Controlled parity of cooper pair tunneling in a hybrid superconducting qubit

Superconducting quantum circuits derive their nonlinearity from the Josephson energy-phase relation. Besides the fundamental $$\cos \phi$$ term, this relation can also contain higher Fourier harmonics $$\cos (k\phi )$$ corresponding to correlated tunneling of k Cooper pairs. The parity of the dominant tunneling process, i.e. whether an odd or even number of Cooper pairs tunnel, results in qualitatively different properties, and controlling this opens up a wide range of applications in superconducting technology. However, access to even-dominated regimes has remained challenging and has so far relied on complex multi-junction or all-hybrid architectures. Here, we demonstrate a simple “harmonic parity qubit”; an element that combines two aluminum-oxide tunnel junctions in parallel to a gate-tunable InAs/Al nanowire junction forming a SQUID, and use spectroscopy versus flux to reconstruct its energy-phase relation at 85 gate voltage points. At half flux quantum, the odd harmonics of the Josephson potential can be suppressed by up to two orders of magnitude relative to the even harmonics, producing a double-well potential dominated by even harmonics with minima near ± π/2. The ability to control harmonic parity enables supercurrent carried by pairs of Cooper pairs and provides a new building block for Fourier engineering in superconducting circuits. Engineering and controlling higher harmonics of the Josephson energy-phase relation is important for protected superconducting circuits and Hamiltonian design. Here, the authors demonstrate a compact hybrid Josephson element that enables gate tunable control of harmonic parity, achieving strong suppression of odd harmonics and access to an even harmonic dominated regime.