Superconducting quantum circuits derive their nonlinearity from the Josephson energy-phase relation. Besides the fundamental cosϕ term, this relation can also contain higher Fourierharmonics cos(kϕ) 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“ (HPQ); 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.
Tunable Josephson harmonics open up for new qubit design. We demonstrate a superconducting circuit element with a tunnel junction in series with a SQUID loop, yielding a highly magnetic-fluxtunable harmonic content of the Josephson potential. We analyze spectroscopy of the first four qubit transitions with a circuit model which includes the internal mode, revealing a second harmonic up to ∼10% of the fundamental harmonic. Interestingly, a sweet spot where the dispersive shift vanishes is achieved by balancing the dispersive couplings to the internal and qubit modes. The highly tunable set-up provides a route toward protected qubits, and customizable nonlinear microwave devices.
A semiconductor transmon with an epitaxial Al shell fully surrounding an InAs nanowire core is investigated in the low EJ/EC regime. Little-Parks oscillations as a function of fluxalong the hybrid wire axis are destructive, creating lobes of reentrant superconductivity separated by a metallic state at a half-quantum of applied flux. In the first lobe, phase winding around the shell can induce topological superconductivity in the core. Coherent qubit operation is observed in both the zeroth and first lobes. Splitting of parity bands by coherent single-electron coupling across the junction is not resolved beyond line broadening, placing a bound on Majorana coupling, EM/h < 10 MHz, much smaller than the Josephson coupling EJ/h ~ 4.7 GHz.[/expand]
The coherent tunnelling of Cooper pairs across Josephson junctions (JJs) generates a nonlinear inductance that is used extensively in quantum information processors based on superconductingcircuits, from setting qubit transition frequencies and interqubit coupling strengths, to the gain of parametric amplifiers for quantum-limited readout. The inductance is either set by tailoring the metal-oxide dimensions of single JJs, or magnetically tuned by parallelizing multiple JJs in superconducting quantum interference devices (SQUIDs) with local current-biased flux lines. JJs based on superconductor-semiconductor hybrids represent a tantalizing all-electric alternative. The gatemon is a recently developed transmon variant which employs locally gated nanowire (NW) superconductor-semiconductor JJs for qubit control. Here, we go beyond proof-of-concept and demonstrate that semiconducting channels etched from a wafer-scale two-dimensional electron gas (2DEG) are a suitable platform for building a scalable gatemon-based quantum computer. We show 2DEG gatemons meet the requirements by performing voltage-controlled single qubit rotations and two-qubit swap operations. We measure qubit coherence times up to ~2 us, limited by dielectric loss in the 2DEG host substrate.