Claudio Chamon

Nonplanar qubit with tunable gauge symmetry

  1. Muqing Yu,
  2. Han Bi,
  3. Hengli Lo,
  4. Vishvesha Sridhar,
  5. Guilherme Delfino,
  6. Dmitry Green,
  7. Claudio Chamon,
  8. Nadya Mason,
  9. and Andrew P. Higginbotham
Circuit quantum electrodynamics embeds Josephson junction qubits within superconducting cavities, and has emerged as a leading approach to quantum computing and quantum simulation.
Despite the many permutations of circuit geometry that have been explored, Josephson connectivities have so far been planar, making them effectively low-dimensional. Here we show that a non-planar qubit — a 3×3 crossbar Josephson array — gives rise to flux-tunable ℤ3 combinatorial gauge symmetry (CGS), potentially enabling spin-liquid behavior when networked into a lattice. The observed excitation spectrum shows excellent agreement with predictions from a neural network trained to generate variational quantum states, demonstrating that we have predictive power over our high-dimensional quantum system. Fine-structure splittings near the CGS point are compatible with weak tunneling or symmetry breaking due to experimental imperfections. We additionally use the superconducting cavity to externally induce symmetry breaking, observing a restoration of symmetry at the CGS point where ground states differ only by a ℤ3 phase. This work initiates a general program exploring lattice gauge theories using the toolbox of circuit quantum electrodynamics. More broadly, introducing non-planar Josephson connectivities opens a vast space for experimental and theoretical exploration of structures in almost any imaginable dimensionality and geometry.
arxiv pdf

A superconducting circuit realization of combinatorial gauge symmetry

  1. Claudio Chamon,
  2. and Dmitry Green
We propose a superconducting wire array that realizes a family of quantum Hamiltonians that possess combinatorial gauge symmetry — a local symmetry where monomial transformations
play a central role. This physical system exhibits a rich structure. In the classical limit its ground state consists of two superimposed spin liquids; one is a crystal of small loops containing disordered U(1) degrees of freedom, and the other is a soup of loops of all sizes associated to Z2 topological order. We show that the classical results carry over to the quantum case when fluctuations are gradually tuned via the wire capacitances, yielding Z2 quantum topological order. In an extreme quantum limit where the capacitances are all small, we arrive at an effective quantum spin Hamiltonian that we conjecture would sustain Z2 quantum topological order with a gap of the order of the Josephson coupling in the array. The principles behind the construction for superconducting arrays extends to other bosonic and fermionic systems, and offers a promising path towards topological qubits and the study of other many-body systems.
arxiv pdf