Implementation of a Walsh-Hadamard gate in a superconducting qutrit

  1. M. A. Yurtalan,
  2. J. Shi,
  3. M. Kononenko,
  4. A. Lupascu,
  5. and S. Ashhab
We have implemented a Walsh-Hadamard gate, which performs a quantum Fourier transform, in a superconducting qutrit. The qutrit is encoded in the lowest three energy levels of a capacitively
shunted flux device, operated at the optimal flux-symmetry point. We use an efficient decomposition of the Walsh-Hadamard gate into two unitaries, generated by off-diagonal and diagonal Hamiltonians respectively. The gate implementation utilizes simultaneous driving of all three transitions between the three pairs of energy levels of the qutrit, one of which is implemented with a two-photon process. The gate has a duration of 35 ns and an average fidelity over a representative set of states, including preparation and tomography errors, of 99.2%, characterized with quantum state tomography. Compensation of ac-Stark and Bloch-Siegert shifts is essential for reaching high gate fidelities.

Simulating systems of itinerant spin-carrying particles using arrays of superconducting qubits and resonators

  1. S. Ashhab
We propose potential setups for the quantum simulation of itinerant spin-carrying particles in a superconducting qubit-resonator array. The standard Jaynes-Cummings-Hubbard setup studied
by several authors is readily amenable to being used as a quantum simulator for some spin-related phenomena. A more complex setup where multiple qubits and multiple resonator modes are utilized in the simulation gives a higher level of complexity, allowing for example the simulation of external magnetic fields and spin-orbit coupling. This proposal could be implemented in state-of-the-art superconducting circuits in the near future.