though such information cannot reverse incidents, this can be valuable for users, operators and key management system.

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arXiv2023

The Gell-Mann feature map of qutrits and its applications in classification tasks

Recent advancements in quantum hardware have enabled the realization of high-dimensional quantum states. This work investigates the potential of qutrits in quantum machine learning, leveraging their larger state space for enhanced supervised learning tasks. To that end, the Gell-Mann feature map is introduced which encodes information within an $8$-dimensional Hilbert space. The study focuses on classification problems, comparing Gell-Mann feature map with maps generated by established qubit and classical models. We test different circuit architectures and explore possibilities in optimization techniques. By shedding light on the capabilities and limitations of qutrit-based systems, this research aims to advance applications of low-depth quantum circuits.

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arXiv2023

Classification of data with a qudit, a geometric approach

We propose a model for data classification using isolated quantum $d$-level systems or else qudits. The procedure consists of an encoding phase where classical data are mapped on the surface of the qudit's Bloch hyper-sphere via rotation encoding, followed by a rotation of the sphere and a projective measurement. The rotation is adjustable in order to control the operator to be measured, while additional weights are introduced in the encoding phase adjusting the mapping on the Bloch's hyper-surface. During the training phase, a cost function based on the average expectation value of the observable is minimized using gradient descent thereby adjusting the weights. Using examples and performing a numerical estimation of lossless memory dimension, we demonstrate that this geometrically inspired qudit model for classification is able to solve nonlinear classification problems using a small number of parameters only and without requiring entangling operations.

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arXiv2021

Compiling universal quantum circuits

We propose a method of compiling that permits to identify quantum circuits able to simulate arbitrary $n$-qubit unitary operations via the adjustment of angles in single-qubit gates therein. The method of compiling itself extends older quantum control techniques and stays computationally tractable for several qubits. As an application we identify compiling universal circuits for $3$, $4$ and $5$ qubits consisting of $16$, $64$ and $ 256$ CNOTs respectively.

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arXiv2020

Detecting the event of a single photon loss on quantum signals

We design a scheme for detecting a single photon loss from multi-modal quantum signals transmitted via a fiber or in free space. This consists of a special type of unitary coding transformation, the controlled-squeezing, applied prior to the transmission on the signal composed by information and ancilla modes. At the receiver, the inverse unitary transformation is applied -decoding, and the ancilla modes are measured via photon detection. The outcome reveals whether a photon loss has occurred. Distortion of the information part of the signal caused by an ancilla photon loss can be corrected if the encoding transformation is appropriately selected. Loss of a photon from the information part of the signal can be detected with the probability exponentially close to unity. In contrast to the schemes of decoherence free subspaces and quantum error correction protocols, this methods allows one to make use of entire Hilbert space dimensionality. We discuss possible ways of synthesizing the required encoding-decoding transformations.

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arXiv2020

Investigating bound entangled two-qutrit states via the best separable approximation

We use the linear programming algorithm introduced by Akulin et al. [V. M. Akulin, G. A. Kabatiansky, and A. Mandilara, Phys. Rev. A 92, 042322 (2015)] to perform best separable approximation on two-qutrit random density matrices. We combine the numerical results with theoretical methods in order to generate random representative families of positive partial transposed bound entangled (BE) states and analyze their properties. Our results are disclosing that for the two-qutrit system the BE states have negligible volume and that these form tiny `islands' sporadically distributed over the surface of the polytope of separable states. %We devise a method for estimating numerically the average thickness of these formations and their frequency of occurrence. The detected families of BE states are found to be located under a layer of pseudo one-copy undistillable negative partial transposed states with the latter covering the vast majority of the surface of the separable polytope.

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arXiv2020

Classical and quantum dispersion-free coherent propagation by tailoring multi-modal coupling

It is shown that tailored breaking of the translational symmetry through weak scattering in waveguides and optical fibers can control chromatic dispersions of the individual modes at any order; thereby, it overcomes the problem of coherent classical and quantum signal transmission at long distances. The methodology is based on previously developed quantum control techniques and gives an analytic solution in ideal scattering conditions; it has been also extended to incorporate and correct non-unitary effects in the presence of weak back-scattering. In practice, it requires scatterers able to couple different modes and carefully designed dispersion laws giving a null average quadratic dispersion in the spectral vicinity of the operational frequency.

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arXiv2018

Quantum compiling with diffusive sets of gates

Given a set of quantum gates and a target unitary operation, the most elementary task of quantum compiling is the identification of a sequence of the gates that approximates the target unitary to a determined precision $\varepsilon$. Solovay-Kitaev theorem provides an elegant solution which is based on the construction of successively tighter `nets' around the unity comprised by successively longer sequences of gates. The procedure for the construction of the nets, according to this theorem, requires accessibility to the inverse of the gates as well. In this work, we propose a method for constructing nets around unity without this requirement. The algorithmic procedure is applicable to sets of gates which are diffusive enough, in the sense that sequences of moderate length cover the space of unitary matrices in a uniform way. We prove that the number of gates sufficient for reaching a precision $\varepsilon$ scales as $ \log (1/\varepsilon )^{\log 3 / log 2} $ while the pre-compilation time is increased as compared to thatof the Solovay-Kitaev algorithm by the exponential factor 3/2.

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arXiv2015

An alternative representation for pure symmetric states of qubits and its applications to entanglement classification

We prove that the vast majority of symmetric states of qubits can be decomposed in a unique way into a superposition of spin 1/2 coherent states. For the case of two qubits, the proposed decomposition reproduces the Schmidt decomposition and therefore, in the case of a higher number of qubits, can be considered as its generalization. We analyze the geometrical aspects of the proposed representation and its invariant properties under the action of local unitary and local invertible transformations. As an application, we identify the most general classes of entanglement and representative states for any number of qubits in a symmetric state.

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arXiv2015

The Essentially Entangled Component of Multipartite Mixed Quantum States, its Properties and an Efficient Algorithm for its Extraction

We introduce with geometric means a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled one, which contains no product states components. We show that this convex decomposition can be achieved in practice with the help of an algorithm based on linear programming, which in the general case scales polynomially with the dimension of the multipartite system. Furthermore, we suggest methods for analyzing the multipartite entanglement content of the essentially entangled component and derive analytically an upper bound for its rank. We illustrate the algorithm at an example of a composed system of total dimension 12 undergoing loss of coherence due to classical noise and we trace the time evolution of its essentially entangled component. We suggest a "geometric" description of entanglement dynamics and show how it explains the well-known phenomena of sudden death and revival of multipartite entanglement.

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arXiv2013

Purity and Gaussianity bounded uncertainty relation

Bounded uncertainty relations provide the minimum value of the uncertainty assuming some additional information on the state. We derive analytically an uncertainty relation bounded by a pair of constraints, those of purity and Gaussianity. In a limiting case this uncertainty relation reproduces the purity-bounded derived by V I Man'ko and V V Dodonov and the Gaussianity-bounded one [Phys. Rev. A 86, 030102R (2012)].

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arXiv2012

Quantum uncertainty relation saturated by the eigenstates of the harmonic oscillator

We re-derive the Schrödinger-Robertson uncertainty principle for the position and momentum of a quantum particle. Our derivation does not directly employ commutation relations, but works by reduction to an eigenvalue problem related to the harmonic oscillator, which can then be further exploited to find a larger class of constrained uncertainty relations. We derive an uncertainty relation under the constraint of a fixed degree of Gaussianity and prove that, remarkably, it is saturated by all eigenstates of the harmonic oscillator. This goes beyond the common knowledge that the (Gaussian) ground state of the harmonic oscillator saturates the uncertainty relation.

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arXiv2012

Quantum bit commitment under Gaussian constraints

Quantum bit commitment has long been known to be impossible. Nevertheless, just as in the classical case, imposing certain constraints on the power of the parties may enable the construction of asymptotically secure protocols. Here, we introduce a quantum bit commitment protocol and prove that it is asymptotically secure if cheating is restricted to Gaussian operations. This protocol exploits continuous-variable quantum optical carriers, for which such a Gaussian constraint is experimentally relevant as the high optical nonlinearity needed to effect deterministic non-Gaussian cheating is inaccessible.

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