Sreejith G J | Searcharxiv

arXiv2021

Star-topology Registers: NMR and Quantum Information Perspectives

Quantum control of large spin registers is crucial for many applications ranging from spectroscopy to quantum information. A key factor that determines the efficiency of a register for implementing a given information processing task is its network topology. One particular type, called star-topology, involves a central qubit uniformly interacting with a set of ancillary qubits. A particular advantage of the star-topology quantum registers is in the efficient preparation of large entangled states, called NOON states, and their generalized variants. Thanks to the robust generation of such correlated states, spectral simplicity, ease of polarization transfer from ancillary qubits to the central qubit, as well as the availability of large spin-clusters, the star-topology registers have been utilized for several interesting applications over the last few years. Here we review some recent progress with the star-topology registers, particularly via nuclear magnetic resonance methods.

quant-ph↗

arXiv2019

Mean field approximations for short range four body interactions at $ν=3/5$

Trial wavefunctions like the Moore-Read and Read-Rezayi states which minimize short range multibody interactions are candidate states for describing the fractional quantum Hall effects at filling factors $ν= 1/2$ and $ν= 2/5$ in the second Landau level. These trial wavefunctions are unique zero energy states of three body and four body interaction Hamiltonians respectively but are not close to the ground states of the Coulomb interaction. Previous studies using extensive parameter scans have found optimal two body interactions that produce states close to these. Here we focus on short ranged four body interaction and study two mean field approximations that reduce the four body interactions to two body interactions by replacing composite operators with their incompressible ground state expectation values. We present the results for pseudopotentials of these approximate interactions. Comparison of finite system spectra of the four body and the approximate interactions at filling fraction $ν=3/5$ show that these approximations produce good effective descriptions of the low energy structure of the four body ineraction Hamiltonian. The approach also independently reproduces the optimal two body interaction inferred from parameter scans. We also show that for $n=3$, but not for $n=4$, the mean field approximations of the $n$-body interaction is equivalent to particle hole symmetrization of the interaction.

cond-mat.str-el↗