arXiv subjects

Giuseppe Di Molfetta

Publications and source records attributed to Giuseppe Di Molfetta.

At least 19 recordsLinked to original sources

arXiv2026

Two-dimensional quantum lattice gas algorithm for anisotropic Burger-like equations

Building on hybrid quantum lattice gas algorithm, we revisit the possibilities of this quantum lattice model. By deriving a correction to the predicted viscosity, we provide analytical and numerical results that refine original formulation. We introduce a minimal 2D generalization of the algorithm, which allows to simulate anisotropic Burgers like equations while retaining only two lattice velocities. This approach opens a promising route toward embedding momentum conservation and advancing toward Navier Stokes dynamics in 2D, going beyond Frisch, Hasslacher and Pomeau (FHP) and lattice Boltzmann method (LBM) with a quantum native model. We highlight how the presented algorithm results more efficient in full state evolution than other quantum nonlinear solvers, nonetheless its advantages respect to classical lattice gas methods. Being this model between classical and quantum computation, it gives a unique perspective on simulating nonlinearities with quantum computers, confirming quantum lattice gas models as a crucial playground for quantum simulations of nonlinearities.

quant-ph↗

arXiv2026

Unconditionally successful quantum Time-Marching algorithm via LCU for nonlinear Burgers equation

Most recently proposed quantum algorithms for solving linear and nonlinear partial differential equations rely on non-unitary operations. These operations are typically implemented probabilistically, requiring postselection and thus increasing the computational cost. We show that quantum lattice gas algorithms enable unconditionally successful quantum simulation of nonlinearities, yielding, to our knowledge, the first quantum algorithm for Burgers equation whose time steps can be concatenated without probabilistic failure. The key idea is to exploit the correspondence between the stochasticity of quantum measurement in the linear combination of unitaries framework and the intrinsic randomness of the classical lattice gas algorithm. In doing so, we identify general properties that characterize probabilistic classical algorithms amenable to this time-marching formulation, and illustrate the approach with an additional application.

quant-ph↗

arXiv2026

Qubit-Boson Hybrid Beam-Splitter Gate with Kerr Nonlinearity in Circuit QED for Many-Body Dynamics

We introduce a hybrid qubit-boson beam-splitter gate in which a microwave cavity mode couples to an exchange-dressed two-level subsystem of an interacting two-qubit system in the presence of Kerr nonlinearity. Starting from a general circuit quantum electrodynamics (cQED) model, we derive the corresponding hybrid qubit-cavity interaction, develop its open-system description including photon- and qubit-sector-bath-induced dissipation and obtain in the weak-dissipation regime an analytical expression for the average gate fidelity. We further identify carbon-nanotube circuit QED as a concrete platform for implementing and controlling the gate, provide a representative operating regime and perform noiseless and noisy numerical simulations to study the gate dynamics and benchmark the analytical results. Beyond this implementation route, the proposed hybrid primitive provides a natural building block for many-body dynamics, including quantum-cellular-automaton (QCA) and lattice-gauge-inspired architectures and, through its collision-model reformulation, also suggests connections to noisy QCA, non-Markovian extensions and reservoir-style quantum information processing.

quant-ph↗

arXiv2026

Quantum Computing : A New Frontier for Science and Society

This short report explores the (non exhaustive) current state of quantum technologies, their potential applications, and the challenges that must be addressed to harness their full potential. In particular we will focus on the quantum computer architecture and its ecosystem. Such architecture represents a complex, multi-layered system that integrates quantum and classical components to enable the execution of quantum algorithms. This manuscript is then organized as follows : first we will introduce the quantum processing unit, the lowest layer of a quantum computer. Then we will progress from the lowest to the higher layer of the system architectures : measurement, circuit control, error correction and mitigation system, the quantum compiler and finally the software stack, with particular emphasis on the interactions between these components

quant-ph↗

arXiv2026

On Quantum Perceptron Learning via Quantum Search

With the growing interest in quantum machine learning, the perceptron, a fundamental building block in traditional machine learning, has emerged as a valuable model for exploring the potential of quantum algorithms. In this work, we make two principal contributions. First, we revisit the \emph{quantum version space perceptron} algorithm proposed by Kapoor et al. (2016), by identifying and correcting a flawed complexity assumption. We show that the query complexity of the algorithm is dimension-dependent, which has significant implications for its behaviour in high-dimensional regimes under worst-case scenarios. Second, we propose and analyse two \emph{quantum-enhanced} cutting-plane algorithms for perceptron learning. Specifically, we leverage established quantum subroutines such as \emph{Grover's search} and \emph{quantum walk search}, and provide detailed algorithmic constructions together with query and arithmetic complexity analyses. Our results establish improved complexity bounds under an idealised implementation framework and noise-free quantum computational models, offering insights into the trade-offs between margin dependence, dimensional dependence, and quantum resources. These findings provide a refined understanding of quantum perceptron models and their theoretical computational complexity properties.

quant-ph↗

arXiv2025

Noisy simulations of Quantum Walk and Quantum Walk search via Quantum Cellular Automata on a semiconducting spin processor emulator

In this work we map NISQ-friendly implementations of the non-interacting QCA to a circuit Quantum Electrodynamics (cQED) hardware. We perform both noiseless and noisy simulations of the QCA one particle sector, namely the Quantum Walk, on $N$-cycles and $N \times N$ torus graphs. Moreover, within this framework, we also investigate the search problem and present a circuit for preparing the W state (i.e., the Dicke state with hamming weight one) using only N-1 $\sqrt{\text{iSWAP}}$ gates and no ancilla qubits. The noiseless simulations are conducted with the Qiskit Aer simulator, while the noisy simulations with C12 Quantum Electronics' in-house noisy emulator, \textit{Callisto}. We benchmark the performance of our implementations by analyzing the simulations via relevant metrics and quantities such as the state count distributions, the Hellinger Fidelity, the $\ell^{1}$ distance, the hitting time, and success probability. Our results demonstrate that the QCA framework, in combination with cQED processors, holds promise as an effective platform for early NISQ implementations of Quantum Walk and Quantum Walk Search algorithms.

quant-ph↗

arXiv2025

Non-unitary enhanced transfer efficiency in quantum walk search on complex networks

The task of finding an element in an unstructured database is known as spatial search and can be expressed as a quantum walk evolution on a graph. In this article, we modify the usual search problem by adding an extra trapping vertex to the graph, which is only connected to the target element. We study the transfer efficiency of the walker to a trapping site, using the search problem as a case study. Thus, our model offers no computational advantage for the search problem, but focuses on information transport in an open environment with a search Hamiltonian. The walker evolution is a mix between classical and quantum walk search dynamics. The balance between unitary and non-unitary dynamics is tuned with a parameter, and we numerically show that depending on the graph topology and the connectivity of the target element, this hybrid approach can outperform a purely classical or quantum evolution for reaching the trapping site. We show that this behavior is only observed in the presence of an extra trapping site, and that depending on the topology and a tunable parameter controlling the strength of the oracle, a hybrid regime composed of 90% coherent dynamics can lead to either the highest or worst transfer efficiency to the trapping site. We also relate the performance of an hybrid regime to the entropy's decay rate. As the introduction of non-unitary operations may be considered as noise, we interpret this phenomena as a noisy-assisted quantum evolution.

quant-ph↗

arXiv2025

Sampled-Based Guided Quantum Walk: Non-variational quantum algorithm for combinatorial optimization

We introduce SamBa-GQW, a novel quantum algorithm for solving binary combinatorial optimization problems of arbitrary degree with no use of any classical optimizer. The algorithm is based on a continuous-time quantum walk on the solution space represented as a graph. The walker explores the solution space to find its way to vertices that minimize the cost function of the optimization problem. The key novelty of our algorithm is an offline classical sampling protocol that gives information about the spectrum of the problem Hamiltonian. Then, the extracted information is used to guide the walker to high quality solutions via a quantum walk with a time-dependent hopping rate. We investigate the performance of SamBa-GQW on several quadratic problems, namely MaxCut, maximum independent set, portfolio optimization, and higher-order polynomial problems such as LABS, MAX-$k$-SAT and a quartic reformulation of the travelling salesperson problem. We empirically demonstrate that SamBa-GQW finds high quality approximate solutions on problems up to a size of $n=20$ qubits by only sampling $n^2$ states among $2^n$ possible decisions. SamBa-GQW compares very well also to other guided quantum walks and QAOA.

quant-ph↗

arXiv2025

A quantum walk inspired model for distributed computing on arbitrary graphs

A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. For a long time, these models have interested the community for their nice properties such as locality or translation invariance. This work introduces a model of distributed computation for arbitrary graphs inspired by quantum cellular automata. As a by-product, we show how this model can reproduce the dynamic of a quantum walk on graphs. In this context, we investigate the communication cost for two interaction schemes. Finally, we explain how this particular quantum walk can be applied to solve the search problem and present numerical results on different types of topologies.

quant-ph↗

arXiv2025

Quantum collision circuit, quantum invariants and quantum phase estimation procedure for fluid dynamic lattice gas automata

Lattice Gas Cellular Automata (LGCA) is a classical numerical method widely known and applied to simulate several physical phenomena. In this paper, we study the translation of LGCA on quantum computers (QC) using computational basis encoding (CBE), developing methods for different purposes. In particular, we clarify and discuss some fundamental limitations and advantages in using CBE and quantum walk as streaming procedure. Using quantum walks affect the possible encoding of classical states in quantum orthogonal states, feature linked to the unitarity of collision and to the possibility of getting a quantum advantage. Then, we give efficient procedures for optimizing collisional quantum circuits, based on the classical features of the model. This is applied specifically to fluid dynamic LGCA. Alongside, a new collision circuit for a 1-dimensional model is proposed. We address the important point of invariants in LGCA providing a method for finding how many invariants appear in their QC formulation. Quantum invariants outnumber the classical expectations, proving the necessity of further research. Lastly, we prove the validity of a method for retrieving any quantity of interest based on quantum phase estimation (QPE).

quant-ph↗

arXiv2024

A relativistic discrete spacetime formulation of 3+1 QED

This work provides a relativistic, digital quantum simulation scheme for both $2+1$ and $3+1$ dimensional quantum electrodynamics (QED), based on a discrete spacetime formulation of theory. It takes the form of a quantum circuit, infinitely repeating across space and time, parametrised by the discretization step $Δ_t=Δ_x$. Strict causality at each step is ensured as circuit wires coincide with the lightlike worldlines of QED; simulation time under decoherence is optimized. The construction replays the logic that leads to the QED Lagrangian. Namely, it starts from the Dirac quantum walk, well-known to converge towards free relativistic fermions. It then extends the quantum walk into a multi-particle sector quantum cellular automata in a way which respects the fermionic anti-commutation relations and the discrete gauge invariance symmetry. Both requirements can only be achieved at cost of introducing the gauge field. Lastly the gauge field is given its own electromagnetic dynamics, which can be formulated as a quantum walk at each plaquette.

quant-ph↗

arXiv2024

Dirac quantum walk on tetrahedra

Discrete-time Quantum Walks (QWs) are transportation models of single quantum particles over a lattice. Their evolution is driven through causal and local unitary operators. QWs are a powerful tool for quantum simulation of fundamental physics as some of them have a continuum limit converging to well-known physics partial differential equations, such as the Dirac or the Schrödinger equation. In this work, we show how to recover the Dirac equation in (3+1)-dimensions with a QW evolving in a tetrahedral space. This paves the way to simulate the Dirac equation on a curved spacetime. This also suggests an ordered scheme for propagating matter over a spin network, of interest in Loop Quantum Gravity where matter propagation has remained an open problem.

quant-ph↗

arXiv2023

A quantum walk-based scheme for distributed searching on arbitrary graphs

A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. Searching in this mathematical framework has interested the community since a long time. However, most results consider spatial search on regular graphs. This work introduces a new quantum walk-based searching scheme, designed to search nodes or edges on arbitrary graphs. As byproduct, such new model allows to generalise quantum cellular automata, usually defined on regular grids, to quantum anonymous networks, allowing a new physics-like mathematical environment for distributed quantum computing.

quant-ph↗

arXiv2023

Large-Scale Quantum Separability Through a Reproducible Machine Learning Lens

The quantum separability problem consists in deciding whether a bipartite density matrix is entangled or separable. In this work, we propose a machine learning pipeline for finding approximate solutions for this NP-hard problem in large-scale scenarios. We provide an efficient Frank-Wolfe-based algorithm to approximately seek the nearest separable density matrix and derive a systematic way for labeling density matrices as separable or entangled, allowing us to treat quantum separability as a classification problem. Our method is applicable to any two-qudit mixed states. Numerical experiments with quantum states of 3- and 7-dimensional qudits validate the efficiency of the proposed procedure, and demonstrate that it scales up to thousands of density matrices with a high quantum entanglement detection accuracy. This takes a step towards benchmarking quantum separability to support the development of more powerful entanglement detection techniques.

quant-ph↗

arXiv2023

Twisted quantum walks, generalised Dirac equation and Fermion doubling

Quantum discrete-time walkers have, since their introduction, demonstrated applications in algorithmic and in modeling and simulating a wide range of transport phenomena. They have long been considered the discrete-time and discrete space analogue of the Dirac equation and have been used as a primitive to simulate quantum field theories precisely because of some of their internal symmetries. In this paper we introduce a new family of quantum walks, said twisted, which admits, as continuous limit, a generalized Dirac operator equipped with a dispersion term. Moreover, this quadratic term in the energy spectrum acts as an effective mass, leading to a regularization of the well known Fermion doubling problem.

quant-ph↗

arXiv2023

Optimality conditions for spatial search with multiple marked vertices

We contribute to fulfil the long-lasting gap in the understanding of the spatial search with multiple marked vertices. The theoretical framework is that of discrete-time quantum walks (QW), \textit{i.e.} local unitary matrices that drive the evolution of a single particle on the lattice. QW based search algorithms are well understood when they have to tackle the fundamental problem of finding only one marked element in a $d-$dimensional grid and it has been proven they provide a quadratic advantage over classical searching protocols. However, once we consider to search more than one element, the behaviour of the algorithm may be affected by the spatial configuration of the marked elements and even the quantum advantage is no longer guaranteed. Here our main contribution is threefold~: (i)~we provide \textit{sufficient conditions for optimality} for a multi-items QWSearch algorithm~; (ii)~we provide analytical evidences that \textit{almost, but not all} spatial configurations with multiple marked elements are optimal; and (iii)~we numerically show that the computational advantage with respect to the classical counterpart is not always certain and it does depend on the proportion of searched elements over the total number of grid points.

quant-ph↗

arXiv2022

Entanglement dynamics and ergodicity breaking in a quantum cellular automaton

Ergodicity breaking is observed in the blockade regime of Rydberg atoms arrays, in the form of low entanglement eigenstates known as scars, which fail to thermalize. The signature of these states persists in periodically driven systems, where they coexist with an extensive number of chaotic states. Here we investigate a quantum cellular automaton based on the classical rule that updates a site if its two neighbors are in the lower state. We show that the breaking of ergodicity extends to chaotic states. The dynamical breaking of ergodicity is controlled by chiral quasiparticle excitations which propagate entanglement. Evidence of nonlocal entanglement is found, showing that these nonthermal chaotic states may be useful to quantum computation.

quant-ph↗

arXiv2022

Quantum Perceptron Revisited: Computational-Statistical Tradeoffs

Quantum machine learning algorithms could provide significant speed-ups over their classical counterparts; however, whether they could also achieve good generalization remains unclear. Recently, two quantum perceptron models which give a quadratic improvement over the classical perceptron algorithm using Grover's search have been proposed by Wiebe et al. arXiv:1602.04799 . While the first model reduces the complexity with respect to the size of the training set, the second one improves the bound on the number of mistakes made by the perceptron. In this paper, we introduce a hybrid quantum-classical perceptron algorithm with lower complexity and better generalization ability than the classical perceptron. We show a quadratic improvement over the classical perceptron in both the number of samples and the margin of the data. We derive a bound on the expected error of the hypothesis returned by our algorithm, which compares favorably to the one obtained with the classical online perceptron. We use numerical experiments to illustrate the trade-off between computational complexity and statistical accuracy in quantum perceptron learning and discuss some of the key practical issues surrounding the implementation of quantum perceptron models into near-term quantum devices, whose practical implementation represents a serious challenge due to inherent noise. However, the potential benefits make correcting this worthwhile.

quant-ph↗