Quantum Lattice Boltzmann Methods (QLBM) have emerged as a promising candidate for quantum realizations of computational fluid dynamics solvers. However, despite intensive research into the QLBM in recent years, methods for imposing boundary conditions remain limited both in terms of efficiency and expressivity. In this work, we introduce a new method for imposing simple boundary conditions on QLBM that overcomes several limitations of current approaches. Our method forgoes the partitioning of the solid domain into segments and instead applies a single, coherent operation on the entire boundary. We show that our method requires fewer resources both asymptotically and practically for bounce-back and specular reflection boundary conditions.
Quantum Lattice Boltzmann Methods (QLBM) have emerged as a promising candidate for quantum realizations of computational fluid dynamics solvers. However, despite intensive research into the QLBM in recent years, methods for imposing boundary conditions remain limited both in terms of efficiency and expressivity. In this work, we introduce a new method for imposing simple boundary conditions on QLBM that overcomes several limitations of current approaches. Our method forgoes the partitioning of the solid domain into segments and instead applies a single, coherent operation on the entire boundary. We show that our method requires fewer resources both asymptotically and practically for bounce-back and specular reflection boundary conditions.
The quantum lattice Boltzmann method (QLBM) holds promise for efficient fluid simulations, yet the treatment of realistic boundary conditions, particularly solid wall boundary with arbitrary geometry, remains a critical open challenge. We propose a QLBM algorithm that incorporates wall boundaries as well as inlet/outlet velocity conditions. Building upon the existing QLBM with ensemble transformations, we adopt a density-matrix encoding that offers greater flexibility in circuit design and enables the implementation of non-unitary operations through Kraus operators. For boundary enforcement, we design a quantum implementation of the half-way bounce-back scheme and introduce a component exchange step prior to the streaming step, which naturally enforces the no-slip condition without modifying the transport operation. Inlet and outlet conditions are imposed via controlled SWAP operations combined with ancilla registers prepared in the prescribed velocity states. Our QLBM is quantitatively validated through simulations of two-dimensional flows past a backward-facing step, a cylinder, and an obstacle with complex geometry, demonstrating both accuracy and extensibility of our boundary algorithm.
The simulation of gas flows for reentry problems can require to resolve a larger range of spatial scales in order to accurately model the physics of the flow field. In hypersonic flows, the modeling additionally requires to cover a large range in the velocity subspace of the phase space. Scale resolving methods like the Direct Simulation Monte Carlo (DSMC) method have been developed but can become computationally very expensive and unfeasible. Therefore, approximation methods allowing coarser grids are used which, however, may not be sufficiently accurate. To enable more efficient simulation methods, first approaches of a quantum lattice-gas model have been developed but these model do not scale efficiently with the grid resolution. Building on these quantum algorithms, promising modeling approaches using a quantum lattice Boltzmann method (QLBM) with amplitude encoding have shown to efficiently deal with very large grids and fine discretizations. Fine resolution of position and velocity space in the context of lattice Boltzmann methods (LBM) translate to many grid cells and a large set of velocity vectors in the LBM velocity discretization stencil, which can be encoded to scale efficiently in a qubit representation using the QLBM. For the investigation of collisionless flows a method based on Todorova et al. has been adopted and extended (cf. Fig. 1) to build upon our previous publication. The streaming and boundary interaction are modeled as two independent modular blocks, where the streaming block is adapted to be performed independently of the boundary. Additionally, our quantum algorithm includes the summation of the velocity distribution functions to calculate the mass density distribution directly in the quantum simulation. In contrast to a summation by classical post processing, the quantum summation block enables further development to extract reduced data from the quantum computer. This is a key point to not having to extract the entire high dimensional quantum state vector. In this study, a hypersonic collisionless flow around a flat plate with specular reflection is simulated using a quantum lattice Boltzmann method and compared with results using the established DSMC method for modeling rarefied flows. The quantum simulation is performed using a quantum algorithm simulator. Further approaches on how to extend the specular reflection model to a diffusive reflecting model are sketched out.
The Quantum Lattice Boltzmann Method (QLBM) is one of the most promising approaches for realizing the potential of quantum computing in simulating computational fluid dynamics. Many recent works mostly focus on classical simulation, and rely on full state tomography. Several key algorithmic issues like observable readout, data encoding, and impractical circuit depth remain unsolved. As a result, these are not directly realizable on any quantum hardware. We present a series of novel algorithmic advances which allow us to implement the QLBM algorithm, for the first time, on a quantum computer. Hardware results for the time evolution of a 2D Gaussian initial density distribution subject to a uniform advection-diffusion field are presented. Furthermore, 3D simulation results are presented for particular non-uniform advection fields, devised so as to avoid the problem of diminishing probability of success due to repeated post-selection operations required for multiple timesteps. We demonstrate the evolution of an initial quantum state governed by the advection-diffusion equation, accounting for the iterative nature of the explicit QLBM algorithm. A tensor network encoding scheme is used to represent the initial condition supplied to the advection-diffusion equation, significantly reducing the two-qubit gate count affording a shorter circuit depth. Further reductions are made in the collision and streaming operators. Collectively, these advances give a path to realizing more practical, 2D and 3D QLBM applications with non-trivial velocity fields on quantum hardware.
Classical computational fluid dynamics (CFD) methods encounter significant computational bottlenecks in large systems and at high Reynolds number flows due to the rapid increase in degrees of freedom, even on flagship supercomputers. As quantum computers emerge, the Quantum Lattice Boltzmann Method (QLBM) has been proposed as a quantum-native alternative for solving fluid dynamics problems. However, until recently, nearly all studies have relied on classical quantum simulators rather than real quantum hardware. This study presents a benchmark of a one-dimensional QLBM implementation executed on three different IBM Quantum hardware. We design and test a quantum circuit for the advection-diffusion equation using amplitude encoding, a Bhatnagar-Gross-Krook (BGK)-type collision operator, and a streaming step with periodic boundary conditions. Our numerical experiments evaluate transpiled two-qubit gate count, total circuit depth, runtime, and accuracy metrics including maximum absolute error (L∞ norm) and root-mean-square error (RMSE). We find that the present collision and streaming operators dominate the overall cost and become the primary scalability bottleneck on current hardware. To mitigate the prohibitive cost of full quantum state tomography on hardware-based benchmarking exercises, we introduce a sampler-based measurement strategy that reconstructs macroscopic density fields directly from computational-basis measurements. This approach substantially reduces measurement overhead while preserving the expected advection-diffusion dynamics on hardware. These results provide a quantitative assessment of QLBM performance in the noisy intermediate-scale quantum (NISQ) regime and identify the principal algorithmic and experimental limitations that must be addressed for QLBM to become viable for fluid dynamics.
The Quantum Lattice Boltzmann Method (QLBM) has emerged as one of the most promising quantum computing approaches for the numerical simulation of problems in computational fluid dynamics (CFD). The dynamics is formulated in terms of mesoscopic particle distribution functions governed by a discrete Boltzmann transport equation, comprising local streaming and collision operations. In this work, the resulting macroscopic behavior corresponds to the advection-diffusion equation, which we adopt as a canonical model problem for transport phenomena. Building upon recent progress in QLBM implementations, we advance towards more realistic problem settings that better reflect conventional CFD requirements. We address, for the first time, transport under the action of non uniform velocity fields on quantum hardware. We implement our demonstration using IonQ's trapped-ion systems including Forte generation systems and a 64-qubit Barium development system similar to the forthcoming IonQ Tempo line. We identify the density readout and subsequent reloading of the fluid density as a potential bottleneck of the current algorithm and discuss several approaches to mitigate this bottleneck. We identify the use of MPS shadow tomography as a promising method to efficiently scale the readout to large system with complex density distributions. Lastly, we introduce and simulate a novel method to implement wall boundaries for advection-diffusion in QLBM, and discuss the prospects of scaling to higher-complexity problems.
To simulate highly-resolved flow fields, we extend the Quantum Lattice Boltzmann Method (QLBM) to be able to simulate multiple time steps without state extraction or reinitialization. We adjust and extend given QLBM approaches from the literature to completely remove the need to measure or reinitialize the flow field in between the simulation time steps. Therefore, our algorithm does not require to sample the entire flow field at any time. We solve the linear advection-diffusion problem with periodic boundary conditions and derive all necessary equations and build the corresponding quantum circuit diagrams, including details on the QLBM blocks and explicitly drawing the circuit gates. We discuss the general decay of a QLBM step and how that effects our algorithm. The new algorithm is verified on 1D and 2D test cases using the shot method of IBMs Qiskit package. We show excellent agreement and convergence between our QLBM and the classical Lattice Boltzmann method. The conclusion section includes a discussion on the advantages of our algorithm as well as limitations and to what extent it is more efficient.