SU(2) Non-Abelian Gauge Field Theory on Digital Quantum Computers
The paper presents a novel approach to simulating one-dimensional SU(2) non-Abelian gauge field theories using digital quantum computers. The authors have developed an improved mapping of these gauge theories onto qubit degrees of freedom, allowing for more efficient quantum simulations. This advancement reduces the unphysical Hilbert space required, optimizing quantum circuits through insensitivity to interactions within this space. The paper utilizes local gauge symmetry to represent angular momentum alignment analytically, which results in qubit registers encoding the total angular momentum along each link.
Central to the paper is the formulation and implementation of SU(2) gauge field theory in one dimension on IBM's digital quantum hardware. The authors employ the Hamiltonian formulation of lattice gauge theories, which traditionally includes exponentially large Hilbert space sectors. These sectors contain unphysical states but are needed to maintain spatially localized interactions while fulfilling gauge constraints. Current limitations of quantum hardware—such as high error rates and low gate fidelities—make it challenging to prevent the dispersion of states into these unphysical spaces. The techniques used in earlier simulations fail to scale efficiently and address multi-dimensional lattices with non-trivial gauge groups, a gap this paper seeks to bridge by focusing on one-dimensional systems.
Within their setup, the authors present explicit circuit designs to implement time evolution operations for SU(2) gauge fields with angular momentum truncation Λj=1/2 using minimal qubit resources. The physical and unphysical space interactions, crucial for simulation fidelity, are calculated and optimized for the available quantum computing hardware. Key results from their IBM quantum device implementation show significant progress, with techniques allowing for error mitigation and maintaining gauge invariance in the simulation process.
The implementation of time evolution with one and two Trotter steps reveals observable dynamics characteristic of SU(2) gauge fields within the physical subspace. The survival probability metric—the likelihood of the simulated system remaining within the gauge-invariant space—serves as an indicator of simulation integrity, underpinning the robustness required for quantum error correction strategies in future practical applications.
The implications of this research, both theoretical and practical, are profound. By further refining qubit mapping techniques, this paper contributes toward scalable quantum simulations of non-Abelian gauge theories, setting the stage for exploring higher-dimensional pseudo-dynamics and more complex symmetry-breaking processes characteristic of real-world nuclear forces. As quantum computing hardware improves, these methods will likely be pivotal in expanding our understanding of quantum chromodynamics (QCD) and related phenomena. Additionally, this approach holds promise for enhancing quantum computation's role in lattice gauge theories, potentially influencing widespread domains in nuclear and particle physics.
For future research directions, extending the analytic techniques beyond one-dimensional systems and comparing against alternative digital formulations will be crucial for realizing quantum computations that reflect physically relevant gauge theories. The synergy of this paper's methodological advancements and hardware capabilities will be vital for pushing the boundaries of quantum simulations in high-energy physics.