Site-wise manipulations and Mott insulator-superfluid transition of interacting photons using superconducting circuit simulators

The Bose Hubbard model (BHM) of interacting bosons in a lattice has been a paradigm in many-body physics, and it exhibits a Mott insulator (MI)-superfluid (SF) transition at integer filling. Here a quantum simulator of the BHM using a superconducting circuit is proposed. Specifically, a superconducting transmission line resonator supporting microwave photons is coupled to a charge qubit to form one site of the BHM, and adjacent sites are connected by a tunable coupler. To obtain a mapping from the superconducting circuit to the BHM, we focus on the dispersive regime where the excitations remain photon-like. Standard perturbation theory is implemented to locate the parameter range where the MI-SF transition may be simulated. This simulator allows single-site manipulations and we illustrate this feature by considering two scenarios where a single-site manipulation can drive a MI-SF transition. The transition can be analyzed by mean-field analyses, and the exact diagonalization was implemented to provide accurate results. The variance of the photon density and the fidelity metric clearly show signatures of the transition. Experimental realizations and other possible applications of this simulator are also discussed.Comment: 13 pages, 9 figure

Using RIXS to uncover elementary charge and spin excitations in correlated materials

Despite significant progress in resonant inelastic x-ray scattering (RIXS) experiments on cuprates at the Cu L-edge, a theoretical understanding of the cross-section remains incomplete in terms of elementary excitations and the connection to both charge and spin structure factors. Here we use state-of-the-art, unbiased numerical calculations to study the low energy excitations probed by RIXS in undoped and doped Hubbard model relevant to the cuprates. The results highlight the importance of scattering geometry, in particular both the incident and scattered x-ray photon polarization, and demonstrate that on a qualitative level the RIXS spectral shape in the cross-polarized channel approximates that of the spin dynamical structure factor. However, in the parallel-polarized channel the complexity of the RIXS process beyond a simple two-particle response complicates the analysis, and demonstrates that approximations and expansions which attempt to relate RIXS to less complex correlation functions can not reproduce the full diversity of RIXS spectral features

A quantum-inspired tensor network method for constrained combinatorial optimization problems

Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we propose a quantum inspired algorithm for general locally constrained combinatorial optimization problems by encoding the constraints directly into a tensor network state. The optimal solution can be efficiently solved by borrowing the imaginary time evolution from a quantum many-body system. We demonstrate our algorithm with the open-pit mining problem numerically. Our computational results show the effectiveness of this construction and potential applications in further studies for general combinatorial optimization problems