Matrix-product-state simulations for qubits-waveguide systems in real space

We present a matrix-product-state (MPS) based numerical approach for simulating the dynamics of systems composed of several qubits and a common one-dimensional waveguide. In the presented approach, the one-dimensional waveguide is modeled in real space to utilize the property of MPS representation: MPS representation is efficient for low-entangled states in spatially one-dimensional systems. Besides, the range of interaction does not depend on the number of qubits, unlike the frequency space approaches. Within the approach, photons propagating in the waveguide are described as the Bogoliubov excitations. Because of this treatment, even a vacuum state for photons is entangled, and an allowed occupation number for bosonic degrees of freedom should be set to a relatively high value. Even though the presented approach contains these difficulties, the recently proposed controlled bond expansion approaches make the approach practical. We demonstrate the potential of the presented approach by simulating the superradiant phenomena within the Hamiltonian dynamics.