Vladimir I Man'ko

Circuit-QED simulator of the Bose-Hubbard model for quantum spin dynamics

  1. Ivan V. Dudinets,
  2. Jaehee Kim,
  3. Tomás Ramos,
  4. Aleksey K. Fedorov,
  5. Vladimir I Man'ko,
  6. and Joonsuk Huh
We demonstrate an experimentally feasible circuit-QED Bose-Hubbard simulator that reproduces the complex spin dynamics of Heisenberg models. Our method relies on mapping spin-1/2 systems
onto bosonic states via the polynomially expanded Holstein-Primakoff (HP) transformation. The HP transformation translates the intricate behavior of spins into a representation that is compatible with bosonic devices like those in a circuit QED setup. For comparison, we also implement the Dyson-Maleev (DM) encoding for spin-1/2 and show that, in this limit, DM and HP are equivalent. We show the equivalence of the DM and the HP transformations for spin-1/2 systems. Rigorous numerical analyses confirm the effectiveness of our HP-based protocol. Specifically, we obtain the concurrence between the spin dynamics and the behavior of microwave photons within our circuit QED-based analog simulator that is designed for the Bose-Hubbard model. By utilizing the microwave photons inherent to circuit QED devices, our framework presents an accessible, scalable avenue for probing quantum spin dynamics in an experimentally viable setting.
arxiv pdf

Hidden correlations in indivisible qudits as a resource for quantum technologies on examples of superconducting circuits

  1. Margarita A Man'ko,
  2. and Vladimir I Man'ko
We show that the density-matrix states of noncomposite qudit systems satisfy entropic and information relations like the subadditivity condition, strong subadditivity condition, and
Araki–Lieb inequality, which characterize hidden quantum correlations of observables associated with these indivisible systems. We derive these relations employing a specific map of the entropic inequalities known for density matrices of multiqudit systems to the inequalities for density matrices of single-qudit systems. We present the obtained relations in the form of mathematical inequalities for arbitrary Hermitian NxN-matrices. We consider examples of superconducting qubits and qudits. We discuss the hidden correlations in single-qudit states as a new resource for quantum technologies analogous to the known resource in correlations associated with the entanglement in multiqudit systems.
arxiv pdf