arXiv subjects

Ljubomir Budinski

Publications and source records attributed to Ljubomir Budinski.

10 recordsLinked to original sources

arXiv2026

Quantum machine learning for the quantum lattice Boltzmann method: Trainability of variational quantum circuits for the nonlinear collision operator across multiple time steps

This study investigates the application of quantum machine learning (QML) to approximate the nonlinear component of the collision operator within the quantum lattice Boltzmann method (QLBM). To achieve this, we train a variational quantum circuit (VQC) to construct an operator $U$. When applied to the post-linear-collision quantum state $\ket{Ψ_i}$, this operator yields a final state $\ket{Ψ_f} = U\ket{Ψ_i}$ that successfully replicates the nonlinear collision dynamics derived from the Bhatnagar-Gross-Krook (BGK) approximation. Within this framework, we present two distinct architectures: the R1 model and the R2 model. The R1 model is designed for quantum simulations that involve multiple time steps without intermediate measurements, focusing on accurately capturing nonlinear dynamics in continuous evolution. In contrast, the R2 model is tailored to achieve the high-precision reconstruction of the nonlinear operator for a single time step with an unitary operator.

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arXiv2026

Quantum lattice Boltzmann method for several time steps: A local Carleman linearization algorithm

This article presents a novel encoding for quantum Lattice Boltzmann method algorithm using Carleman linearization. In contrast to previous articles \cite{Sanavio2024LatticeBC,sanavio2025carleman}, the encoding used allows for local collision rules while keeping a higher probability to obtain the right result, which is of the order of $10^{-2}$. The algorithm scales as $O(log_2^2(N)+Q^3)$ each time step with $N$ the number of lattice sites of the 2D lattice and $Q$ the number of channels with a constant number of qubits when using dynamical circuits.

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arXiv2026

Quantum algorithm for the lattice Boltzmann method with applications on real quantum devices

We introduce a novel quantum algorithm for the lattice Boltzmann method (LBM) based on the one-step simplified LBM. The structure of the algorithm allows for more flexibility in modelling different physics in contrast to earlier quantum algorithms for the LBM, while retaining computational efficiency in terms of the gate and qubit complexity. The new algorithm has potential for full end-to-end quantum utility especially for linear problems. We discuss the implementation of examples in linear acoustics, as well as a nonlinear Navier-Stokes problem that was solved on an IBM QPU in a hybrid simulation loop.

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arXiv2025

Quantum Orthogonal Separable Physics-Informed Neural Networks

This paper introduces Quantum Orthogonal Separable Physics-Informed Neural Networks (QO-SPINNs), a novel architecture for solving Partial Differential Equations, integrating quantum computing principles to address the computational bottlenecks of classical methods. We leverage a quantum algorithm for accelerating matrix multiplication within each layer, achieving a $\mathcal O(d\log d/ε^2)$ complexity, a significant improvement over the classical $\mathcal O(d^2)$ complexity, where $d$ is the dimension of the matrix, $ε$ the accuracy level. This is accomplished by using a Hamming weight-preserving quantum circuit and a unary basis for data encoding, with a comprehensive theoretical analysis of the overall architecture provided. We demonstrate the practical utility of our model by applying it to solve both forward and inverse PDE problems. Furthermore, we exploit the inherent orthogonality of our quantum circuits (which guarantees a spectral norm of 1) to develop a novel uncertainty quantification method. Our approach adapts the Spectral Normalized Gaussian Process for SPINNs, eliminating the need for the computationally expensive spectral normalization step. By using a Quantum Orthogonal SPINN architecture based on stacking, we provide a robust and efficient framework for uncertainty quantification (UQ) which, to our knowledge, is the first UQ method specifically designed for Separable PINNs. Numerical results based on classical simulation of the quantum circuits, are presented to validate the theoretical claims and demonstrate the efficacy of the proposed method.

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arXiv2025

Adaptive Lattice Gas Algorithm: Classical and Quantum implementations

Lattice gas algorithms (LGA) are a class of algorithms including, in chronological order, binary lattice gas cellular automata (LGCA), integer lattice gas algorithms (ILGA) and lattice Boltzmann method (LBM). They are largely used for simulating non-linear systems. Starting from 1-dimensional ILGA, we design an algorithm where we carry out a fraction of the possible collisions. These fractions are then adapted to reproduce LBM equilibrium distributions, resulting in an adaptive lattice gas algorithm (ALGA) that achieves the same simulation results of LBM. Considering this, we develop a quantum algorithm that involves a linear collision operator and capable of simulating the same phenomena, while still using a measurement and reinitialization procedure. Multi-time-step implementation is possible in some specific cases briefly discussed.

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arXiv2025

Efficient Quantum Lattice Gas Automata

This study presents a novel quantum algorithm for lattice gas automata simulation with a single time step, demonstrating logarithmic complexity in terms of $CX$ gates. The algorithm is composed of three main steps: collision, mapping, and propagation. A computational complexity analysis and a comparison using different error rates and number of shots are provided. Despite the impact of noise, our findings indicate that accurate simulations could be achieved already on current noisy devices. This suggests potential for efficient simulation of classical fluid dynamics using quantum lattice gas automata, conditional on advancements to expand the current method to multiple time steps and state preparation.

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arXiv2025

Float Lattice Gas Automata: A connection between Molecular Dynamics and Lattice Boltzmann Method for quantum computers

Building upon the Integer Lattice Gas Automata framework of Blommel \textit{et al.} \cite{PhysRevE.97.023310}, we introduce a simplified, fluctuation-free variant. This approach relies on floating-point numbers and closely mirrors the Lattice Boltzmann Method (LBM), with the key distinction being a novel collision operator. This operator, derived from the ensemble average of transition probabilities, generates nonlinear terms. We propose this new Float Lattice Gas Automata (FLGA) collision as a computationally efficient alternative to traditional and quantum LBM implementations.

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arXiv2024

Utilizing classical programming principles in the Intel Quantum SDK: implementation of quantum lattice Boltzmann method

We explore the use of classical programming techniques in implementing the quantum lattice Boltzmann method in the Intel Quantum SDK -- a software tool for quantum circuit creation and execution on Intel quantum hardware. As hardware access is limited, we use the state vector simulator provided by the SDK. The novelty of this work lies in leveraging classical techniques for the implementation of quantum algorithms. We emphasize the refinement of algorithm implementation and devise strategies to enhance quantum circuits for better control over problem variables. To this end, we adopt classical principles such as modularization, which allows for systematic and controlled execution of complex algorithms. Furthermore, we discuss how the same implementation could be expanded from state vector simulations to execution on quantum hardware with minor adjustments in these configurations.

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arXiv2023

Efficient parallelization of quantum basis state shift

Basis state shift is central to many quantum algorithms, most notably the quantum walk. Efficient implementations are of major importance for achieving a quantum speedup for computational applications. We optimize the state shift algorithm by incorporating the shift in different directions in parallel. This provides a significant reduction in the depth of the quantum circuit in comparison to the currently known methods, giving a linear scaling in the number of gates versus working qubits in contrast to the quadratic scaling of the state-of-the-art method based on the quantum Fourier transform. For a one-dimensional array of size $2^n$ for $n > 4$, we derive the total number of $15n + 74$ two-qubit $CX$ gates in the parallel circuit, using a total of $2n-2$ qubits including an ancilla register for the decomposition of multi-controlled gates. We focus on the one-dimensional and periodic shift, but note that the method can be extended to more complex cases.

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arXiv2022

Quantum algorithm for the Navier Stokes equations by using the streamfunction vorticity formulation and the lattice Boltzmann method

A new algorithm for solving the Navier-Stokes equations (NSE) on a quantum device is presented. For the fluid flow equations the stream function-vorticity formulation is adopted, while the lattice Boltzmann method (LBM) is utilized for solving the corresponding system of equations numerically for one time step. Following the nature of the lattice Boltzmann method, the proposed quantum algorithm consists of five major sections: initialization, collision, propagation, boundary condition implementation, and calculation of macroscopic quantities. The collision and boundary condition step is quantumly implemented by applying the standard-form encoding approach, while the quantum walk procedure is applied for the propagation step. The algorithm is implemented by using IBM's quantum computing software development framework Qiskit, while for the verification purposes two-dimensional (2D) cavity flow is simulated and compared with classical code.

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