Planar superconducting resonators with internal quality factors above one million

Abstract

We describe the fabrication and measurement of microwave coplanar waveguide resonators with internal quality factors above 10 7 at high microwave powers and over 10 6 at low powers, with the best low power results approaching 2 × 10 6 , corresponding to ∼ 1 photon in the resonator. These quality factors are achieved by controllably producing very smooth and clean interfaces between the resonators' aluminum metallization and the underlying single crystal sapphire substrate. Additionally, we describe a method for analyzing the resonator microwave response, with which we can directly determine the internal quality factor and frequency of a resonator embedded in an imperfect measurement circuit.High quality factor microwave resonators provide critical elements for superconducting electromagnetic radiation detectors 1 , quantum memories 2,3 , and quantum computer architectures 4 . Good performance and stability can be achieved for such applications using aluminum resonators patterned on sapphire substrates. Aluminum is a favored material due to its robust oxide and reasonable transition temperature, and sapphire provides an excellent substrate due to its very low microwave loss tangent 5 δ ∼ 10 −8 and its chemical inertness. However, the quality factors measured in such resonators is lower than expected; recent simulations 6 and experiments 7 suggest that the unexplained loss arises mostly from imperfections at the metal-substrate interface. Using an experimental apparatus with minimal stray magnetic fields and infrared light at the sample 8 , here we show that careful substrate preparation and cleaning yields aluminumon-sapphire resonators with significantly higher internal quality factors Q i . We also introduce a new method for evaluating the resonator microwave response.The aluminum for the resonators was deposited on cplane sapphire substrates in one of three deposition systems: A high vacuum DC sputter system (base pressure P base = 6 × 10 −8 Torr), a high vacuum electron-beam evaporator (P base = 5 × 10 −8 Torr) or an ultra-high vacuum (UHV) molecular beam epitaxy (MBE) system (P base = 6 × 10 −10 Torr) with electron-beam deposition. The sapphire substrates were first sonicated in a bath of acetone then isopropanol followed by a deionized water rinse. For the sputter-deposited and e-beam evaporated samples, we further cleaned the substrates prior to Al de-

Fabrication and characterization of aluminum airbridges for superconducting microwave circuits

“…We fabricated the resonators from an aluminum film deposited on a highresistivity silicon subtrate and etched with a BCl 3 /Cl 2 inductively coupled plasma. 19 We have also used the process on a sapphire substrate with comparable results. We designed the resonators with 10 µm center traces and 5 µm gaps to match the dimensions of our typical feedlines, and designed the resonant frequencies to range from 5 to 6 GHz.…”

“…We determined Q i by measuring the transmission through a feedline that was capacitively coupled to each resonator (see Ref. 19 for measurement details). We varied the drive power such that the photon population n p in the resonator ranged from single photon levels up to 10 7 photons, at which point the resonators became non-linear.…”

Superconducting quantum circuits at the surface code threshold for fault tolerance

“…The device is made in a fivestep deposition process, (I) Al deposition and control wiring etch, (II) crossover dielectric deposition, (III) crossover Al deposition, (IV) Qubit capacitor and resonator etch, (V) Josephson junction deposition. The qubit capacitor, ground plane, readout resonators, and control wiring are made using molecular beam epitaxy (MBE)-grown Al on sapphire [3]. The control wiring is patterned using lithography and etching with a BCl 3 /Cl 2 reactive ion etch.…”

“…A quantum computer can solve hard problems -such as prime factoring 1,2 , database searching 3,4 , and quantum simulation 5 -at the cost of needing to protect fragile quantum states from error. Quantum error correction 6 provides this protection, by distributing a logical state among many physical qubits via quantum entanglement.…”

“…The CZ gate fidelity is limited by three error mechanisms: Decoherence (55% of the total error), control error (24%), and state leakage (21%), see Supplementary Information. Decoherence can be suppressed with enhanced materials and optimised fabrication 24,25 . Imperfections in control arise primarily from reflections and stray inductances in wiring, and can be improved using conventional microwave techniques.…”