Sphere Packing on a Quantum Computer for Chromatography Modeling

TL;DR

This paper explores quantum computing methods to model sphere packing in chromatography, aiming to incorporate particle-level phenomena and estimate quantum resources needed for realistic simulations.

Contribution

It formulates sphere packing models for chromatography on quantum computers and provides a resource scaling analysis for future quantum advantage.

Findings

Quantum approximate optimization algorithm applied to homogeneous packing.

Classical simulations of heterogeneous packing.

Resource estimates for quantum simulation of complex models.

Abstract

Column chromatography is an important process in downstream biopharmaceutical manufacturing that enables high-selectivity separation of proteins through various modalities, such as affinity, ion exchange, hydrophobic interactions, or a combination of the aforementioned modes. Current mechanistic models of column chromatography typically abstract particle-level phenomena, in particular adsorption kinetics. A mechanistic model capable of incorporating particle-level phenomena would increase the value derived from mechanistic models. To this end, we model column chromatography via sphere packing, formulating three versions, each with increasing complexity. The first, homogeneous circle packing, is recast as maximum independent set and solved by the Quantum Approximate Optimization Algorithm on a quantum computer. The second, heterogeneous circle packing, is formulated as a graphical optimization problem and solved via classical simulations, accompanied by a road map to a quantum solution. An extension to the third, heterogeneous sphere packing, is formulated mathematically in a manner suitable to a quantum solution. Finally, detailed resource scaling is conducted to estimate the quantum resources required to simulate the most realistic model, providing a pathway to quantum advantage.