Ciavarella Anthony N, Bauer Christian W
Physics Division, <a href="https://ror.org/02jbv0t02">Lawrence Berkeley National Laboratory</a>, Berkeley, California 94720, USA.
Department of Physics, <a href="https://ror.org/01an7q238">University of California</a>, Berkeley, Berkeley, California 94720, USA.
Phys Rev Lett. 2024 Sep 13;133(11):111901. doi: 10.1103/PhysRevLett.133.111901.
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 N_{c}. 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.
量子色动力学（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。通过根据面元自由度对规范不变希尔伯特空间进行参数化，我们展示了希尔伯特空间和相互作用如何以(N_{c})的倒数幂展开。在这种展开的主导阶，哈密顿量在所需的希尔伯特空间大小以及所涉及的相互作用类型方面都显著简化。通过根据局部能量态对所得希尔伯特空间进行截断，我们给出了明确的构造，这些构造允许在量子比特和量子三态上对(SU(3))规范场进行简单表示。这种形式允许在ibm_torino上对(5×5)和(8×8)晶格上的(SU(3))晶格规范理论的实时动力学进行模拟，其CNOT深度为113。
