Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCalculating the Greens function of two-site Fermionic Hubbard model in a photonic system
102
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The Greens function has been an indispensable tool to study many-body systems that remain one of the biggest challenges in modern quantum physics for decades. The complicated calculation of Greens function impedes the research of many-body systems. The appearance of the noisy intermediate-scale quantum devices and quantum-classical hybrid algorithm inspire a new method to calculate Greens function. Here we design a programmable quantum circuit for photons with utilizing the polarization and the path degrees of freedom to construct a highly-precise variational quantum state of a photon, and first report the experimental realization for calculating the Greens function of the two-site Fermionic Hubbard model, a prototypical model for strongly-correlated materials, in photonic systems. We run the variational quantum eigensolver to obtain the ground state and excited states of the model, and then evaluate the transition amplitudes among the eigenstates. The experimental results present the spectral function of Greens function, which agrees well with the exact results. Our demonstration provides the further possibility of the photonic system in quantum simulation and applications in solving complicated problems in many-body systems, biological science, and so on.
rate research
Read More
We show that polaritons in an array of interacting micro-cavities with strong atom-photon coupling can form a two-component Bose-Hubbard model. Both polariton species are thereby protected against spontaneous emission as their atomic part is stored in two ground states of the atoms. The parameters of the effective model can be tuned via the driving strength of external lasers. We also describe a method to measure the number statistics in one cavity for each polariton species independently.
Applications of the Huckel (tight binding) model are ubiquitous in quantum chemistry and solid state physics. The matrix representation of this model is isomorphic to an unoriented vertex adjacency matrix of a bipartite graph, which is also the Laplacian matrix plus twice the identity. In this paper, we analytically calculate the determinant and, when it exists, the inverse of this matrix in connection with the Greens function, $mathbf{G}$, of the $Ntimes N$ Huckel matrix. A corollary is a closed form expression for a Harmonic sum (Eq. 12). We then extend the results to $d-$dimensional lattices, whose linear size is $N$. The existence of the inverse becomes a question of number theory. We prove a new theorem in number theory pertaining to vanishing sums of cosines and use it to prove that the inverse exists if and only if $N+1$ and $d$ are odd and $d$ is smaller than the smallest divisor of $N+1$. We corroborate our results by demonstrating the entry patterns of the Greens function and discuss applications related to transport and conductivity.
We study the phase diagram of the fermionic Hubbard model on the hexagonal lattice in the space of on-site and nearest neighbor couplings with Hybrid-Monte-Carlo simulations. With pure on-site repulsion this allows to determine the critical coupling strength for spin-density wave formation with the standard approach of introducing a small mass term, explicitly breaking the sublattice symmetry. The analogous mass term for charge-density wave formation above a critical nearest-neighbor repulsion, on the other hand, would introduce a fermion sign problem. The competition between the two and the phase diagram in the space of the two coouplings can however be studied in simulations without explicit sublattice symmetry breaking. Our results compare qualitatively well with the Hartree-Fock phase diagram. We furthermore demonstrate how spin-symmetry breaking by the Euclidean time discretization can be avoided also, when using an improved fermion action based on an exponetial transfer matrix with exact sublattice symmetry.
The efficient simulation of correlated quantum systems is the most promising near-term application of quantum computers. Here, we present a measurement of the second Renyi entropy of the ground state of the two-site Fermi-Hubbard model on a $5$-qubit programmable quantum computer based on trapped ions. Our work illustrates the extraction of a non-linear characteristic of a quantum state using a controlled-swap gate acting on two copies of the state. This scalable measurement of entanglement on a universal quantum computer will, with more qubits, provide insights into many-body quantum systems that are impossible to simulate on classical computers.
We develop a workflow to use current quantum computing hardware for solving quantum many-body problems, using the example of the fermionic Hubbard model. Concretely, we study a four-site Hubbard ring that exhibits a transition from a product state to an intrinsically interacting ground state as hopping amplitudes are changed. We locate this transition and solve for the ground state energy with high quantitative accuracy using a variational quantum algorithm executed on an IBM quantum computer. Our results are enabled by a variational ansatz that takes full advantage of the maximal set of commuting $mathbb{Z}_2$ symmetries of the problem and a Lanczos-inspired error mitigation algorithm. They are a benchmark on the way to exploiting near term quantum simulators for quantum many-body problems.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
