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Characterization of a Double-Loop Four-Josephson-Junction Flux Qubit with Controllable Energy Gap

Yoshihiro Shimazu, Y. Saito, Z. Wada

Published Aug 19, 2024• 0 citations
Publisher

Abstract

Superconducting qubits are employed for the practical implementation of scalable quantum information processors. Fault-tolerant quantum computation schemes using superconducting qubits is under intensive study. Among the various kinds of superconducting qubits, flux qubits have a significant advantage in that they can be made insensitive to randomly fluctuating charges in the substrate. Here, the characterization results of a double-loop four-Josephson-junction flux qubit is reported. By varying the magnetic flux in one of the two loops, the energy gap at the classical degeneracy point can be controlled in situ. The basic operation of the system is illustrated by the appearance of a qubit step on a two-dimensional flux map. The energy gap can be indirectly estimated from the shape of the qubit step. The dependence of the shape of the qubit step on the control flux, which is analyzed in terms of the step height and maximum slope, is in good agreement with the simulation results, thereby implicitly indicating that the energy gap is varied from almost zero, less than the thermal energy, to a value higher than 50 GHz. Spectroscopic measurements directly demonstrated the controllability of the energy gap. In addition, doublet splitting due to intercell tunneling was observed for the first time.

DOI
10.9734/bpi/crpps/v3/1313

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Superconducting qubits are employed for the practical implementation of scalable quantum information processors. Fault-tolerant quantum computation schemes using superconducting qubits is under intensive study. Among the various kinds of superconducting qubits, flux qubits have a significant advantage in that they can be made insensitive to randomly fluctuating charges in the substrate. Here, the characterization results of a double-loop four-Josephson-junction flux qubit is reported. By varying the magnetic flux in one of the two loops, the energy gap at the classical degeneracy point can be controlled in situ. The basic operation of the system is illustrated by the appearance of a qubit step on a two-dimensional flux map. The energy gap can be indirectly estimated from the shape of the qubit step. The dependence of the shape of the qubit step on the control flux, which is analyzed in terms of the step height and maximum slope, is in good agreement with the simulation results, thereby implicitly indicating that the energy gap is varied from almost zero, less than the thermal energy, to a value higher than 50 GHz. Spectroscopic measurements directly demonstrated the controllability of the energy gap. In addition, doublet splitting due to intercell tunneling was observed for the first time.
We report the measurements of a double-loop four-Josephson-junction flux qubit. By varying the magnetic flux in one of the two loops, the energy gap at the classical degeneracy point can be controlled in situ. The basic operation of the system is illustrated by the appearance of a qubit step on a two-dimensional flux map. The energy gap can be indirectly estimated from the shape of the qubit step. The dependence of the shape of the qubit step on the control flux, which is analyzed in terms of the step height and maximum slope, is in good agreement with the simulation results, thereby implicitly indicating that the energy gap is varied from almost zero, less than the thermal energy, to a value higher than 50 GHz.
A double-loop four-Josephson-junction (4-JJ) flux qubit has an advantage over a three-Josephson-junction flux qubit in that the energy gap Δ at the symmetry point can be controlled in situ by varying the magnetic flux in one of the two loops. We report the results of a microwave spectroscopy measurement of a 4-JJ qubit. The magnetic fluxes in the two loops were controlled via a magnetic field and control flux. The excitation energy spectra at various values of control flux indicate the tunability of Δ via the control flux. Two branches of the excitation spectra were observed.
For gradiometric three-Josephson-junction flux qubits, we perform a systematic study on the tuning of the minimal transition frequency, the so-called qubit gap. By replacing one of the qubit's Josephson junctions by a dc superconducting quantum interference device (SQUID), the critical current of this SQUID and, in turn, the qubit gap can be tuned in situ by a control flux threading the SQUID loop. We present spectroscopic measurements demonstrating a well-defined controllability of the qubit gap between zero and more than 10 GHz. This is important for tuning the qubit into and out of resonance with other superconducting quantum circuits in scalable architectures, while still operating it at its symmetry point with optimal dephasing properties. The experimental data agree very well with model calculations based on the full qubit Hamiltonian. From a numerical fit, we determine the Josephson coupling and the charging energies of the qubit junctions. The derived values agree well with those measured for other junctions fabricated on the same chip. We also demonstrate the biasing of gradiometric flux qubits near the symmetry point by trapping an odd number of flux quanta in the gradiometer loop. In this way, we study the effect of the significant kinetic inductance, thereby obtaining valuable information for the qubit design.
Abstract. For gradiometric three-Josephson-junction flux qubits, we perform a systematic study on the tuning of the minimal transition frequency, the so-called qubit gap. By replacing one of the qubit’s Josephson junctions by a dc SQUID, the critical current of this SQUID and, in turn, the qubit gap can be tuned in situ by a control flux threading the SQUID loop. We present spectroscopic measurements demonstrating a well-defined controllability of the qubit gap between zero and more than 10 GHz. This is important for tuning the qubit into and out of resonance with other superconducting quantum circuits in scalable architectures, while still operating it at its symmetry point with optimal dephasing properties. The experimental data agree very well with model calculations based on the full qubit Hamiltonian. From a numerical fit, we determine the Josephson coupling and the charging energies of the qubit junctions. The derived values agree well with those measured for other junctions fabricated on the same chip. We also demonstrate the biasing of gradiometric flux qubits near the symmetry point by trapping an odd number of flux quanta in the gradiometer loop. In this way, we study the effect of the significant kinetic inductance, thereby obtaining valuable information for the qubit design.
We experimentally demonstrate the in situ tunability of the minimum energy splitting (gap) of a superconducting flux qubit by means of an additional flux loop. Pulses applied via a local control line allow us to tune the gap over a range of several GHz on a nanosecond time scale. The strong flux sensitivity of the gap (up to approximately 0.7 GHz/mPhi0) opens up the possibility to create different types of tunable couplings that are effective at the degeneracy point of the qubit. We investigate the dependence of the relaxation time and the Rabi frequency on the qubit gap.
A double-loop four-Josephson-junction (4-JJ) flux qubit is a tunable qubit wherein the potential profile can be varied in situ via two applied magnetic fluxes. This provides a high level of control over state transitions. Here, we report the results of spectroscopic measurements on this system. We observed microwave resonances associated with the first and second excited states. A branch of resonances that is most likely attributable to the third excited state was also observed. The excitation energy spectra for these levels were in qualitative agreement with the results of simplified calculations performed using an effective Hamiltonian with two phases. The three lowest levels characterized in this study may allow novel applications, including those proposed theoretically in the past. Our analysis showed that the potential exhibited a crossover from the commonly used double-well regime to the novel single-well regime. This indicates the possibility of manipulation and readout of a 3-JJ (and 4-JJ) qubit in the single-well regime using a simple technique.