Quantum processing unit comprising one or more superconducting qubits based on phase-biased linear and non-linear inductive-energy elements

A quantum processing unit comprising:

• a dielectric substrate;
• and
• at least one superconducting qubit provided on the dielectric substrate, each of the at least one superconducting qubit including:
• a distributed-element resonator comprising at least two conductors separated by at least one gap, wherein the distributed-element resonator is configured as a coplanar waveguide (CPW) resonator, and the at least two conductors comprise a center superconductor and a superconducting ground plane, the center superconductor serving as a linear inductive-energy element,
• a non-linear inductive-energy element including at least one Josephson element embedded in the CPW resonator such that the respective superconducting qubit is free of isolated superconducting islands, and
• a phase-biasing element,
• wherein the phase-biasing element is configured to bias a superconducting phase difference across the linear inductive-energy element and the non-linear inductive-energy element by generating and threading a magnetic field through the at least one gap of the distributed-element resonator such that quadratic potential energy terms associated with the linear inductive-energy element and the non-linear inductive-energy element are at least partly cancelled by one another, and
• wherein the phase-biasing element comprises at least one of (i) one or more coils, or (ii) flux-bias lines.