We attempt the use of a unitary operator to approximate the lattice Boltzmann collision operator. We use a modified amplitude encoding to bypass the renormalization that would have required classical processing at every step (thus eroding any quantum advantage to be had). We describe the hard-wiring of the lattice Boltzmann symmetries into the quantum circuit and show that, for the specific case of the cavity flow, approximating the nonlinear system is limited to low velocities. These findings may help us understand better the possibilities of nonlinear simulations on a quantum computer, and also pave the way for a discussion on how quantum machine learning might be harnessed to address more complex problems.

We propose a quantum algorithm for solving physical problems represented by the lattice Boltzmann formulation. Specifically, we deal with the case of a single phase, incompressible fluid obeying the Bhatnagar-Gross-Krook model. We use the framework introduced by Kowalski that links the nonlinear dynamics of a system to the evolution of bosonic modes, assigning a Carleman linearization order to the truncation in the bosonic Fock space of the bosons. The streaming and collision steps are both achieved via unitary operators. A quantized version of the nonlinear collision term has been implemented, without introducing variables of discrete densities coupled from neighbouring sites, unlike the classical Carleman technique. We use the compact mapping of the bosonic modes to qubits that uses a number of qubits which scales logarithmically with the size of truncated bosonic Fock space. The work can be readily extended to the multitude of multiphysics problems which could adapt the lattice Boltzmann formulation.

We discuss the viability of ensemble simulations of fluid flows on quantum computers. The basic idea is to formulate a functional Liouville equation for the probability distribution of the flow field configuration and recognize that, due to its linearity, such an equation is in principle more amenable to quantum computing than the dynamic equations of fluid motion. After suitable marginalization and associated closure, the Liouville approach is shown to require several hundreds of logical qubits, hence calling for a major thrust in current noise correction and mitigation techniques.

We present a pedagogical introduction to the current state of quantum computing algorithms for the simulation of classical fluids. Different strategies, along with their potential merits and liabilities, are discussed and commented on.

We present a pedagogical introduction to a quantum computing algorithm for the simulation of classical fluids, based on the Carleman linearization of a second-quantized version of lattice kinetic theory. Prospects and limitations for the case of fluid turbulence are discussed and commented on.

We explore the Carleman linearization of the collision term of the lattice Boltzmann formulation, as a first step towards formulating a quantum lattice Boltzmann algorithm. Specifically, we deal with the case of a single, incompressible fluid with the Bhatnagar Gross and Krook equilibrium function. Under this assumption, the error in the velocities is proportional to the square of the Mach number. Then, we showcase the Carleman linearization technique for the system under study. We compute an upper bound to the number of variables as a function of the order of the Carleman linearization. We study both collision and streaming steps of the lattice Boltzmann formulation under Carleman linearization. We analytically show why linearizing the collision step sacrifices the exactness of streaming in lattice Boltzmann, while also contributing to the blow up in the number of Carleman variables in the classical algorithm. The error arising from Carleman linearization has been shown analytically and numerically to improve exponentially with the Carleman linearization order. This bodes well for the development of a corresponding quantum computing algorithm based on the lattice Boltzmann equation.

The Navier-Stokes equations describing fluid dynamics predate the thorough development of thermodynamics, let alone quantum mechanics. This is disconcerting given the utility of the hydrodynamic interpretation in the latter field. In this piece, we motivate the modernization of the fluid dynamics field through the progress that has been made in quantum mechanics and quantum computing.

Exposure to air pollutants has been associated with deleterious health effects that cause premature mortality and a range of morbidities. Air quality in the Mediterranean is of particular interest due to an array of environmental and anthropogenic conditions that make it an air-pollution hotspot. However, the scarcity of data for the region's emission inventories inhibits accurate and holistic assessment. Lebanon, located on the eastern board of the Mediterranean, faces several challenges including an unsustainable transport sector, an unregulated power generation sector, and high urban densities, all of which amplify the air-quality crisis. This paper presents an air pollutant emission inventory for two major emission sources in Lebanon, diesel generators and light duty vehicles (LDVs) of the transport sector, and uncovers trends for over a decade. The exhaust emissions for carbon dioxide, nitrogen oxide, carbon monoxide, sulfur dioxide, and fine particulate matter for diesel generators and for LDVs were estimated by assimilating different approaches and data sources through the use of survey data and national statistics for a higher tier. Our results uncovered that diesel generators consumed almost 1.6 million tons of fuel and emitted about 2 Gg of fine particulate matter in 2016. LDVs doubled in number over a decade and were responsible for approximately 0.20 Gg of fine particulate matter emissions in 2015. While the market for diesel generators appeared to have saturated, ownership of passenger cars per passengers continued to increase, while vehicle age, conditions, and, thus, emissions continued to augment. The results highlight the need for greater government intervention to meet the national electricity demand and promote public transportation and discourage private transportation, especially for energy-inefficient vehicles.