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arXiv:1703.05643 · Physical review. B./Physical review. B

Anharmonicity of a superconducting qubit with a few-mode Josephson junction

Anders Kringhøj, Lucas Casparis, Michael Hell, T. W. Larsen, Ferdinand Kuemmeth, Martin Leijnse, Karsten Flensberg, Peter Krogstrup, J. Nygård, Karl D. Petersson, Charles M. Marcus

Published Feb 21, 2018• 67 citations
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Abstract

Coherent operation of gate-voltage-controlled hybrid transmon qubits (gatemons) based on semiconductor nanowires was recently demonstrated. Here we experimentally investigate the anharmonicity in epitaxial InAs-Al Josephson junctions, a key parameter for their use as a qubit. Anharmonicity is found to be reduced by roughly a factor of 2 compared to conventional metallic junctions and dependent on gate voltage. Experimental results are consistent with a theoretical model, indicating that Josephson coupling is mediated by a small number of highly transmitting modes in the semiconductor junction.

DOI
10.1103/physrevb.97.060508

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Coherent operation of gate-voltage-controlled hybrid transmon qubits (gatemons) based on semiconductor nanowires was recently demonstrated. Here we experimentally investigate the anharmonicity in epitaxial InAs-Al Josephson junctions, a key parameter for their use as a qubit. Anharmonicity is found to be reduced by roughly a factor of 2 compared to conventional metallic junctions and dependent on gate voltage. Experimental results are consistent with a theoretical model, indicating that Josephson coupling is mediated by a small number of highly transmitting modes in the semiconductor junction.
The anharmonicity of a transmon qubit, defined as the difference in energy level spacing, is a key design parameter. In transmons built from hybrid superconductor-semiconductor Josephson elements, the anharmonicity is tunable with gate voltages that control both the Josephson energy and the weak link transparency. In Sn-InAs nanowire transmons, we use two-tone microwave spectroscopy to extract anharmonicity ranging in absolute value from the transmon charging energy EcE_cEc​ to values smaller than Ec/10E_c/10Ec​/10. This behavior contrasts with the predictions of the multi-channel short-junction model, which sets a lower limit on anharmonicity at Ec/4E_c/4Ec​/4. Coherent operation of the qubit is still possible at the point of the lowest anharmonicity. These findings demonstrate the potential of quantum circuits that benefit from widely electrically tunable anharmonicity.
Recent experiments have demonstrated superconducting transmon qubits with semiconductor nanowire Josephson junctions. These hybrid gatemon qubits utilize field effect tunability characteristic of semiconductors to allow complete qubit control using gate voltages, potentially a technological advantage over conventional flux-controlled transmons. Here, we present experiments with a two-qubit gatemon circuit. We characterize qubit coherence and stability and use randomized benchmarking to demonstrate single-qubit gate errors below 0.7% for all gates, including voltage-controlled Z rotations. We show coherent capacitive coupling between two gatemons and coherent swap operations. Finally, we perform a two-qubit controlled-phase gate with an estimated fidelity of 91%, demonstrating the potential of gatemon qubits for building scalable quantum processors.
We investigate a semiconductor nanowire-based gatemon qubit with epitaxial Al on two facets of the nanowire, allowing gate control of wire density. Two segments have the Al removed, one forming a Josephson junction, and the other operating as a transistor, providing in situ switching between dc transport and qubit operation. Gating the nanowire (NW) changes the rate of decay of qubit frequency in magnetic field applied parallel to the NW. Gating the Josephson junction can lead additionally to nonmonotonic behavior of the qubit frequency in parallel magnetic field. A detailed model of the wire and junction yields behavior consistent with experiment, and allows us to propose that gating the bulk wire affects the rate of frequency decay in fields due to changes in the bulk potential distribution, while nonmonotonic behavior of the frequency is due to the interference of Andreev bound states in the junction. Gating the junction further allows access to the multimode regime, where fluctuations in qubit frequency are measured to be considerably smaller than the theoretical ``universal'' value, also smaller than numerics, and consistent with previous measurements of fluctuating critical currents.
We introduce a hybrid qubit based on a semiconductor nanowire with an epitaxially grown superconductor layer. Josephson energy of the transmonlike device ("gatemon") is controlled by an electrostatic gate that depletes carriers in a semiconducting weak link region. Strong coupling to an on-chip microwave cavity and coherent qubit control via gate voltage pulses is demonstrated, yielding reasonably long relaxation times (~0.8 μs) and dephasing times (~1 μs), exceeding gate operation times by 2 orders of magnitude, in these first-generation devices. Because qubit control relies on voltages rather than fluxes, dissipation in resistive control lines is reduced, screening reduces cross talk, and the absence of flux control allows operation in a magnetic field, relevant for topological quantum information.
Superconducting transmon qubits based on hybrid superconductor-semiconductor Josephson junctions (gatemons) offer gate tunability, but their relaxation times remain well below those of state-of-the-art transmons, and the origin of this discrepancy is not fully understood. Here, we co-fabricate gatemons and SIS-junction transmons with nominally identical circuit layouts, gate dielectrics, and control lines, so that the Josephson element is the only intentional distinction. Across multiple chips, transmons in this architecture reach relaxation times in the tens of microseconds, whereas gatemons saturate in the few-microsecond range. Using the transmons as on-chip references, we construct a loss budget including Purcell decay, spontaneous emission through the control line, and internal dielectric loss, and find that the corresponding T1 limits exceed all measured gatemon values by more than an order of magnitude. Temperature-dependent T1 measurements follow a common quasiparticle-activation model and yield similar superconducting gaps for S-Sm-S and SIS junctions, indicating that the reduced gatemon coherence is dominated by additional temperature-independent, junction-intrinsic dissipation.
We study a gate-tunable superconducting qubit (gatemon) based on a thin InAs-Al hybrid nanowire. Using a gate voltage to control its Josephson energy, the gatemon can reach the strong coupling regime to a microwave cavity. In the dispersive regime, we extract the energy relaxation time T 1 ∼ 0.56 μs and the dephasing time T 2 * ∼ 0.38 μs. Since thin InAs-Al nanowires can have fewer or single sub-band occupation and recent transport experiment shows the existence of nearly quantized zero-bias conductance peaks, our result holds relevancy for detecting Majorana zero modes in thin InAs-Al nanowires using circuit quantum electrodynamics.