Simulation of Effective Dirac Dynamic via Quantum Walks on Digital Quantum Computers

Articles in Press

Document Type : Applicable

Author
Zeynab Kiamehr
Tafresh UniversityDepartment of Physics, Faculty of Basic Sciences, Tafresh University, Tafresh, Iran
10.22034/jmrph.2026.122919.0
Abstract
Quantum field theory (QFT) forms the fundamental basis of many areas in physics and is indispensable for our understanding of the universe. This research shows that simulating QFT using digital quantum computers is not merely a numerical computation, but rather a foundational problem in physical modeling that simultaneously depends on the theoretical structure of QFT, the choice of quantum algorithm, the definition of fidelity metrics, and the limitations of existing hardware. Since the equations of quantum field theories are generally complex and analytically intractable, employing quantum walks as a computational framework provides an alternative approach that enables the exploration of these theories in regimes inaccessible to classical methods. Within this framework, digital quantum walks serve as a natural algorithmic implementation for simulating the dynamics of quantum fields, as their discrete structure aligns well with the intrinsic architecture of NISQ-era quantum processors and, in the continuum limit, converges toward fundamental equations such as the Dirac equation. However, simulations and implementations on IBM’s superconducting quantum hardware reveal a high sensitivity to noise: even within non-interacting models, noise effects can fundamentally distort the interference patterns of the probability distributions. Consequently, defining a precise quantitative metric to assess simulation validity becomes crucial. The adoption of Hellinger fidelity as the central measure enables a systematic comparison between the probability distributions obtained from ideal simulations, noisy models, and experimental data, clearly indicating the extent to which the simulated dynamics can be interpreted as a valid representation of QFT.
Keywords
Quantum simulation
quantum field theory (QFT)
quantum walk
Hellinger Fidelity
quantum hardware noise
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Journal Of Modern Research Physics

Articles in Press, Accepted Manuscript
Available Online from 30 September 2026