Enhanced coherence of all-nitride superconducting qubits epitaxially grown on silicon substrate

Improving the coherence of superconducting qubits is a fundamental step towards the realization of fault-tolerant quantum computation. However, coherence times of quantum circuits made from conventional aluminium-based Josephson junctions are limited by the presence of microscopic two-level systems in the amorphous aluminum oxide tunnel barriers. Here, we have developed superconducting qubits based on NbN/AlN/NbN epitaxial Josephson junctions on silicon substrates which promise to overcome the drawbacks of qubits based on Al/AlO$_{x}$/Al junctions. The all-nitride qubits have great advantages such as chemical stability against oxidation, resulting in fewer two-level fluctuators, feasibility for epitaxial tunnel barriers that reduce energy relaxation and dephasing, and a larger superconducting gap of $\sim$5.2 meV for NbN, compared to $\sim$0.3 meV for aluminium, which suppresses the excitation of quasiparticles. By replacing conventional MgO by a silicon substrate with a TiN buffer layer for epitaxial growth of nitride junctions, we demonstrate a qubit energy relaxation time $T$$_{1}$=16.3 $\mu$s and a spin-echo dephasing time $T$$_{2}$=21.5 $\mu$s. These significant improvements in quantum coherence are explained by the reduced dielectric loss compared to previously reported NbN-based qubits with MgO substrates ($T$$_{1}$$\approx$$T$$_{2}$$\approx$0.5 $\mu$s). These results are an important step towards constructing a new platform for superconducting quantum hardware.


Introduction
Since the first demonstration of nanosecond-scale quantum coherence in a charge qubit in 1999 1 , superconducting qubits have developed into a leading platform for scalable quantum computing, as evidenced by recent key demonstrations including quantum algorithms 2,3 , quantum error correction [4][5][6] and quantum supremacy 7 . However, their gate fidelities still need to be improved further for building a fault-tolerant quantum computer, even though two-qubit gates with fidelities as high as 99.7% 8 have recently been achieved (cf. the case of trapped-ion qubits above 99.9% 9 ).
The remarkable progress of superconducting qubits has to a large extent resulted from the innovative five-order increase in their coherence times by improving circuit designs, materials and fabrication processes [10][11][12] . Looking at material-based improvements, most of the research has been focused on materials for capacitors or microwave resonators (e.g., niobium titanium nitride (NbTiN) 13 , TiN 14 , and tantalum (Ta) 15 instead of the commonly used niobium (Nb) or aluminum (Al)) in order to reduce microwave dielectric loss induced by uncontrolled defects in oxides at their surfaces and interfaces. In contrast, alternative materials for the Josephson junctions (JJs) of the qubits have not been studied adequately, even though it has been pointed out that the coherence times of superconducting quantum circuits made from conventional Al-based JJs are limited by energy or phase relaxation due to microscopic two-level systems (TLSs) in the amorphous aluminum oxide (AlOx) tunnel barriers [16][17][18] . Therefore, a breakthrough in the further improvement of superconducting qubits can be expected by exploring alternative materials for JJs.
One promising approach to reduce the number of TLSs in a JJ is to use a crystalline tunnel barrier as demonstrated with epitaxial Al2O3 layers grown on crystalline Re films 19,20 . From this viewpoint, fully epitaxial nitride JJs consisting of NbN/AlN/NbN tri-layers are highly attractive candidates as an alternative material technology for superconducting quantum circuits. This is because such epitaxially grown nitride JJs have great potential to solve material-related concerns, including the TLS problem, owing to their high crystal quality and chemical stability against oxidation. Moreover, due to the large superconducting gap (2 ~ 5.2 meV) and relatively high transition temperature (~ 16 K) of NbN 21 , quasiparticle excitation can be suppressed. One point that requires attention when using an AlN tunnel barrier is its piezoelectric property, i.e. the coupling between the electric field concentrated at the JJ and the underlying crystal lattice, which leads to substantial qubit decoherence via phonon emission 22 . In previous studies of phase qubits using an amorphous AlN barrier, energy relaxation times were as short as ~10 ns due to piezoelectricity 23,24 . However, the detrimental piezoelectric effect can be avoided when the AlN barrier is grown epitaxially in the cubic phase because of its lattice-inversion symmetry. In an early attempt with epitaxially grown cubic-phase AlN tunnel barriers 25 , longer relaxation times of 500 ns were observed in transmon qubits consisting of fully epitaxial NbN/AlN/NbN JJs on a single-crystal MgO substrate, commonly used because it allows good lattice matching between the materials. These coherence times were limited by the dielectric loss from the MgO substrate rather than the intrinsic properties of the NbN-based JJs themselves. In the context of NbN-based qubits, it is worth mentioning that an early report of a phase qubit using an epitaxially grown 10 μm -size NbN/AlN/NbN JJ also showed a relatively long phase coherence time of about 5 μs 26 . It has been characterized using a direct current (DC) readout so that the phase qubit is quite insensitive to the dielectric loss of substrate, which explains the relatively long coherence times obtained in that work.
Yet, the development of NbN-based qubits is still inadequate despite the superior properties of NbN as an alternative material for superconducting quantum hardware.
More research is required in this direction to go beyond conventional Al-based qubits.
In this article, we report a significant improvement in quantum coherence of an epitaxially grown NbN-based superconducting qubit. To suppress the dominant dielectric loss from the MgO substrate, which has limited the energy relaxation time ( 1 ) in the previous work 25 , we adopted a Si substrate with a TiN buffer layer for epitaxial growth of NbN/AlN/NbN junctions 27 . The loss tangent of the high-resistivity Si substrate is much lower than that of MgO, as reported in Ref. 28 (5 × 10 −6 − 12 × 10 −6 for the former and 0.5 × 10 −4 − 0.8 × 10 −4 for the latter). Additionally, for the qubit design, we employed the structure of a capacitively-shunted (C-shunt) flux qubit, which brings several advantages such as enhanced coherence and reproducibility as well as higher anharmonicity compared to transmon qubits [29][30][31] . With these modifications, we achieved coherence times as long as tens of microseconds using an all-nitride qubit with epitaxial JJs on a Si substrate. These coherence times are more than an order of magnitude longer than those obtained with qubits grown on MgO substrates. We explain that this improvement in coherence times can be attributed mainly to the reduced dielectric loss when replacing the MgO substrate with the Si substrate. These results shed light on the role of alternative material technologies in improving superconducting quantum circuits

Results and discussions
All-nitride C-shunt flux qubit. Our circuit is made of epitaxially grown NbN with a TiN buffer layer on a Si substrate. It consists of a C-shunt flux qubit that is based on epitaxial NbN/AlN/NbN JJs and is capacitively coupled to a half-wavelength superconducting coplanar waveguide resonator (CPW) (see Fig. 1). A detailed experimental setup together with device parameters are found in the Methods.
Spectroscopy of resonator. First, we assess the resonator properties as shown in Fig. 2(a). Currently they are lower than those of Al-based C-shunt flux qubits coupled to twodimensional resonators on Si substrates 30 (showing 1 =55 μs). However, there is still room for improvements in a number of aspects to increase 1 further, and the significant improvement over state-of-the-art all-nitride qubits is an important step in that direction.
The temporal variation of 1 is usually explained by quasiparticle fluctuations 30 and instability of TLS defects 34,35 . When compared to Al-based single-junction Xmon-type transmon qubits in Ref. 35  we found that the 1 data of our nitride qubit show little temporal variation, 1~ 10% of � 1 . Such a narrow Gaussian distribution is also observed in Al-based C-shunt flux qubits 30 and discussed as an indication that quasiparticles did not strongly influence this device. We therefore believe that our nitride qubit is also not strongly affected by quasiparticles. The instances of large deviation in 1 to lower values outside the Gaussian peak in Fig. 3(c To support the argument that the substrate material is responsible for this improvement, we briefly discuss the predicted limit on the quality factor for the MgO substrate material. As reported in Ref. 25  Device parameters. The fabricated qubit-resonator architecture is depicted in Fig. 1. Our qubit has three JJs, all with circular shapes. Two JJs (i.e., JJ2 and JJ3 in Fig. 1(b)) were designed to have 1.08 µm-diameters (using a mask size of 1.28 µm diameter and expecting a reduction of 0.2 µm after the fabrication process), and the third junction (JJ1 in Fig. 1(b)) was designed to have a 0.70 µm diameter (using a mask size of 0.9 µm diameter) to get a smaller area by a factor α of 0.42. The actual junction diameters after fabrication were 1.07 µm and 0.645 µm, giving the somewhat reduced ratio of α = 0.36 as confirmed by scanning electron microscopy images, shown in Fig. 1(c).  from the laser scanning microscope system. Figure 1(e) shows a cross-sectional schematic view of the qubit part indicated by the dashed line in the inset of Fig. 1(b).
For the dispersive readout, the qubit is coupled to a half-wavelength (6.0-mm long) CPW resonator. The center conductor is 10 µm wide, separated from the lateral ground planes by a 6 µm gap, resulting in a wave impedance of the coplanar waveguide =50 Ω for optimal impedance matching with conventional microwave components.
Experimental setup. The qubit chip was mounted in a sample holder made of gold-plated copper ( Fig. 1(a)), which is thermally anchored to the mixing chamber of a dilution refrigerator. For magnetic shielding, the sample holder is covered by a three-layer shield consisting of one aluminum-based superconducting and two µ-metal magnetic shields.
The resonator and qubits are characterized at a base temperature of ~10 mK in a dilution refrigerator. For characterizing the resonator, microwave transmission 21 was measured using a vector network analyzer or a heterodyne setup using an IQ mixer and a digitizer. For spectroscopy and coherence measurements of the qubit, we used an additional microwave drive and a commercial analogue-to-digital converter 38 , so that the qubit state is read out dispersively via the resonator in a circuit QED architecture.

Data availability
The data that support the findings of this study are available from the corresponding authors upon reasonable request.    The pulse sequences for the measurements are shown in the insets. The pulse sequences include a pulse with a 40 ns duration, /2 pulses with same duration but half the amplitude of the pulses, and readout pulses with 400 ns duration. Here the driving frequency in both measurements is detuned by 5 MHz from the qubit frequency and each