We characterize a fluxonium qubit consisting of a Josephson junction inductively shunted with a NbTiN nanowire superinductance. We explain the measured energy spectrum by means of a multimode theory accounting for the distributed nature of the superinductance and the effect of the circuit nonlinearity to all orders in the Josephson potential. Using multiphoton Raman spectroscopy, we address multiple fluxonium transitions, observe multilevel Autler-Townes splitting and measure an excited state lifetime of T1 = 20 µs. By measuring T1 at different magnetic flux values, we find a crossover in the lifetime limiting mechanism from capacitive to inductive losses.The development of superinductors [1-5] has received significant interest due to their potential to provide noise protection in superconducting qubits [6][7][8]. Moreover, inductively shunted Josephson junction based superconducting circuits are known to be immune to charge noise [1], and to flux noise in the limit of large inductances [9][10][11][12]. Despite remarkable progress, the superinductances that have been so far reported in the literature are still small compared to those needed for qubit protection [7,8,11,12].A thin-film nanowire built from a disordered superconductor constitutes an alternative approach to reach the required superinductance regime. High-kinetic inductance superconducting materials, such as NbTiN and TiN, have been studied in the context of microwave detectors [13][14][15], parametric amplifiers [16][17][18], and rfSQUID qubits [19,20]. In a nanowire, the inertia of the Cooper pair condensate is manifested as the kinetic inductance of the superconducting wire, and can be expressed aswhere m is the free electron mass, e is the electron charge and n s is the density of Cooper pairs [14,21]. The second bracketed term in Eq. (1) is a geometric factor dependent on the length l, width w, and thickness d of the nanowire. By choosing a disordered superconductor with a low n s and fabricating a sufficiently long and thin wire, the kinetic inductance can be made large enough to reach the superinductance regime. In this regime, the presence of stray ground capacitance and the large kinetic inductance lower the frequencies of the self-resonant modes of the device. As is the case of long junction arrays [2], the multimode structure of the device needs to be taken into account to produce an accurate theoretical description [22,23].In this Letter, we demonstrate a fluxonium circuit integrating a NbTiN nanowire superinductance. We charac- * These authors contributed equally to this work.terize the effect of the nanowire modes on the qubit spectrum with a multimode circuit theory accounting for the distributed nature of the superinductance. Importantly, and in contrast to previous approaches tailored to weakly anharmonic qubits [24,25], our theory incorporates the circuit nonlinearity to all orders in the Josephson potential. Such difference allows us to treat the strong anharmonicity of the fluxonium qubit efficiently, and to retain the effect of ch...

Practical quantum computing will require error rates well below those achievable with physical qubits. Quantum error correction1,2 offers a path to algorithmically relevant error rates by encoding logical qubits within many physical qubits, for which increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low for logical performance to improve with increasing code size. Here we report the measurement of logical qubit performance scaling across several code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find that our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, in terms of both logical error probability over 25 cycles and logical error per cycle ((2.914 ± 0.016)% compared to (3.028 ± 0.023)%). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a 1.7 × 10−6 logical error per cycle floor set by a single high-energy event (1.6 × 10−7 excluding this event). We accurately model our experiment, extracting error budgets that highlight the biggest challenges for future systems. These results mark an experimental demonstration in which quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation.

Atomic and atom-like defects in the solid-state are widely explored for quantum computers, networks and sensors. Rare earth ions are an attractive class of atomic defects that feature narrow spin and optical transitions that are isolated from the host crystal, allowing incorporation into a wide range of materials. However, the realization of long electronic spin coherence times is hampered by magnetic noise from abundant nuclear spins in the most widely studied host crystals. Here, we demonstrate that Er 3+ ions can be introduced via ion implantation into TiO2, a host crystal that has not been studied extensively for rare earth ions and has a low natural abundance of nuclear spins. We observe efficient incorporation of the implanted Er 3+ into the Ti 4+ site (40% yield), and measure narrow inhomogeneous spin and optical linewidths (20 and 460 MHz, respectively) that are comparable to bulk-doped crystalline hosts for Er 3+ . This work demonstrates that ion implantation is a viable path to studying rare earth ions in new hosts, and is a significant step towards realizing individually addressed rare earth ions with long spin coherence times for quantum technologies. *

A roadmap is provided for building a quantum engineering education program to satisfy U.S. national and international workforce needs.Background: The rapidly growing quantum information science and engineering (QISE) industry will require both quantumaware and quantum-proficient engineers at the bachelor's level.Research Question: What is the best way to provide a flexible framework that can be tailored for the full academic ecosystem?Methodology: A workshop of 480 QISE researchers from across academia, government, industry, and national laboratories was convened to draw on best practices; representative authors developed this roadmap.Findings: 1) For quantum-aware engineers, design of a first quantum engineering course, accessible to all STEM students, is described; 2) for the education and training of quantumproficient engineers, both a quantum engineering minor accessible to all STEM majors, and a quantum track directly integrated into individual engineering majors are detailed, requiring only Manuscript

In this work, we demonstrate the use of frequency-tunable superconducting NbTiN coplanar waveguide microresonators for multi-frequency pulsed electron spin resonance (ESR) experiments. By applying a bias current to the center pin, the resonance frequency (∼7.6 GHz) can be continuously tuned by as much as 95 MHz in 270 ns without a change in the quality factor of 3000 at 2K. We demonstrate the ESR performance of our resonators by measuring donor spin ensembles in silicon and show that adiabatic pulses can be used to overcome magnetic field inhomogeneities and microwave power limitations due to the applied bias current. We take advantage of the rapid tunability of these resonators to manipulate both phosphorus and arsenic spins in a single pulse sequence, demonstrating pulsed double electron-electron resonance (DEER). Our NbTiN resonator design is useful for multi-frequency pulsed ESR and should also have applications in experiments where spin ensembles are used as quantum memories.Superconducting microresonators have dramatically enhanced the detection sensitivity of conventional electron spin resonance (ESR). Recently, single-shot detection of 10 7 spins has been demonstrated at 2K using coplanar waveguide (CPW) resonators 1,2 , and further improvements in the readout at mK temperatures have enabled detection of 10 3 spins 3,4 using lumped-element resonators. As a result, these resonators are routinely used for the manipulation of spin ensembles and have also been proposed as buses for coherently coupling superconducting qubits with spins 5,6 . The resonance frequencies of CPW and lumped-element resonators are typically fixed by fabrication, and conventional methods used to tune the resonance frequency post-fabrication using superconducting quantum interference devices are incompatible with the high magnetic fields that are typically necessary for X-band ESR. A method that enables frequency tunability of superconducting microresonators at high magnetic fields is thus desirable for multifrequency ESR. The ability to tune the resonance frequency on-demand also allows greater control of spin dynamics 7,8 as well as the coupled spin-cavity dynamics in the strong-coupling regime where spin ensembles are used as quantum memories 6,9 . In this work, we fabricate frequency-tunable CPW resonators that are compatible with high magnetic fields following recently developed techniques 10-12 . We show multi-frequency ESR with 31 P donors in 28 Si, finding no effect on spin coherence when the resonators are operated at different frequencies. We show that the resonance frequency can be tuned in no more than ∼270 ns. As a practical application, we take advantage of the rapid tunability of our resonators to manipulate 31 P and 75 As donor spin ensembles that are 33 MHz apart in a single pulse sequence.