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Tunable anharmonicity in Sn-InAs nanowire transmons beyond the short junction limit

Amrita Purkayastha, Amritesh Sharma, Param J. Patel, An-Hsi Chen, Connor P. Dempsey, Shreyas Asodekar, Subhayan Sinha, Maxime Tomasian, Mihir Pendharkar, Christopher J. Palmstrøm, Moïra Hocevar, Kun Zuo, Michael Hatridge, Sergey M. Frolov

Abstract

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 $E_c$ to values smaller than $E_c/10$. This behavior contrasts with the predictions of the multi-channel short-junction model, which sets a lower limit on anharmonicity at $E_c/4$. 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.

Tunable anharmonicity in Sn-InAs nanowire transmons beyond the short junction limit

Abstract

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 to values smaller than . This behavior contrasts with the predictions of the multi-channel short-junction model, which sets a lower limit on anharmonicity at . 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.

Paper Structure

This paper contains 12 sections, 2 equations, 12 figures, 1 table.

Table of Contents

  1. Introduction
  2. Device and Measurement Description
  3. Results: Gate-dependent anharmonicity
  4. Discussion
  5. Duration and Volume of Study
  6. Data availability
  7. Acknowledgments
  8. Competing Interests
  9. Methods
  10. HFSS simulations
  11. Alternative Explanations: devices E and F.
  12. Additional Data

Figures (12)

  • Figure 1: (a) Simplified energy diagram of a transmon (red). The black dashed curve is the parabolic potential of a harmonic oscillator. (b) Schematic current-phase relations of different weak link junctions. Insulator based junction (SIS JJ, blue), Semiconducting weak link in the short junction limit (Short JJ limit, red, $\tau = 0.99$), long junction (Long JJ limit, green). (c) Schematic of the capacitively coupled readout resonator and transmon, overlaid with an SEM image of the nanowire junction and aluminum leads with side gate (false color). (d) Transmission in two tone spectroscopy with transitions and anharmonicity indicated.
  • Figure 2: Device A: (a) Two-tone spectroscopy as a function of side gate voltage $V_g$ swept from low to high. Both $f_{01}$ and $f_{02}/2$ transitions are visible and changing non monotonically with $V_g$. (b) and (c) Two-tone spectroscopy as a function of drive power and drive frequency at $V_g=1.427V$ and $V_g=1.627V$ respectively showing the clearly resolvable $f_{01}$ and $f_{02}/2$ dips. The separation between $f_{01}$ and $f_{02}/2$ for (b) and (c) are 127 MHz and 15 MHz respectively.
  • Figure 3: (a) Anharmonicity normalized with the designed charging energy, $\alpha/E_c$ plotted as a function of gate voltage $V_g$, for different qubit frequencies $f_{01}$ indicated by the color bar.(b)Anharmonicity $\alpha/h$ as a function of $f_{01}$, with corresponding gate voltages indicated by the color bar, for Device A.(c) and (d) show the same plots as in (a) and (b), respectively, for Device B.
  • Figure 4: (a)Rabi oscillations as function of pulse duration and drive frequency at fixed drive amplitude of 0.64 a.u. (b) Relaxation time $T_1$ extracted from fit to decaying excited state population. (c) Ramsey measurements and fit to a decaying oscillation. (d) The Hahn echo sequence and fit to a decaying function. Demodulated transmission amplitude is given in arbitrary units (a.u.).
  • Figure S1: Eigenmode simulation of a single Transmon qubit
  • ...and 7 more figures