arXiv subjects

Armando Bellante

Publications and source records attributed to Armando Bellante.

6 recordsLinked to original sources

arXiv2026

Compiling Quantum Regular Language States

State preparation compilers for quantum computers typically sit at two extremes: general-purpose routines that treat the target as an opaque amplitude vector, and bespoke constructions for a handful of well-known state families. We ask whether a compiler can instead accept simple, structure-aware specifications while providing predictable resource guarantees. We answer this by designing and implementing a quantum state-preparation compiler for regular language states (RLS): uniform superpositions over bitstrings accepted by a regular description, and their complements. Users describe the target state via (i) a finite set of bitstrings, (ii) a regular expression, or (iii) a deterministic finite automaton (DFA), optionally with a complement flag. By translating the input to a DFA, minimizing it, and mapping it to an optimal matrix product state (MPS), the compiler obtains an intermediate representation (IR) that exposes and compresses hidden structure. The efficient DFA representation and minimization offloads expensive linear algebra computation in exchange of simpler automata manipulations. The combination of the regular-language frontend and this IR gives concise specifications not only for RLS but also for their complements that might otherwise require exponentially large state descriptions. This enables state preparation of an RLS or its complement with the same asymptotic resources and compile time. We outline two hardware-aware backends: SeqRLSP, which yields linear-depth, ancilla-free circuits for linear nearest-neighbor architectures via sequential generation, and TreeRLSP, which achieves logarithmic depth on all-to-all connectivity via a tree tensor network. We prove depth and gate-count bounds scaling with the system size and the state's maximal Schmidt rank, and we give explicit compile-time bounds that expose the benefit of our approach. We implement and evaluate the pipeline.

quant-ph↗

arXiv2025

Quantum Sparse Recovery and Quantum Orthogonal Matching Pursuit

We study quantum sparse recovery in non-orthogonal, overcomplete dictionaries: given coherent quantum access to a state and a dictionary of vectors, the goal is to reconstruct the state up to $\ell_2$ error using as few vectors as possible. We first show that the general recovery problem is NP-hard, ruling out efficient exact algorithms in full generality. To overcome this, we introduce Quantum Orthogonal Matching Pursuit (QOMP), the first quantum analogue of the classical OMP greedy algorithm. QOMP combines quantum subroutines for inner product estimation, maximum finding, and block-encoded projections with an error-resetting design that avoids iteration-to-iteration error accumulation. Under standard mutual incoherence and well-conditioned sparsity assumptions, QOMP provably recovers the exact support of a $K$-sparse state in polynomial time. As an application, we give the first framework for sparse quantum tomography with non-orthogonal dictionaries in $\ell_2$ norm, achieving query complexity $\widetilde{O}(\sqrt{N}/\epsilon)$ in favorable regimes and reducing tomography to estimating only $K$ coefficients instead of $N$ amplitudes. In particular, for pure-state tomography with $m=O(N)$ dictionary vectors and sparsity $K=\widetilde{O}(1)$ on a well-conditioned subdictionary, this circumvents the $\widetilde{\Omega}(N/\epsilon)$ lower bound that holds in the dense, orthonormal-dictionary setting, without contradiction, by leveraging sparsity together with non-orthogonality. Beyond tomography, we analyze QOMP in the QRAM model, where it yields polynomial speedups over classical OMP implementations, and provide a quantum algorithm to estimate the mutual incoherence of a dictionary of $m$ vectors in $O(m/\epsilon)$ queries, improving over both deterministic and quantum-inspired classical methods.

quant-ph↗

arXiv2025

The Generalized Skew Spectrum of Graphs

This paper proposes a family of permutation-invariant graph embeddings, generalizing the Skew Spectrum of graphs of Kondor & Borgwardt (2008). Grounded in group theory and harmonic analysis, our method introduces a new class of graph invariants that are isomorphism-invariant and capable of embedding richer graph structures - including attributed graphs, multilayer graphs, and hypergraphs - which the Skew Spectrum could not handle. Our generalization further defines a family of functions that enables a trade-off between computational complexity and expressivity. By applying generalization-preserving heuristics to this family, we improve the Skew Spectrum's expressivity at the same computational cost. We formally prove the invariance of our generalization, demonstrate its improved expressiveness through experiments, and discuss its efficient computation.

cs.LG↗

arXiv2025

Evaluating the Potential of Quantum Machine Learning in Cybersecurity: A Case-Study on PCA-based Intrusion Detection Systems

Quantum computing promises to revolutionize our understanding of the limits of computation, and its implications in cryptography have long been evident. Today, cryptographers are actively devising post-quantum solutions to counter the threats posed by quantum-enabled adversaries. Meanwhile, quantum scientists are innovating quantum protocols to empower defenders. However, the broader impact of quantum computing and quantum machine learning (QML) on other cybersecurity domains still needs to be explored. In this work, we investigate the potential impact of QML on cybersecurity applications of traditional ML. First, we explore the potential advantages of quantum computing in machine learning problems specifically related to cybersecurity. Then, we describe a methodology to quantify the future impact of fault-tolerant QML algorithms on real-world problems. As a case study, we apply our approach to standard methods and datasets in network intrusion detection, one of the most studied applications of machine learning in cybersecurity. Our results provide insight into the conditions for obtaining a quantum advantage and the need for future quantum hardware and software advancements.

quant-ph↗

arXiv2022

Quantum matching pursuit: A quantum algorithm for sparse representations

Representing signals with sparse vectors has a wide range of applications that range from image and video coding to shape representation and health monitoring. In many applications with real-time requirements, or that deal with high-dimensional signals, the computational complexity of the encoder that finds the sparse representation plays an important role. Quantum computing has recently shown promising speed-ups in many representation learning tasks. In this work, we propose a quantum version of the well-known matching pursuit algorithm. Assuming the availability of a fault-tolerant quantum random access memory, our quantum matching pursuit lowers the complexity of its classical counterpart of a polynomial factor, at the cost of some error in the computation of the inner products, enabling the computation of sparse representation of high-dimensional signals. Besides proving the computational complexity of our new algorithm, we provide numerical experiments that show that its error is negligible in practice. This work opens the path to further research on quantum algorithms for finding sparse representations, showing suitable quantum computing applications in signal processing.

quant-ph↗

arXiv2021

Quantum algorithms for SVD-based data representation and analysis

This paper narrows the gap between previous literature on quantum linear algebra and practical data analysis on a quantum computer, formalizing quantum procedures that speed-up the solution of eigenproblems for data representations in machine learning. The power and practical use of these subroutines is shown through new quantum algorithms, sublinear in the input matrix's size, for principal component analysis, correspondence analysis, and latent semantic analysis. We provide a theoretical analysis of the run-time and prove tight bounds on the randomized algorithms' error. We run experiments on multiple datasets, simulating PCA's dimensionality reduction for image classification with the novel routines. The results show that the run-time parameters that do not depend on the input's size are reasonable and that the error on the computed model is small, allowing for competitive classification performances.

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