MRI Scientists Propose Quantum Approach to Differential Equations

In recently published research, imaging scientists at NYU Langone Health and its Center for Advanced Imaging Innovation and Research in collaboration with colleagues at NASA Ames Research Center and the Superconducting Quantum Materials and Systems (SQMS) Center at Fermilab propose a new approach to solving differential equations on quantum hardware.

Ordinary differential equations, also known as ODEs, are widely used across scientific and engineering fields to describe, analyze, and predict the dynamic behavior of complex systems, such as electromagnetic fields, enzyme reactions, and economic and climate models. But the complexity of ODEs poses computational and accuracy challenges to conventional numerical solvers. Quantum computers have the potential to run such calculations at higher speeds and on a greater scale, but only if technical obstacles, which include noise and physical errors, are overcome .

In a paper titled “A Quantum Approach for Implementing Fixed-Point Arithmetic in Solving Ordinary Differential Equations,” led by NYU Langone’s José E. Cruz Serrallés, PhD, postdoctoral fellow, and Riccardo Lattanzi, PhD, professor of radiology, the researchers draw on quantum-inspired techniques and classical methods to demonstrate that “given enough qubits to achieve the desired accuracy, solving an ordinary differential equation with fixed-point arithmetic is feasible.”

Although fixed-point arithmetic is by definition more limited than its floating-point counterpart, it has the advantage of being “significantly less complex to implement in terms of gate operations,” write the authors, referring to the manipulations of quantum bits (qubits) fundamental to performing computations.

One potential application contemplated by the investigators is “to explore the use of quantum computing to simulate the dynamics of bulk magnetization in magnetic resonance imaging (MRI),” where modeling of the highly dynamic and complex interactions between magnetic fields and physical bodies remains an area of active research.

The method reported in the paper was presented by Dr. Serrallés at IEEE Quantum Week 2024 in Montreal and is part of a scientific partnership between our imaging research center at NYU Langone Health and Fermilab’s SQMS Center, which has highlighted this advance as one enabling classical scientific computing on quantum hardware with exact fixed-point arithmetic.

A version of this post first appeared on the CAI²R LinkedIn.