Two promising architectures for solid-state quantum information processing are electron spins in semiconductor quantum dots and the collective electromagnetic modes of superconductingcircuits. In some aspects, these two platforms are dual to one another: superconducting qubits are more easily coupled but are relatively large among quantum devices (∼mm), while electrostatically-confined electron spins are spatially compact (∼μm) but more complex to link. Here we combine beneficial aspects of both platforms in the Andreev spin qubit: the spin degree of freedom of an electronic quasiparticle trapped in the supercurrent-carrying Andreev levels of a Josephson semiconductor nanowire. We demonstrate coherent spin manipulation by combining single-shot circuit-QED readout and spin-flipping Raman transitions, finding a spin-flip time TS=17 μs and a spin coherence time T2E=52 ns. These results herald a new spin qubit with supercurrent-based circuit-QED integration and further our understanding and control of Andreev levels — the parent states of Majorana zero modes — in semiconductor-superconductor heterostructures.
By coupling a superconducting weak link to a microwave resonator, recent experiments probed the spectrum and achieved the quantum manipulation of Andreev states in various systems.However, the quantitative understanding of the response of the resonator to changes in the occupancy of the Andreev levels, which are of fermionic nature, is missing. Here, using Bogoliubov-de Gennes formalism to describe the weak link and a general formulation of the coupling to the resonator, we calculate the shift of the resonator frequency as a function of the levels occupancy and describe how transitions are induced by phase or electric field microwave drives. We apply this formalism to analyze recent experimental results obtained using circuit-QED techniques on superconducting atomic contacts and semiconducting nanowire Josephson junctions.
Spectral properties of a quantum circuit are efficiently read out by monitoring the resonance frequency shift it induces in a microwave resonator coupled to it. When the two systemsare strongly detuned, theory attributes the shift to an effective resonator capacitance or inductance that depends on the quantum circuit state. At small detuning, the shift arises from the exchange of virtual photons, as described by the Jaynes-Cummings model. Here we present a theory bridging these two limits and illustrate, with several examples, its necessity for a general description of quantum circuits readout.