2106.08394_Schwinger Quantum sim

Last updated Dec 29, 2024

• Literature

• Schwinger model 1+1D $U(1)$ gauge theory

• Coupled to thermal environment of scalar field

• Real time dynamics: classical cost scales exponentially with system size

• Hamiltonian formulation of QFTs: Large hilbert spaces only possible with QC

• Initial state prep: Important and hard

1. Ground state for real time in vacuum
2. Thermal state for real time at finite T

To prepare thermal state different methods:

1. quantum metropolis
2. imaginary time evolution
3. coupling to heat bath

Kogut Susskind Hamiltonian formulation

• Staggered fermions

• Jordan wigner trafo Leads to Hamiltonian with pauli matrices for fermions and ladde roperators for gauge links

• Has infinite gauge degrees of freedom

• solve by imposing cutoff on electric flux

• Enwirontment hamlitonian for thermal scalar field

• interaction term $\phi\bar\psi\psi$

• Derive lindblad equation

• Solve with known algorithm (anciallary qubit)

• goes to thermal equilibrium