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...
We present systematic measurements of the quality factors of surface acoustic wave (SAW) resonators on ST-X quartz in the gigahertz range at a temperature of $10 \, \textrm{mK}$. We demonstrate a internal quality factor $Q_\mathrm{i}$ approaching $0.5$ million at $0.5 \, \textrm{GHz}$ and show that $Q_\mathrm{i}\geq4.0\times10^4$ is achievable up to $4.4 \, \textrm{GHz}$. We show evidence for a polynomial dependence of propagation loss on frequency, as well as a weak drive power dependence of $Q_\mathrm{i}$ that saturates at low power, the latter being consistent with coupling to a bath of two-level systems. Our results indicate that SAW resonators are promising devices for integration with superconducting quantum circuits.Comment: 5 pages, 4 figure
Surface acoustic wave (SAW) devices based on thin films of ZnO are a well established technology. However, SAW devices on bulk ZnO crystals are not practical at room temperature due to the significant damping caused by finite electrical conductivity of the crystal. Here, by operating at low temperatures, we demonstrate effective SAW devices on the (0001) surface of bulk ZnO crystals, including a delay line operating at SAW wavelengths of λ = 4 and 6 µm and a one-port resonator at a wavelength of λ = 1.6 µm. We find that the SAW velocity is temperature dependent, reaching v ≃ 2.68 km/s at 10 mK. Our resonator reaches a maximum quality factor of Q i ≃ 1.5 × 10 5 , demonstrating that bulk ZnO is highly viable for low temperature SAW applications. The performance of the devices is strongly correlated with the bulk conductivity, which quenches SAW transmission above about 200 K.
Superconducting circuits are well established as a strong candidate platform for the development of quantum computing. In order to advance to a practically useful level, architectures are needed which combine arrays of many qubits with selective qubit control and readout, without compromising on coherence. Here we present a coaxial circuit QED architecture in which qubit and resonator are fabricated on opposing sides of a single chip, and control and readout wiring are provided by coaxial wiring running perpendicular to the chip plane. We present characterisation measurements of a fabricated device in good agreement with simulated parameters and demonstrating energy relaxation and dephasing times of $T_1 = 4.1\,\mu$s and $T_2 = 5.7\,\mu$s respectively. The architecture allows for scaling to large arrays of selectively controlled and measured qubits with the advantage of all wiring being out of the plane.Comment: 4 pages, 3 figures, 1 tabl
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