Fully Quantum Lattice Gas Automata Building Blocks for Computational Basis State Encodings

TL;DR

This paper introduces new quantum lattice gas automata building blocks using computational basis state encodings, enhancing simulation efficiency and flexibility for quantum CFD modeling.

Contribution

It presents novel quantum LGA components, including initial condition setups, boundary conditions, collision operators, and measurement circuits, with detailed complexity analysis and open-source implementations.

Findings

Efficient quantum circuits for initial conditions and boundary patterns

A collision operator modeling less restricted interactions

Complexity analysis of quantum LGA algorithms

Abstract

Lattice Gas Automata (LGA) is a classical method for simulating physical phenomena, including Computational Fluid Dynamics (CFD). Quantum LGA (QLGA) is the family of methods that implement LGA schemes on quantum computers. In recent years, QLGA has garnered attention from researchers thanks to its potential of efficiently modeling CFD processes by either reducing memory requirements or providing simultaneous representations of exponentially many LGA states. In this work, we introduce novel building blocks for QLGA algorithms that rely on computational basis state encodings. We address every step of the algorithm, from initial conditions to measurement, and provide detailed complexity analyses that account for all discretization choices of the system under simulation. We introduce multiple ways of instantiating initial conditions, efficient boundary condition implementations for novel geometrical patterns, a novel collision operator that models less restricted interactions than previous implementations, and quantum circuits that extract quantities of interest out of the quantum state. For each building block, we provide intuitive examples and open-source implementations of the underlying quantum circuits.