Renormalization of Multi-Qubit Bath Coupling

While perfectly implemented quantum bits promise an exponential speedup compared to classical computation, the physical realization has proven to be a challenging field of research as a physical two level system can never be engineered to be completely decoupled from its environment. Whether this coupling is sought to be suppressed to increase gate fidelities or used for adiabatic quantum computing, it is essential to understand the inevitable effects of the environment.
In this work we use renormalization group techniques to investigate a multi-qubit system affected by an ohmic bath. We confirm the well studied single spin case which is solved e.g. via adiabatic renormalization and show how it translates to multiple qubits. We derive the flow of effective coupling constants and characterize fixpoints as well as scaling thereof thus characterizing the influence of the bath.