We report observations of transitions between excited states in the Jaynes-Cummings ladder of circuit quantum electrodynamics with electron spins (spin circuit QED). We show that unexplained features in recent experimental work correspond to such transitions and present an input-output framework that includes these effects. In new experiments, we first reproduce previous observations and then reveal both excited-state transitions and multiphoton transitions by increasing the probe power and using two-tone spectroscopy. This ability to probe the Jaynes-Cummings ladder is enabled by improvements in the coupling-to-decoherence ratio, and shows an increase in the maturity of spin circuit QED as an interesting platform for studying quantum phenomena.

We report the coherent coupling of two electron spins at a distance via virtual microwave photons. Each spin is trapped in a silicon double quantum dot at either end of a superconducting resonator, achieving spin-photon couplings up to around gs/2p=40 MHz. As the two spins are brought into resonance with each other, but detuned from the photons, an avoided crossing larger than the spin linewidths is observed with an exchange splitting around 2J/2p=20 MHz. In addition, photon-number states are resolved from the shift 2?s/2p=-13 MHz that they induce on the spin frequency. These observations demonstrate that we reach the strong dispersive regime of circuit quantum electrodynamics with spins. Achieving spin-spin coupling without real photons is essential to long-range two-qubit gates between spin qubits and scalable networks of spin qubits on a chip.

Quantum computers (QC) promise to solve certain computational problems exponentially faster than a classical computer due to the superposition and entanglement properties of quantum bits (qubits). Among several qubit technologies, spin qubits are a promising candidate for large-scale QC, since (1) they have a small footprint allowing them to be densely integrated and (2) they can operate at relatively high temperatures (\gt1\mathrm{K}) [1], potentially reducing system cost and complexity.

Circuit quantum electrodynamics (QED) employs superconducting microwave resonators as quantum buses. In circuit QED with semiconductor quantum-dot-based qubits, increasing the resonator impedance is desirable as it enhances the coupling to the typically small charge dipole moment of these qubits. However, the gate electrodes necessary to form quantum dots in the vicinity of a resonator inadvertently lead to a parasitic port through which microwave photons can leak, thereby reducing the quality factor of the resonator. This is particularly the case for high-impedance resonators, as the ratio of their total capacitance over the parasitic port capacitance is smaller, leading to larger microwave leakage than for 50-ω resonators. Here, we introduce an implementation of on-chip filters to suppress the microwave leakage. The filters comprise a high-kinetic-inductance nanowire inductor and a thin-film capacitor. The filter has a small footprint and can be placed close to the resonator, confining microwaves to a small area of the chip. The inductance and capacitance of the filter elements can be varied over a wider range of values than their typical spiral inductor and interdigitated capacitor counterparts. We demonstrate that the total linewidth of a 6.4 GHz and approximately 3-kω resonator can be improved down to 540 kHz using these filters.