Quantum superpositions of distinct coherent states in a single-mode harmonic oscillator, known as "cat states," have been an elegant demonstration of Schrödinger's famous cat paradox. Here, we realize a two-mode cat state of electromagnetic fields in two microwave cavities bridged by a superconducting artificial atom, which can also be viewed as an entangled pair of single-cavity cat states. We present full quantum state tomography of this complex cat state over a Hilbert space exceeding 100 dimensions via quantum nondemolition measurements of the joint photon number parity. The ability to manipulate such multicavity quantum states paves the way for logical operations between redundantly encoded qubits for fault-tolerant quantum computation and communication.

We study the energy relaxation times ($T_1$) of superconducting transmon qubits in 3D cavities as a function of dielectric participation ratios of material surfaces. This surface participation ratio, representing the fraction of electric field energy stored in a dissipative surface layer, is computed by a two-step finite-element simulation and experimentally varied by qubit geometry. With a clean electromagnetic environment and suppressed non-equilibrium quasiparticle density, we find an approximately proportional relation between the transmon relaxation rates and surface participation ratios. These results suggest dielectric dissipation arising from material interfaces is the major limiting factor for the $T_1$ of transmons in 3D cQED architecture. Our analysis also supports the notion of spatial discreteness of surface dielectric dissipation.Comment: Main text: 5 pages 4 figures; Supplementary Materials: 6 pages 4 figures 1 tabl

Significant advances in coherence render superconducting quantum circuits a viable platform for fault-tolerant quantum computing. To further extend capabilities, highly coherent quantum systems could act as quantum memories for these circuits. A useful quantum memory must be rapidly addressable by Josephson junction-based artificial atoms, while maintaining superior coherence. We demonstrate a novel superconducting microwave cavity architecture that is highly robust against major sources of loss that are encountered in the engineering of circuit QED systems. The architecture allows for storage of quantum superpositions in a resonator on the millisecond scale, while strong coupling between the resonator and a transmon qubit enables control, encoding, and readout at MHz rates. This extends the maximum available coherence time attainable in superconducting circuits by almost an order of magnitude compared to earlier hardware. Our design is an ideal platform for studying coherent quantum optics and marks an important step towards hardware-efficient quantum computing in Josephson junction-based quantum circuits.

Superconducting circuits have attracted growing interest in recent years as a promising candidate for fault-tolerant quantum information processing. Extensive efforts have always been taken to completely shield these circuits from external magnetic fields to protect the integrity of the superconductivity. Here we show vortices can improve the performance of superconducting qubits by reducing the lifetimes of detrimental single-electron-like excitations known as quasiparticles. Using a contactless injection technique with unprecedented dynamic range, we quantitatively distinguish between recombination and trapping mechanisms in controlling the dynamics of residual quasiparticle, and show quantized changes in quasiparticle trapping rate because of individual vortices. These results highlight the prominent role of quasiparticle trapping in future development of superconducting qubits, and provide a powerful characterization tool along the way.

Three-dimensional microwave cavities have recently been combined with superconducting qubits in the circuit quantum electrodynamics (cQED) architecture. These cavities should have less sensitivity to dielectric and conductor losses at surfaces and interfaces, which currently limit the performance of planar resonators. We expect that significantly (>103 ) higher quality factors and longer lifetimes should be achievable for 3D structures. Motivated by this principle, we have reached internal quality factors greater than 0.5×10 9 and intrinsic lifetimes of 0.01 seconds for multiple aluminum superconducting cavity resonators at single photon energies and millikelvin temperatures. These improvements could enable long lived quantum memories with submicrosecond access times when strongly coupled to superconducting qubits.In circuit quantum electrodynamics (cQED), microwave resonators protect superconducting qubits from decoherence, suppress spontaneous emission 1 , allow for quantum non-demolition measurements 2,3 , and serve as quantum memories 4 . Single photon lifetimes between 10-50 µs (Q≈10 6 ) have been achieved in thin film resonators with careful surface preparation and geometrical optimization 5-7 . The route toward an optimal geometry also sheds light on the physical mechanisms responsible for damping. Planar resonators with larger features are generally found to be higher quality, which is interpreted as loss dominated by surface elements 5-9 , as the relative energy stored in surface defects is inversely proportional to the size of the resonator.Three dimensional, macroscopic cavity resonators are at the extreme limit of this trend and historically exhibit remarkable lifetimes 10 . Progress with superconducting niobium cavities for particle acceleration has led to dwell times of seconds for RF field strengths of 10 MeV/m at 2 K bath temperatures 11 . At the much lower drive powers corresponding to single-photon excitations, or fields of ∼1 µV/m, storage time in excess of 100 ms has been achieved in three dimensional, niobium Fabry Perot resonators at 51 GHz and 0.8 K 12 , and also in 3D, niobium micromaser cavities at 22 GHz and 0.15 K 13 . The coupling of superconducting qubits to 3D microwave cavities 14 could lead to cQED-type experiments with coherence on these timescales.We have set out to construct very high quality microwave cavities (Q≫10 6 ) in superconducting aluminum while focusing on geometries that may be compatible a) Electronic mail: robert.schoelkopf@yale.edu with single-photon cQED experiments at ∼10 GHz and 20 mK. We study two types of waveguide cavities (rectangular and cylindrical) that support a diversity of modes to test the effects of material purity and surface treatment on cavity lifetimes in the quantum regime. We find that pure, chemically etched aluminum produces the best results, with rectangular resonators reaching lifetimes, τ int =Q int /ω of 1.2 ms (Q int =6.9×10 7 ) and cylindrical resonators as long as 10.4 ms (Q int =7.4×10 8 ). Realizing these timescales in cQED experime...