High-Fidelity Two-Qubit Gates between Fluxonium Qubits with a Resonator Coupler

We take a bottom-up first-principles approach to designing a two-qubit gate between fluxonium qubits for minimal error, speed, and control simplicity. Our proposed architecture consists of two fluxoniums coupled via a resonator. The use of a simple linear coupler has many practical benefits, including the possibility of material optimization for suppressing loss, reducing fabrication complexity, and increasing yield by circumventing the need for Josephson junctions. Crucially, a resonator-as-coupler approach also suggests a clear path to increased connectivity between fluxonium qubits, by reducing capacitive loading when the coupler has a high impedance. After performing analytic and numerical analyses of the circuit Hamiltonian and gate dynamics, we tune circuit parameters to destructively interfere sources of coherent error, revealing an efficient fourth-order scaling of coherent error with gate duration. For component properties from the literature, we predict an open-system average controlled- <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <a:mi>Z</a:mi> </a:math> () gate infidelity of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <d:mn>1.86</d:mn> <d:mo>×</d:mo> <d:msup> <d:mn>10</d:mn> <d:mrow> <d:mo>−</d:mo> <d:mn>4</d:mn> </d:mrow> </d:msup> </d:math> in 70 ns.