arXiv subjects

Michele Minervini

Publications and source records attributed to Michele Minervini.

10 recordsLinked to original sources

arXiv2026

Quantum thermodynamics and semidefinite optimization: Boltzmann, Fermi-Dirac, and Bose-Einstein frameworks

Here we argue how quantum thermodynamics offers a unifying interpretation for a wide class of semidefinite programs (SDPs) that arise in quantum information. Three SDP variable constraints, namely trace-one density operators, operator-bounded measurements, and the unbounded positive semidefinite cone, admit thermodynamic regularizations associated with Boltzmann, Fermi-Dirac, and Bose-Einstein statistics, respectively. In each case the entropy-regularized dual is unconstrained and concave in a chemical-potential vector, and the primal optimum is a thermal operator of the matched statistics. The dual gradient and Hessian are thermal expectation values, enabling hybrid quantum-classical algorithms for solving a wide variety of SDPs.

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arXiv2026

Quantum Spectral Anomaly Detection

A core task in quantum anomaly detection is to compute an anomaly score that quantifies how strongly a test quantum state deviates from a given quantum dataset assumed to be normal. Classically, principal component analysis (PCA) for centered data computes the anomaly score by evaluating the test sample relative to the subspace spanned by the selected leading eigenvectors. However, for quantum data that lack a standard centering, explicitly recovering principal eigenvectors, constructing full Gram matrices, or loading quantum-random-access-memory-style data can be more costly than estimating the anomaly score itself. To avoid these costs, we propose Quantum Spectral Anomaly Detection (QSPADE), which computes PCA-like anomaly scores directly from the spectrum of the average state of the normal dataset. By replacing hard PCA rank selection with a smooth, temperature-controlled spectral threshold, QSPADE makes near-threshold spectral components contribute partially to the anomaly score. This makes the score vary continuously rather than jump when a borderline component is included or excluded, and makes it less sensitive to noise or arbitrary hard cutoffs near the threshold. In the zero-temperature limit, QSPADE recovers the hard-projector PCA score. The proposed measurement-based quantum detector can be calibrated with a sample complexity independent of the data dimension. Numerical simulations show that QSPADE behaves like kernel-PCA on encoded classical data and detects changes across a transverse-field Ising transition without predefined order parameters. Consequently, QSPADE gives an efficient framework for both quantum-kernel anomaly detection on encoded classical data and the monitoring of quantum-native systems where diagnostic observables are unknown.

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arXiv2026

Quantum principal component analysis without eigenvector recovery

Principal component analysis (PCA) is traditionally implemented through a covariance or kernel matrix, leading-eigenvector extraction, and hard rank-$k$ projection. These steps can be computationally costly in high-dimensional and quantum-data settings, sensitive to small eigengaps, and unnecessary when downstream tasks only require principal-subspace scores. Such score-based objectives are important in applications such as anomaly detection, spectral-energy profiling, and other postselection tasks. To address these needs, we introduce a measurement-based soft PCA framework replacing the hard top-$k$ projector with an entropy-regularized Fermi--Dirac filter. This filter is the unique optimizer of an entropy-regularized variational formulation of PCA and converges to the classical PCA projector in the zero-temperature limit. This filter has a direct interpretation as a quantum measurement, which naturally suggests a quantum approach. For centered covariance operators represented by quantum feature states, a single fixed circuit, together with threshold calibration, accesses all optimal filters for different rank budgets or retained-variance levels without rank-dependent circuit updates or eigenvector recovery. For new inputs, the same calibrated quantum circuit yields soft principal subspace scores, spectral energy profiles, and postselected filtered states. The required centering of both training and test data is performed coherently inside the quantum protocol, which is particularly important for quantum data where no classical feature vectors or centered Gram matrix are directly available. By reframing PCA as a calibrated measurement task, this framework bypasses the need for iterative eigenvector extraction and achieves a dimension-independent sample complexity $O(\eta^{-2})$ for normalized fractional-rank or retained variance scoring at additive accuracy $\eta$.

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arXiv2026

Bose-Einstein thermal operators for semidefinite optimization

We establish that semidefinite programs (SDPs) over the unbounded positive semidefinite cone are mathematically equivalent to thermodynamic systems of independent bosonic modes: the eigenvalues of the optimization variable play the role of expected occupation numbers, the linear objective plays the role of total expected energy, and the linear equality constraints play the role of conserved non-commuting charges. Building on this perspective, we recast general SDPs as bosonic free-energy minimization problems at strictly positive temperature, regularized by the Bose-Einstein entropy; the original SDP is recovered in the zero-temperature limit. The optimal primal variable takes the form of a Bose-Einstein thermal operator parametrized by the dual variables. We prove an approximation-error bound that depends on the ground-space degeneracy and the spectral gap of the dual slack operator, improving on the linear-in-dimension worst-case duality gap of interior-point methods. We also introduce the Bose-Einstein quantum relative entropy as a Bregman divergence on the unbounded positive semidefinite cone, generated by the negative Bose-Einstein entropy. We propose it as a natural divergence for unnormalized positive operators, for which the standard Umegaki relative entropy can become negative, and we show that it satisfies a restricted monotonicity property under affine maps modeling bosonic Gaussian channels. Finally, we develop hybrid quantum-classical algorithms for the regularized SDP using only Hamiltonian simulation, Hadamard tests, and classical sampling, and bound their runtime in closed form. Unlike existing quantum SDP solvers, whose runtimes scale polynomially with an a priori upper bound on the primal trace, our framework operates directly on the unbounded cone, replacing this bound with a dependence on the spectral structure of the dual slack operator.

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arXiv2026

Quantifying the Operational Cost of Multipartite Entanglement

Multipartite entanglement determines the strength and range of interactions in many-body quantum systems. Yet, it is hard to evaluate it, due to the complex structures of quantum states. Here, we introduce a generic method to quantify the k <= N-partite entanglement of an N-particle system, by maximizing an arbitrary bipartite entanglement measure within subsystems of size up to k. The resulting classification of multipartite states captures their experimental cost: creating a k-partite entangled state requires at least k-1 two-particle entangling gates. Further, we analytically calculate the newly defined k-partite entanglement of formation, which generalizes an important bipartite entanglement measure, in several classes of states, including the W states of any dimension.

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arXiv2025

Constrained free energy minimization for the design of thermal states and stabilizer thermodynamic systems

A quantum thermodynamic system is described by a Hamiltonian and a list of conserved, non-commuting charges, and a fundamental goal is to determine the minimum energy of the system subject to constraints on the charges. Recently, [Liu et al., arXiv:2505.04514] proposed first- and second-order classical and hybrid quantum-classical algorithms for solving a dual chemical potential maximization problem, and they proved that these algorithms converge to global optima by means of gradient-ascent approaches. In this paper, we benchmark these algorithms on several problems of interest in thermodynamics, including one- and two-dimensional quantum Heisenberg models with nearest- and next-nearest neighbor interactions and with the charges set to the total x, y, and z magnetizations. We also offer an alternative compelling interpretation of these algorithms as methods for designing ground and thermal states of controllable Hamiltonians, with potential applications in molecular and material design. Furthermore, we introduce stabilizer thermodynamic systems as thermodynamic systems based on stabilizer codes, with the Hamiltonian constructed from a given code's stabilizer operators and the charges constructed from the code's logical operators. We benchmark the aforementioned algorithms on several examples of stabilizer thermodynamic systems, including those constructed from the one-to-three-qubit repetition code, the perfect one-to-five-qubit code, and the two-to-four-qubit error-detecting code. Finally, we observe that the aforementioned hybrid quantum-classical algorithms, when applied to stabilizer thermodynamic systems, can serve as alternative methods for encoding quantum information into stabilizer codes at a fixed temperature, and we provide an effective method for warm-starting these encoding algorithms whenever a single qubit is encoded into multiple physical qubits.

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arXiv2025

Quantum thermodynamics and semi-definite optimization

In quantum thermodynamics, a system is described by a Hamiltonian and a list of non-commuting charges representing conserved quantities like particle number or electric charge, and an important goal is to determine the system's minimum energy in the presence of these conserved charges. In optimization theory, a semi-definite program (SDP) involves a linear objective function optimized over the cone of positive semi-definite operators intersected with an affine space. These problems arise from differing motivations in the physics and optimization communities and are phrased using very different terminology, yet they are essentially identical mathematically. By adopting Jaynes' mindset motivated by quantum thermodynamics, we observe that minimizing free energy in the aforementioned thermodynamics problem, instead of energy, leads to an elegant solution in terms of a dual chemical potential maximization problem that is concave in the chemical potential parameters. As such, one can employ standard (stochastic) gradient ascent methods to find the optimal values of these parameters, and these methods are guaranteed to converge quickly. At low temperature, the minimum free energy provides an excellent approximation for the minimum energy. We then show how this Jaynes-inspired gradient-ascent approach can be used in both first- and second-order classical and hybrid quantum-classical algorithms for minimizing energy, and equivalently, how it can be used for solving SDPs, with guarantees on the runtimes of the algorithms. The approach discussed here is well grounded in quantum thermodynamics and, as such, provides physical motivation underpinning why algorithms published fifty years after Jaynes' seminal work, including the matrix multiplicative weights update method, the matrix exponentiated gradient update method, and their quantum algorithmic generalizations, perform well at solving SDPs.

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arXiv2025

Quantum natural gradient with thermal-state initialization

Parameterized quantum circuits (PQCs) are central to variational quantum algorithms (VQAs), yet their performance is hindered by complex loss landscapes that make their trainability challenging. Quantum natural gradient descent, which leverages the geometry of the parameterized space through quantum generalizations of the Fisher information matrix, offers a promising solution but has been largely limited to pure-state scenarios, with only approximate methods available for mixed-state settings. This paper addresses this question, originally posed in [Stokes et al., Quantum 4, 269 (2020)], by providing exact methods to compute three quantum generalizations of the Fisher information matrix-the Fisher-Bures, Wigner-Yanase, and Kubo-Mori information matrices-for PQCs initialized with thermal states. We prove that these matrix elements can be estimated using quantum algorithms combining the Hadamard test, classical random sampling, and Hamiltonian simulation. By broadening the set of quantum generalizations of Fisher information and realizing their unbiased estimation, our results enable the implementation of quantum natural gradient descent algorithms for mixed-state PQCs, thereby enhancing the flexibility of optimization when using VQAs. Another immediate consequence of our findings is to establish fundamental limitations on the ability to estimate the parameters of a state generated by an unknown PQC, when given sample access to such a state.

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arXiv2025

Evolved Quantum Boltzmann Machines

We introduce evolved quantum Boltzmann machines as a variational ansatz for quantum optimization and learning tasks. Given two parameterized Hamiltonians $G(\theta)$ and $H(\phi)$, an evolved quantum Boltzmann machine consists of preparing a thermal state of the first Hamiltonian $G(\theta)$ followed by unitary evolution according to the second Hamiltonian $H(\phi)$. Alternatively, one can think of it as first realizing imaginary time evolution according to $G(\theta)$ followed by real time evolution according to $H(\phi)$. After defining this ansatz, we provide analytical expressions for the gradient vector and illustrate their application in ground-state energy estimation and generative modeling, showing how the gradient for these tasks can be estimated by means of quantum algorithms that involve classical sampling, Hamiltonian simulation, and the Hadamard test. We also establish analytical expressions for the Fisher-Bures, Wigner-Yanase, and Kubo-Mori information matrix elements of evolved quantum Boltzmann machines, as well as quantum algorithms for estimating each of them, which leads to at least three different general natural gradient descent algorithms based on this ansatz. Along the way, we establish a broad generalization of the main result of [Luo, Proc. Am. Math. Soc. 132, 885 (2004)], proving that the Fisher-Bures and Wigner-Yanase information matrices of general parameterized families of states differ by no more than a factor of two in the matrix (Loewner) order, making them essentially interchangeable for training when using natural gradient descent.

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arXiv2024

Quantitative bounds to propagation of quantum correlations in many-body systems

We investigate how much information about a quantum system can be simultaneously communicated to independent observers, by establishing quantitative limits to bipartite quantum correlations in many-body systems. As recently reported in Phys. Rev. Lett. 129, 010401 (2022), bounds on quantum discord and entanglement of formation between a single quantum system and its environment, e.g., a large number of photons, dictate that independent observers which monitor environment fragments inevitably acquire only classical information about the system. Here, we corroborate and generalize those findings. First, we calculate continuity bounds of quantum discord, which establish how much states with a small amount of quantum correlations deviate from being embeddings of classical probability distributions. Also, we demonstrate a universally valid upper bound to the bipartite entanglement of formation between an arbitrary pair of components of a many-body quantum system. The results confirm that proliferation of classical information in the Universe suppresses quantum correlations.

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