Mohammad Hafezi

Extended Josephson junction qubit system

  1. Andrey Grankin,
  2. Alicia J. Kollár,
  3. and Mohammad Hafezi
Circuit quantum electrodynamics (QED) has emerged as a promising platform for implementing quantum computation and simulation. Typically, junctions in these systems are of a sufficiently
small size, such that only the lowest plasma oscillation is relevant. The interplay between the Josephson effect and charging energy renders this mode nonlinear, forming the basis of a qubit. In this work, we introduce a novel QED architecture based on extended Josephson Junctions (JJs), which possess a non-negligible spatial extent. We present a comprehensive microscopic analysis and demonstrate that each extended junction can host multiple nonlinear plasmon modes, effectively functioning as a multi-qubit interacting system, in contrast to conventional JJs. Furthermore, the phase modes exhibit distinct spatial profiles, enabling individual addressing through frequency-momentum selective coupling to photons. Our platform has potential applications in quantum computation, specifically in implementing single- and two-qubit gates within a single junction. We also investigate a setup comprising several driven extended junctions interacting via a multimode electromagnetic waveguide. This configuration serves as a powerful platform for simulating the generalized Bose-Hubbard model, as the photon-mediated coupling between junctions can create a lattice in both real and synthetic dimensions. This allows for the exploration of novel quantum phenomena, such as topological phases of interacting many-body systems.
arxiv pdf

Engineering three-body interaction and Pfaffian states in circuit QED systems

  1. Mohammad Hafezi,
  2. Prabin Adhikari,
  3. and Jacob M. Taylor
We demonstrate a scheme to engineer the three-body interaction in circuit-QED systems by tuning a fluxonium qubit. Connecting such qubits in a square lattice and controlling the tunneling
dynamics, in the form of a synthesized magnetic field, for the photon-like excitations of the system, allows the implementation of a parent Hamiltonian whose ground state is the Pfaffian wave function. Furthermore, we show that the addition of the next-nearest neighbor tunneling stabilizes the ground state, recovering the expected topological degeneracy even for small lattices. Finally, we discuss the implementation of these ideas with the current technology.
arxiv pdf

Nonlinear Optics Quantum Computing with Circuit-QED

  1. Prabin Adhikari,
  2. Mohammad Hafezi,
  3. and J. M. Taylor
One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary
to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our specific example uses a hybrid quantum system comprising a LC resonator coupled to a superconducting flux qubit to implement a nonlinear coupling. Compared to the self-Kerr nonlinearity, we find that our approach has improved tolerance to noise in the qubit while maintaining fast operation.
arxiv pdf