论文标题
3+1 QED的相对论离散时空公式
A relativistic discrete spacetime formulation of 3+1 QED
论文作者
论文摘要
这项工作为$ 2+1 $和$ 3+1 $尺寸量子电动力学（QED）提供了相对论，数字量子仿真方案，基于理论的离散时空配方。它采用量子电路的形式，通过离散步骤$Δ_T=δ_x$进行参数遍布空间和时间。随着电路线与QED的轻型世界一致，每个步骤的严格因果关系得到确保。优化了在变质下的仿真时间。构造重播导致QED Lagrangian的逻辑。也就是说，它从Dirac Quantum Walk开始，众所周知，可以融入自由学的费米子。然后，它将量子步行扩展到多粒子扇形量子细胞自动机中，以尊重费米子的反通信关系和离散仪表不变性对称性。这两种要求只能以引入量规场的成本来实现。最后，给出了仪表场自己的电磁动力学，可以在每个plaquette上进行量子行走。
This work provides a relativistic, digital quantum simulation scheme for both $2+1$ and $3+1$ dimensional quantum electrodynamics (QED), based on a discrete spacetime formulation of theory. It takes the form of a quantum circuit, infinitely repeating across space and time, parametrised by the discretization step $Δ_t=Δ_x$. Strict causality at each step is ensured as circuit wires coincide with the lightlike worldlines of QED; simulation time under decoherence is optimized. The construction replays the logic that leads to the QED Lagrangian. Namely, it starts from the Dirac quantum walk, well-known to converge towards free relativistic fermions. It then extends the quantum walk into a multi-particle sector quantum cellular automata in a way which respects the fermionic anti-commutation relations and the discrete gauge invariance symmetry. Both requirements can only be achieved at cost of introducing the gauge field. Lastly the gauge field is given its own electromagnetic dynamics, which can be formulated as a quantum walk at each plaquette.
