We present microwave-frequency NbTiN resonators on silicon, systematically achieving internal quality factors above 1 M in the quantum regime. We use two techniques to reduce losses associated with two-level systems: an additional substrate surface treatment prior to NbTiN deposition to optimize the metal-substrate interface, and deep reactive-ion etching of the substrate to displace the substrate-vacuum interfaces away from high electric fields. The temperature and power dependence of resonator behavior indicate that two-level systems still contribute significantly to energy dissipation, suggesting that more interface optimization could further improve performance.Superconducting coplanar waveguide (CPW) microwave resonators are crucial elements in photon detectors 1 , quantum-limited parametric amplifiers 2,3 and narrow-band filters 4 , as well as read-out, interconnect and memory elements in quantum processors based on circuit quantum electrodynamics 5 . They also play a critical role in hybrid devices, connecting superconducting circuits with micro-and nanomechanical resonators 6,7 and solid-state spins 8,9 . In many quantum science and technology applications, resonators must operate in the quantum regime, requiring low temperatures to reach the ground state (thermal energy k B T small compared to the photon energy at resonance, hf r ) and single-photon excitation levels. Under these conditions, however, internal quality factors (Q i s) are typically substantially lower than their high-temperature or high-power values.In the quantum regime, the dominant loss mechanism for high-Q superconducting resonators can be attributed to parasitic two-level systems (TLSs) in the dielectrics 10,11 . TLSs may reside in the bulk substrate 11 , as well as in the metal-substrate, metal-vacuum and substrate-vacuum interfaces 10,[12][13][14][15][16][17][18] where electric fields may be large (see Ref. 19 and references therein for a recent review of material-related loss in superconducting circuits). Interface TLSs are common by-products of the fabrication process, often introduced by impurities associated with substrate surfaces 20,21 and etching chemistry 22 . To our knowledge, the best resonators reported to date 15 (Q i = 1.72 M at 6 GHz) are fabricated by epitaxially growing aluminum on sapphire substrates following careful surface preparation (high-temperature annealing in an oxygen atmosphere). For CPW resonators on silicon (Si) substrates, achieving Q i > 1 M in the quantum regime has proven challenging, with the best resonators reported in Ref. 23.In this letter, we present silicon-based, gigahertzfrequency CPW resonators with Q i systematically above 1 M in the quantum regime, fabricated from niobium titanium nitride (NbTiN) superconducting films. This performance is reached by optimizing two aspects of the fabrication. First, the substrate surface is treated with hexamethyldisilazane (HMDS) immediately prior to metal deposition to reduce losses associated with the metal-substrate interface. Second, we employ highl...

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Nuclear spins are highly coherent quantum objects. In large ensembles, their control and detection via magnetic resonance is widely exploited, e.g. in chemistry, medicine, materials science and mining. Nuclear spins also featured in early ideas [1] and demonstrations [2] of quantum information processing. Scaling up these ideas requires controlling individual nuclei, which can be detected when coupled to an electron [3, 4, 5]. However, the need to address the nuclei via oscillating magnetic fields complicates their integration in multispin nanoscale devices, because the field cannot be localized or screened. Control via electric fields would resolve this problem, but previous methods [6, 7, 8] relied upon transducing electric signals into magnetic fields via the electron-nuclear hyperfine interaction, which severely affects the nuclear coherence. Here we demonstrate the coherent quantum control of a single antimony (spin-7/2) nucleus, using localized electric fields produced within a silicon nanoelectronic device. The method exploits an idea first proposed in 1961 [9] but never realized experimentally with a single nucleus. Our results are quantitatively supported by a microscopic theoretical model that reveals how the purely electrical modulation of the nuclear electric quadrupole interaction, in the presence of lat- † To whom correspondence should be addressed;

A critical ingredient for realizing large-scale quantum information processors will be the ability to make economical use of qubit control hardware. We demonstrate an extensible strategy for reusing control hardware on same-frequency transmon qubits in a circuit QED chip with surface-codecompatible connectivity. A vector switch matrix enables selective broadcasting of input pulses to multiple transmons with individual tailoring of pulse quadratures for each, as required to minimize the effects of leakage on weakly anharmonic qubits. Using randomized benchmarking, we compare multiple broadcasting strategies that each pass the surface-code error threshold for single-qubit gates. In particular, we introduce a selective-broadcasting control strategy using five pulse primitives, which allows independent, simultaneous Clifford gates on arbitrary numbers of qubits.

Most classical dynamical systems are chaotic. The trajectories of two identical systems prepared in infinitesimally different initial conditions diverge exponentially with time. Quantum systems, instead, exhibit quasi-periodicity due to their discrete spectrum. Nonetheless, the dynamics of quantum systems whose classical counterparts are chaotic are expected to show some features that resemble chaotic motion. Among the many controversial aspects of the quantum-classical boundary, the emergence of chaos remains among the least experimentally verified. Time-resolved observations of quantum chaotic dynamics are particularly rare, and as yet unachieved in a single particle, where the subtle interplay between chaos and quantum measurement could be explored at its deepest levels. We present here a realistic proposal to construct a chaotic driven top from the nuclear spin of a single donor atom in silicon, in the presence of a nuclear quadrupole interaction. This system is exquisitely measurable and controllable, and possesses extremely long intrinsic quantum coherence times, allowing for the observation of subtle dynamical behavior over extended periods. We show that signatures of chaos are expected to arise for experimentally realizable parameters of the system, allowing the study of the relation between quantum decoherence and classical chaos, and the observation of dynamical tunneling.

We analyze the electron spin relaxation rate 1/T1 of individual ion-implanted 31 P donors, in a large set of metal-oxide-semiconductor (MOS) silicon nanoscale devices, with the aim of identifying spin relaxation mechanisms peculiar to the environment of the spins. The measurements are conducted at low temperatures (T ≈ 100 mK), as a function of external magnetic field B0 and donor electrochemical potential µ D . We observe a magnetic field dependence of the form 1/T1 ∝ B 5 0 for B0 3 T, corresponding to the phonon-induced relaxation typical of donors in the bulk. However, the relaxation rate varies by up to two orders of magnitude between different devices. We attribute these differences to variations in lattice strain at the location of the donor. For B0 3 T, the relaxation rate changes to 1/T1 ∝ B0 for two devices. This is consistent with relaxation induced by evanescent-wave Johnson noise created by the metal structures fabricated above the donors. At such low fields, where T1 > 1 s, we also observe and quantify the spurious increase of 1/T1 when the electrochemical potential of the spin excited state |↑ comes in proximity to empty states in the charge reservoir, leading to spin-dependent tunneling that resets the spin to |↓ . These results give precious insights into the microscopic phenomena that affect spin relaxation in MOS nanoscale devices, and provide strategies for engineering spin qubits with improved spin lifetimes. arXiv:1812.06644v2 [cond-mat.mes-hall]

Out-of-time-ordered correlation functions (OTOCs) play a crucial role in the study of thermalization, entanglement, and quantum chaos, as they quantify the scrambling of quantum information due to complex interactions. As a consequence of their out-of-time-ordered nature, OTOCs are difficult to measure experimentally. In this Letter we propose an OTOC measurement protocol that does not rely on the reversal of time evolution and is easy to implement in a range of experimental settings. We demonstrate application of our protocol by the characterization of quantum chaos in a periodically driven spin.

Magnetic fields are a standard tool in the toolbox of every physicist and are required for the characterization of materials, as well as the polarization of spins in nuclear magnetic resonance or electron paramagnetic resonance experiments. Quite often, a static magnetic field of sufficiently large, but fixed, magnitude is suitable for these tasks. Here, we present a permanent magnet assembly that can achieve magnetic field strengths of up to 1.5 T over an air gap length of 7 mm. The assembly is based on a Halbach array of neodymium magnets, with the inclusion of the soft magnetic material Supermendur to boost the magnetic field strength inside the air gap. We present the design, simulation, and characterization of the permanent magnet assembly, measuring an outstanding magnetic field stability with a drift rate of |D| < 2.8 ppb/h. Our measurements demonstrate that this assembly can be used for spin qubit experiments inside a dilution refrigerator, successfully replacing the more expensive and bulky superconducting solenoids.