标题： 关于库仑规范下量子电动力学的量子模拟 显示英文标题

标题： On Quantum Simulation of QED in Coulomb Gauge

摘要： 最近的工作（Li, 2406.01204）考虑了在库仑规范下在格点上对量子电动力学（QED）进行量子模拟，其中规范自由度在动量空间的占据基中表示。在这里，我们考虑在位置空间的场基中表示规范自由度，并开发了一种用于实时模拟的量子算法。我们证明，当作用于由费米子和横向规范场组成的物理态时，库仑规范哈密顿量等价于时间规范哈密顿量。库仑规范哈密顿量保证了非物理的纵向规范场不会传播，因此不需要施加任何约束。使用量子傅里叶变换，局部规范场基和共轭变量基可以高效地交换。我们证明了表示物理态的量子比特成本以及实时模拟的门深度与格点大小、能量、时间、精度和哈密顿量参数呈多项式规模。我们专注于格点理论，不讨论QED的连续极限或紫外完成。 显示英文摘要

摘要： A recent work (Li, 2406.01204) considered quantum simulation of Quantum Electrodynamics (QED) on a lattice in the Coulomb gauge with gauge degrees of freedom represented in the occupation basis in momentum space. Here we consider representing the gauge degrees of freedom in field basis in position space and develop a quantum algorithm for real-time simulation. We show that the Coulomb gauge Hamiltonian is equivalent to the temporal gauge Hamiltonian when acting on physical states consisting of fermion and transverse gauge fields. The Coulomb gauge Hamiltonian guarantees that the unphysical longitudinal gauge fields do not propagate and thus there is no need to impose any constraint. The local gauge field basis and the canonically conjugate variable basis are swapped efficiently using the quantum Fourier transform. We prove that the qubit cost to represent physical states and the gate depth for real-time simulation scale polynomially with the lattice size, energy, time, accuracy and Hamiltonian parameters. We focus on the lattice theory without discussing the continuum limit or the UV completion of QED.