67 research outputs found
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
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