We show that in a perpendicularly magnetized Pt/Co bilayer the spin-Hall effect (SHE) in Pt can produce a spin torque strong enough to efficiently rotate and switch the Co magnetization. We calculate the phase diagram of switching driven by this torque, finding quantitative agreement with experiments. When optimized, the SHE torque can enable memory and logic devices with similar critical currents and improved reliability compared to conventional spin-torque switching. We suggest that the SHE torque also affects current-driven magnetic domain wall motion in Pt/ferromagnet bilayers.

The scalable application of quantum information science will stand on reproducible and controllable high-coherence quantum bits (qubits). Here, we revisit the design and fabrication of the superconducting flux qubit, achieving a planar device with broad-frequency tunability, strong anharmonicity, high reproducibility and relaxation times in excess of 40 μs at its flux-insensitive point. Qubit relaxation times T1 across 22 qubits are consistently matched with a single model involving resonator loss, ohmic charge noise and 1/f-flux noise, a noise source previously considered primarily in the context of dephasing. We furthermore demonstrate that qubit dephasing at the flux-insensitive point is dominated by residual thermal-photons in the readout resonator. The resulting photon shot noise is mitigated using a dynamical decoupling protocol, resulting in T2≈85 μs, approximately the 2T1 limit. In addition to realizing an improved flux qubit, our results uniquely identify photon shot noise as limiting T2 in contemporary qubits based on transverse qubit–resonator interaction.

We present measurements of coherence and successive decay dynamics of higher energy levels of a superconducting transmon qubit. By applying consecutive π pulses for each sequential transition frequency, we excite the qubit from the ground state up to its fourth excited level and characterize the decay and coherence of each state. We find the decay to proceed mainly sequentially, with relaxation times in excess of 20 μs for all transitions. We also provide a direct measurement of the charge dispersion of these levels by analyzing beating patterns in Ramsey fringes. The results demonstrate the feasibility of using higher levels in transmon qubits for encoding quantum information. DOI: 10.1103/PhysRevLett.114.010501 PACS numbers: 03.67.Lx, 05.40.Ca, 85.25.Cp Universal quantum information processing is typically formulated with two-level quantum systems, or qubits [1]. However, extending the dimension of the Hilbert space to a d-level system, or "qudit," can provide significant computational advantages. In particular, qudits have been shown to reduce resource requirements [2,3], improve the efficiency of certain quantum cryptanalytic protocols [4][5][6][7], simplify the implementation of quantum gates [8,9], and have been used for simulating multidimensional quantum-mechanical systems [10]. The superconducting transmon qubit [11] is a quantum LC oscillator with the inductor replaced by a Josephson junction [ Fig. 1(a)]. The nonlinearity of the Josephson inductance renders the oscillator weakly anharmonic, which allows selective addressing of the individual energy transitions and, thus, makes the device well-suited for investigating multilevel quantum systems. The transmon's energy potential is shallower than the parabolic potential of an harmonic oscillator, leading to energy levels that become more closely spaced as energy increases [ Fig. 1(b)]. Although leakage to these levels can be a complication when operating the device as a two-level system [12], the existence of higher levels has proven useful for implementing certain quantum gates [13,14]. Full quantum state tomography of a transmon operated as a three-level qutrit has also been demonstrated [15].In this Letter, we investigate the energy decay and the phase coherence of the first five energy levels of a transmon qubit embedded in a three-dimensional cavity [16]. We find the energy decay of the excited states to be predominantly sequential, with nonsequential decay rates suppressed by 2 orders of magnitude. The suppression is a direct consequence of the parity of the wave functions in analogy with the orbital selection rules governing transitions in natural atoms. We find that the sequential decay rates scale as i, where i ¼ 1; …; 4 is the initial excited state, thus, confirming the radiation scaling expected for harmonic oscillators [17,18]. The decay times remain in excess of 20 μs for all states up to i ¼ 4, making them promising resources for quantum information processing applications. In addition, we characterize the quantum phase coherence of the...

Remarkable advancements in coherence and control fidelity have been achieved in recent years with cryogenic solid-state qubits. Nonetheless, thermalizing such devices to their milliKelvin environments has remained a long-standing fundamental and technical challenge. In this context, we present a systematic study of the first-excited-state population in a 3D transmon superconducting qubit mounted in a dilution refrigerator with a variable temperature. Using a modified version of the protocol developed by Geerlings et al., we observe the excited-state population to be consistent with a Maxwell-Boltzmann distribution, i.e., a qubit in thermal equilibrium with the refrigerator, over the temperature range 35-150 mK. Below 35 mK, the excited-state population saturates at approximately 0.1%. We verified this result using a flux qubit with ten times stronger coupling to its readout resonator. We conclude that these qubits have effective temperature T eff ¼ 35 mK. Assuming T eff is due solely to hot quasiparticles, the inferred qubit lifetime is 108 μs and in plausible agreement with the measured 80 μs. Superconducting qubits are increasingly promising candidates to serve as the logic elements of a quantum information processor. This assertion reflects, in part, several successes over the past decade addressing the fundamental operability of this qubit modality [1][2][3]. A partial list includes a 5-orders-of-magnitude increase in the coherence time T 2 [4], the active initialization of qubits in their ground state [1,5], the demonstration of low-noise parametric amplifiers [6][7][8][9][10][11][12] enabling high-fidelity readout [13][14][15][16], and the implementation of a universal set of high-fidelity gates [17]. In addition, prototypical quantum algorithms [18][19][20] and simulations [21,22] have been demonstrated with few-qubit systems, and the basic parity measurements underlying certain error detection protocols are now being realized with qubit stabilizers [23][24][25][26][27][28] and photonic memories [29].Concomitant with these advances is an enhanced ability to improve our understanding of the technical and fundamental limitations of single qubits. The 3D transmon [30] has played an important role in this regard, because its relatively clean electromagnetic environment, predominantly low-loss qubit-mode volume, and resulting long coherence times make it a sensitive test bed for probing these limitations.One such potential limitation is the degree to which a superconducting qubit is in equilibrium with its cryogenic environment. Consider a typical superconducting qubit with a level splitting E ge ¼ hf ge , with f ge ¼ 5 GHz, mounted in a dilution refrigerator at temperature T ¼ 15 mK, such that E ge ≫ k B T. Ideally, such a qubit in thermal equilibrium with the refrigerator will have a thermal population P jei ≈ 10 −5 % of its first excited state according to Maxwell-Boltzmann statistics. In practice, however, the empirical excited-state population reported for various superconducting qubits (featuring similar...