Understanding degenerate ground states and protection in new superconducting quantum circuits

Xinyuan You

Michael Stern

W. C. Smith, Angela Kou, X. Xiao +2 more

Abstract We present a protected superconducting qubit based on an effective circuit element that only allows pairs of Cooper pairs to tunnel. These dynamics give rise to a nearly degenerate ground state manifold indexed by the parity of tunneled Cooper pairs. We show that, when the circuit element is shunted by a large capacitance, this manifold can be used as a logical qubit that we expect to be insensitive to multiple relaxation and dephasing mechanisms.

Yasunobu Nakamura

Joshua M. Dempster, Bo Fu, David Ferguson +2 more

A recent theoretical proposal suggests that a simple circuit utilizing two superinductors may produce a qubit with ground-state degeneracy [Brooks, Phys. Rev. A 87, 052306 (2013)]. We perform a full circuit analysis along with exact diagonalization of the circuit Hamiltonian to elucidate the nature of the spectrum and low-lying wave functions of this $0\text{\ensuremath{-}}\ensuremath{\pi}$ device. We show that the ground-state degeneracy is robust to disorder in charge, flux, and critical current as well as insensitive to modest variations in the circuit parameters. Our treatment is nonperturbative, provides access to excited states and matrix elements, and is immediately applicable also to intermediate parameter regimes of experimental interest.

Adam Callison, Eytan Grosfeld, Eran Ginossar

The two degenerate ground states of the anisotropic Heisenberg ($XY$) spin model of a chain of qubits (pseudospins) can encode quantum information, but their degree of protection against local perturbations is known to be only partial. We examine the properties of the system in the presence of nonlocal spin-spin interactions, possibly emerging from the quantum electrodynamics of the device. We find a phase distinct from the $XY$ phase admitting two ground states which are highly protected against all local field perturbations, persisting across a range of parameters. In the context of the $XY$ chain we discuss how the coupling between two ground states can be used to observe signatures of topological edge states in a small controlled chain of superconducting transmon qubits.