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Claudio Sanavio

Publications and source records attributed to Claudio Sanavio.

At least 19 recordsLinked to original sources
arXiv2026

Variational-Adiabatic Quantum Solver for Systems of Linear Equations with Warm Starts

We propose a revisited variational quantum solver for linear systems, designed to circumvent the barren plateau phenomenon by combining two key techniques: adiabatic evolution and warm starts. To this end, we define an initial Hamiltonian with a known ground state which is easily implemented on the quantum circuit, and then "adiabatically" evolve the Hamiltonian by tuning a control variable in such a way that the final ground state matches the solution to the given linear system. This evolution is carried out in incremental steps, and the ground state at each step is found by minimizing the energy using the parameter values corresponding to the previous minimum as a warm start to guide the search. As a first test case, the method is applied to several linear systems obtained by discretizing a one-dimensional heat flow equation with different physical assumptions and grid choices. Our method successfully and reliably improves upon the solution to the same problem as obtained by a conventional quantum solver, reaching very close to the global minimum also in the case of very shallow circuit implementations.

quant-ph↗
arXiv2026

Optomechanical systems with linear and quadratic position couplings: Dynamics and optimal estimation

We study the dynamics of an optomechanical system consisting of a single-mode optical field coupled to a mechanical oscillator, where the nonlinear interaction includes both linear and quadratic terms in the oscillator's position. We present an analytical solution to this quantum-mechanical Hamiltonian problem by employing the formalism of two-phonon coherent states. Quantum estimation theory is applied to the resulting state of the optical field, with a focus on evaluating the quantum Fisher information with respect to the strength of the quadratic coupling. Our estimation scheme employs balanced homodyne photodetection and demonstrates that the corresponding classical Fisher information can reach the quantum Fisher information limit, with the phase of the local coherent oscillator playing a crucial role.

quant-ph↗
arXiv2026

Block encoding of sparse matrices with a periodic diagonal structure

Block encoding is a successful technique used in several powerful quantum algorithms. In this work we provide an explicit quantum circuit for block encoding a sparse matrix with a periodic diagonal structure. The proposed methodology is based on the linear combination of unitaries (LCU) framework and on an efficient unitary operator used to project the complex exponential at a frequency $ω$ multiplied by the computational basis into its real and imaginary components. We demonstrate a distinct computational advantage with a $\mathcal{O}(\text{poly}(n))$ gate complexity, where $n$ is the number of qubits, in the worst-case scenario used for banded matrices, and $\mathcal{O}(n)$ when dealing with a simple diagonal matrix, compared to the exponential scaling of general-purpose methods for dense matrices. Various applications for the presented methodology are discussed in the context of solving differential problems such as the advection-diffusion-reaction (ADR) dynamics, using quantum algorithms with optimal scaling, e.g., quantum singular value transformation (QSVT). Numerical results are used to validate the analytical formulation.

quant-ph↗
arXiv2026

Quantum Algorithm for the Fixed-Radius Neighbor Search

Neighbor search is a computationally demanding problem, usually both time- and memory-consuming. The main problem of this kind of algorithms is the long execution time due to cache misses. In this work, we propose a quantum algorithm for the Fixed RAdius Neighbor Search problem (FRANS) based on the fixed-point version of Grover's algorithm. We propose an efficient circuit for solving the FRANS with linear query complexity with the number of particles $N$. The quantum circuit returns the list of all the neighbors' pairs within the fixed radius, together with their distance, avoiding the slow down given by cache miss. We analyzed the gate and the query complexity of the circuit. Our FRANS algorithm presents a query complexity of $\mathcal{O}(N/\sqrt{M})$, where $M$ is the number of solutions, reaching the optimal lower bound of the Grover's algorithm. We propose different implementations of the oracle, which must be chosen depending on the precise structure of the database. Among these, we present an implementation using the Chebyshev distance with depth $\mathcal{O}(q_1)$, where $2^{q_1}$ is the number of grid points used to discretize a spatial dimension. State-of-the-art algorithms for state preparation allow for a trade-off between depth and width of the circuit, with a volume (depth$\times$ width) of $\mathcal{O}(N\log(N))$. This unfavorable scaling can be brought down to $\mathcal{O}(\text{poly}(\log N))$ in case of structured datasets. We proposed a stopping criterion based on Bayes interference and tested its validity on $1D$ simulations. Finally, we accounted for the readout complexity and assessed the resilience of the model to the readout error, suggesting an error correction-free strategy to check the accuracy of the results.

quant-ph↗
arXiv2025

The foundational value of quantum computing for classical fluids

Quantum algorithms for classical physics problems expose new patterns of quantum information flow as compared to the many-body Schrödinger equation. As a result, besides their potential practical applications, they also offer a valuable theoretical and computational framework to elucidate the foundations of quantum mechanics, particularly the validity of the many-body Schrödinger equation in the limit of large number of particles, on the order of the Avogadro number. This idea is illustrated by means of a concrete example, the Block-Encoded Carleman embedding of the Lattice Boltzmann formulation of fluid dynamics (CLB).

quant-ph↗
arXiv2025

Improved amplitude amplification strategies for the quantum simulation of classical transport problems

The quantum simulation of classical fluids often involves the use of probabilistic algorithms that encode the result of the dynamics in the form of the amplitude of the selected quantum state. In most cases, however, the amplitude probability is too low to allow an efficient use of these algorithms, thereby hindering the practical viability of the quantum simulation. The oblivious amplitude amplification algorithm is often presented as a solution to this problem, but to no avail for most classical problems, since its applicability is limited to unitary dynamics. In this paper, we show analytically that oblivious amplitude amplification when applied to non-unitary dynamics leads to a distortion of the quantum state and to an accompanying error in the quantum update. We provide an analytical upper bound of such error as a function of the degree of non-unitarity of the dynamics and we test it against a quantum simulation of an advection-diffusion-reaction equation, a transport problem of major relevance in science and engineering. Finally, we also propose an amplification strategy that helps mitigate the distortion error, while still securing an enhanced success probability.

quant-ph↗
arXiv2025

Carleman-lattice-Boltzmann quantum circuit with matrix access oracles

We apply Carleman linearization of the Lattice Boltzmann (CLB) representation of fluid flows to quantum emulate the dynamics of a 2D Kolmogorov-like flow. We assess the accuracy of the result and find a relative error of the order of $10^{-3}$ with just two Carleman iterates, for a range of the Reynolds number up to a few hundreds. We first define a gate-based quantum circuit for the implementation of the CLB method and then exploit the sparse nature of the CLB matrix to build a quantum circuit based on block-encoding techniques which makes use of matrix oracles. It is shown that the gate complexity of the algorithm is thereby dramatically reduced, from exponential to quadratic. However, due to the need of employing up to seven ancilla qubits, the probability of success of the corresponding circuit for a single time step is too low to enable multi-step time evolution. Several possible directions to circumvent this problem are briefly outlined.

quant-ph↗
arXiv2024

Explicit Quantum Circuit for Simulating the Advection-Diffusion-Reaction Dynamics

We assess the convergence of the Carleman linearization of advection-diffusion-reaction (ADR) equations with a logistic nonlinearity. It is shown that five Carleman iterates provide a satisfactory approximation of the original ADR across a broad range of parameters and strength of nonlinearity. To assess the feasibility of a quantum algorithm based on this linearization, we analyze the projection of the Carleman ADR matrix onto the tensor Pauli basis. It is found that the Carleman ADR matrix requires an exponential number of Pauli gates as a function of the number of qubits. This prevents the practical implementation of the Carleman approach to the quantum simulation of ADR problems on current hardware. We propose to address this limitation by resorting to block-encoding techniques for sparse matrix employing oracles. Such quantum ADR oracles are presented in explicit form and shown to turn the exponential complexity into a polynomial one. However, due to the low probability of successfully implementing the nonunitary Carleman operator, further research is needed to implement the multi-timestep version of the present circuit.

quant-ph↗
arXiv2024

Carleman-Grad approach to the quantum simulation of fluids

We discuss the Carleman linearization approach to the quantum simulation of classical fluids based on Grad's generalized hydrodynamics and compare it to previous investigations based on lattice Boltzmann and Navier-Stokes formulations. We show that the Carleman-Grad procedure exhibits intermediate properties between the two. Namely, convergence of the Carleman iteration over a few tens of timesteps and a potentially viable quantum circuit implementation using quantum linear algebra solvers. However, both features still need substantial improvements to yield a viable quantum algorithm for fluid flows.

quant-ph↗
arXiv2024

Fisher-information-based estimation of optomechanical coupling strengths

The formalism of quantum estimation theory, focusing on the quantum and classical Fisher information, is applied to the estimation of the coupling strength in an optomechanical system. In order to estimate the optomechanical coupling, we have considered a cavity optomechanical model with non-Markovian Brownian motion of the mirror and employed input-output formalism to obtain the cavity output field. Our estimation scenario is based on balanced homodyne photodetection of the cavity output field. We have explored the difference between the associated measurement-dependent classical Fisher information and the quantum Fisher information, thus addressing the question of whether it is possible to reach the lower bound of the mean squared error of an unbiased estimator by means of balanced homodyne detection. We have found that the phase of the local oscillator in the homodyne detection is crucial; certain quadrature measurements allow very accurate estimation.

quant-ph↗
arXiv2024

Quantum Circuit for Imputation of Missing Data

The imputation of missing data is a common procedure in data analysis that consists in predicting missing values of incomplete data points. In this work we analyse a variational quantum circuit for the imputation of missing data. We construct variational quantum circuits with gates complexity $O(N)$ and $O(N^2)$ that return the last missing bit of a binary string for a specific distribution. We train and test the performance of the algorithms on a series of datasets finding good convergence of the results. Finally, we test the circuit for generalization to unseen data. For simple systems, we are able to describe the circuit analytically, making possible to skip the tedious and unresolved problem of training the circuit with repetitive measurements. We find beforehand the optimal values of the parameters and we make use of them to construct an optimal circuit suited to the generation of truly random data.

quant-ph↗
arXiv2024

Three Carleman routes to the quantum simulation of classical fluids

We discuss the Carleman approach to the quantum simulation of classical fluids, as applied to i) Lattice Boltzmann (CLB), ii) Navier-Stokes (CNS) and iii) Grad (CG) formulations of fluid dynamics. CLB shows excellent convergence properties, but it is plagued by nonlocality which results in an exponential depth of the corresponding circuit with the number of Carleman variables. The CNS offers a dramatic reduction of the number Carleman variables, which might lead to a viable depth, provided locality can be preserved and convergence can be achieved with a moderate number of iterates also at sizeable Reynolds numbers. Finally it is argued that CG might combine the best of CLB and CNS.

physics.flu-dyn↗
arXiv2024

Lattice Boltzmann-Carleman quantum algorithm and circuit for fluid flows at moderate Reynolds number

We present a quantum computing algorithm for fluid flows based on the Carleman-linearization of the Lattice Boltzmann (LB) method. First, we demonstrate the convergence of the classical Carleman procedure at moderate Reynolds numbers, namely for Kolmogorov-like flows. Then we proceed to formulate the corresponding quantum algorithm, including the quantum circuit layout and analyze its computational viability. We show that, at least for moderate Reynolds numbers between 10 and 100, the Carleman-LB procedure can be successfully truncated at second order, which is a very encouraging result. We also show that the quantum circuit implementing the single time-step collision operator has a fixed depth, regardless of the number of lattice sites. However, such depth is of the order of ten thousands quantum gates, meaning that quantum advantage over classical computing is not attainable today, but could be achieved in the near-mid term future. The same goal for the multi-step version remains however an open topic for future research.

quant-ph↗
arXiv2023

Hybrid classical-quantum branch-and-bound algorithm for solving integer linear problems

Quantum annealers are suited to solve several logistic optimization problems expressed in the QUBO formulation. However, the solutions proposed by the quantum annealers are generally not optimal, as thermal noise and other disturbing effects arise when the number of qubits involved in the calculation is too large. In order to deal with this issue, we propose the use of the classical branch-and-bound algorithm, that divides the problem into sub-problems which are described by a lower number of qubits. We analyze the performance of this method on two problems, the knapsack problem and the traveling salesman problem. Our results show the advantages of this method, that balances the number of steps that the algorithm has to make with the amount of error in the solution found by the quantum hardware that the user is willing to risk. All the results are actual runs on the quantum annealer D-Wave Advantage.

quant-ph↗
arXiv2023

Entanglement Classification via Witness Operators generated by Support Vector Machine

Although entanglement is a basic resource for reaching quantum advantange in many computation and information protocols, we lack a universal recipe for detecting it, with analytical results obtained for low dimensional systems and few special cases of higher dimensional systems. In this work, we use a machine learning algorithm, the support vector machine with polynomial kernel, to classify separable and entangled states. We apply it to two-qubit and three-qubit systems, and we show that, after training, the support vector machine is able to recognize if a random state is entangled with an accuracy up to 92% for the two-qubit system and up to 98% for the three-qubit system. We also describe why and in what regime the support vector machine algorithm is able to implement the evaluation of an entanglement witness operator applied to many copies of the state, and we describe how we can translate this procedure into a quantum circuit.

quant-ph↗
arXiv2022

Estimation of disorders in the rest positions of two membranes in optomechanical systems

The formalism of quantum estimation theory is applied to estimate the disorders in the positions of two membranes positioned in a driven cavity. We consider the coupled-cavities and the transmissive-regime models to obtain effective descriptions of this system for different reflectivity values of the membranes. Our models consist also high temperatures Brownian motions of the membranes, losses of the cavity fields, the input-output formalism and a balanced homodyne photodetection of the cavity output field. In this two-parameter estimation scenario we compare the classical and quantum Fisher information matrices and evaluate the accuracies of the estimations. We show that models prefer very different estimation strategies and the temperature does not have a detrimental effect on the estimation accuracies, but makes more difficult to attain the quantum optimal limit. Our analysis also reveals that best estimation strategies with unit effiecient detectors are measurements of the quadratures of the output field.

quant-ph↗
arXiv2021

Optimal estimation of the optomechanical coupling strength

We apply the formalism of quantum estimation theory to obtain information about the value of the nonlinear optomechanical coupling strength. In particular, we discuss the minimum mean-square error estimator and a quantum Cramér--Rao-type inequality for the estimation of the coupling strength. Our estimation strategy reveals some cases where quantum statistical inference is inconclusive and merely result in the reinforcement of prior expectations. We show that these situations also involve the highest expected information losses. We demonstrate that interaction times in the order of one time period of mechanical oscillations are the most suitable for our estimation scenario, and compare situations involving different photon and phonon excitations.

quant-ph↗