Algorithmic Advances Towards a Realizable Quantum Lattice Boltzmann Method

2025-04-15

AI Summary

Quantum Lattice Boltzmann Methods (QLBMs) have long faced practical barriers to hardware implementation—including inefficient classical data encoding, challenging observable readout, and excessive quantum circuit depth. This work presents the first experimental realization of QLBM on real quantum processors. We introduce a tensor-network-based initial-state encoding scheme to significantly enhance data loading efficiency; design decomposable collision and streaming operators combined with a non-uniform convection-field configuration to eliminate post-selection failure; and apply quantum circuit depth compression alongside optimized time-evolution strategies to drastically reduce circuit depth. Experimentally, we successfully simulate 2D Gaussian density advection–diffusion dynamics on physical hardware and achieve the first 3D QLBM simulation under a non-uniform flow field. These results demonstrate both the hardware feasibility and scalability of QLBM for near-term quantum devices.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• Solving key algorithmic issues in Quantum Lattice Boltzmann Method for quantum hardware
• Implementing QLBM on quantum computers with reduced circuit depth and gate count
• Enabling practical 2D and 3D fluid simulations with non-trivial velocity fields

Innovation

• Tensor network encoding reduces circuit depth
• Optimized collision and streaming operators
• Avoids post-selection for multiple timesteps