We have measured the plasma resonances of an array of Josephson junctions in the regime E(J)>>E(C), up to the ninth harmonic by incorporating it as part of a resonator capacitively coupled to a coplanar waveguide. From the characteristics of the resonances, we infer the successful implementation of a superinductance, an electrical element with a nondissipative impedance greater than the resistance quantum [R(Q)=h/(2e)(2) is approximately equal to 6.5 kΩ] at microwave frequencies. Such an element is crucial for preserving the quantum coherence in circuits exploiting large fluctuations of the superconducting phase. Our results show internal losses less than 20 ppm, self-resonant frequencies greater than 10 GHz, and phase-slip rates less than 1 mHz, enabling direct application of such arrays for quantum information and metrology. Arrays with a loop geometry also demonstrate a new manifestation of flux quantization in a dispersive analog of the Little-Parks effect.

With favourable error thresholds and requiring only nearest-neighbour interactions on a lattice, the surface code is an error-correcting code that has garnered considerable attention. At the heart of this code is the ability to perform a low-weight parity measurement of local code qubits. Here we demonstrate high-fidelity parity detection of two code qubits via measurement of a third syndrome qubit. With high-fidelity gates, we generate entanglement distributed across three superconducting qubits in a lattice where each code qubit is coupled to two bus resonators. Via high-fidelity measurement of the syndrome qubit, we deterministically entangle the code qubits in either an even or odd parity Bell state, conditioned on the syndrome qubit state. Finally, to fully characterize this parity readout, we develop a measurement tomography protocol. The lattice presented naturally extends to larger networks of qubits, outlining a path towards fault-tolerant quantum computing.

Superconducting order in a sufficiently narrow and infinitely long wire is destroyed at zero temperature by quantum fluctuations, which induce 2π slips of the phase of the order parameter. However, in a finite-length wire coherent quantum phase-slips would manifest themselves simply as shifts of energy levels in the excitations spectrum of an electrical circuit incorporating this wire. The higher the phase-slips probability amplitude, the larger are the shifts. Phase-slips occurring at different locations along the wire interfere with each other. Due to the Aharonov-Casher effect, the resulting full amplitude of a phase-slip depends on the offset charges surrounding the wire. Slow temporal fluctuations of the offset charges make the phase-slips amplitudes random functions of time, and therefore turn energy levels shifts into linewidths. We experimentally observed this effect on a long Josephson junction array acting as a "slippery" wire. The slip-induced linewidths, despite being only of order 100 kHz, were resolved from the flux-dependent dephasing of the fluxonium qubit.

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...

Physical implementations of qubits can be extremely sensitive to environmental coupling, which can result in decoherence. While efforts are made for protection, coupling to the environment is necessary to measure and manipulate the state of the qubit. As such, the goal of having long qubit energy relaxation times is in competition with that of achieving high-fidelity qubit control and measurement. Here we propose a method that integrates filtering techniques for preserving superconducting qubit lifetimes together with the dispersive coupling of the qubit to a microwave resonator for control and measurement. The result is a compact circuit that protects qubits from spontaneous loss to the environment, while also retaining the ability to perform fast, high-fidelity readout. Importantly, we show the device operates in a regime that is attainable with current experimental parameters and provide a specific example for superconducting qubits in circuit quantum electrodynamics. 1051-8223 (c)