Quantum Simulation of SU(3) Lattice Yang-Mills Theory at Leading Order in Large- Nc Expansion,Physical Review Letters

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Quantum Simulation of SU(3) Lattice Yang-Mills Theory at Leading Order in Large- Nc Expansion
Physical Review Letters ( IF 8.1 ) Pub Date : 2024-09-09 , DOI: 10.1103/physrevlett.133.111901
Anthony N. Ciavarella ₁ , Christian W. Bauer _{1,

2}

Affiliation

Quantum simulations of the dynamics of QCD have been limited by the complexities of mapping the continuous gauge fields onto quantum computers. By parametrizing the gauge invariant Hilbert space in terms of plaquette degrees of freedom, we show how the Hilbert space and interactions can be expanded in inverse powers of Nc. At leading order in this expansion, the Hamiltonian simplifies dramatically, both in the required size of the Hilbert space as well as the type of interactions involved. Adding a truncation of the resulting Hilbert space in terms of local energy states we give explicit constructions that allow simple representations of SU(3) gauge fields on qubits and qutrits. This formulation allows a simulation of the real time dynamics of a SU(3) lattice gauge theory on a 5×5 and 8×8 lattice on ibm_torino with a CNOT depth of 113.

Published by the American Physical Society

2024

中文翻译：

SU（3）晶格 Yang-Mills 理论在大 NC 展开中处于领先阶的量子模拟

QCD 动力学的量子模拟一直受到将连续规范场映射到量子计算机的复杂性的限制。通过根据 plaquette 自由度参数化规范不变的 Hilbert 空间，我们展示了如何在 Nc 的逆幂中扩展 Hilbert 空间和相互作用。在此扩展的主导顺序上，哈密顿量在所需的希尔伯特空间大小以及所涉及的交互类型方面都大大简化了。根据局部能量状态添加生成的希尔伯特空间的截断，我们给出了显式构造，允许在量子比特和量子比特上简单表示 SU（3）规范场。该公式允许在 CNOT 深度为 113 的 ibm_torino 上的 5×5 和 8×8 晶格上模拟 SU（3）晶格规范理论的实时动力学。美国物理学会 2024 年出版

更新日期：2024-09-09

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