Simulating 2+1D Lattice Quantum Electrodynamics at Finite Density with Neural Flow Wavefunctions

The tensor network approach is variational and hence has no sign problem but is mainly Gauge theory coupled to dynamical matter plays a fundamental efficient for problems in 1+1D [6]. While there are recent role in physics. For example, quantum electrodynamics attempts on extending the tensor network approach to (QED) describes the light-matter interaction 2+1D and 3+1D simulations [7-12], the tensor network while quantum chromodynamics (QCD) describes methods are usually more constrained in higher dimensions the quark-gluon interaction, which are the important as well as real time dynamics where the entanglement components of the Standard Model. Meanwhile, exotic grows with system size. It is also an open question gauge theories with matter also arise in theories of condensed on how to utilize the tensor network approach for simulating matter and AMO systems [1-3]. When a dynamical gauge theories with continuous or infinite degrees gauge theory is discretized and placed on a lattice of freedom without imposing a cutoff. With the recent in the Hamiltonian formulation, Gauss's law needs to be development of quantum technologies, quantum computation explicitly imposed. There are various open questions on provides another paradigm for lattice gauge theory understanding both the phase diagram and the real-time simulations [6, 13-27]. Despite the nice proposals and evolution of dynamical gauge theory, which are challenging progress of the field, the performance of the near-term to address in simulations particularly in high spatial quantum algorithms are still limited due to the noisy nature dimensions and in the finite charge density regimes. of the current quantum devices and the large depth Early attempts on simulating lattice gauge theory and qubit numbers required.