Diabatic Gates for Frequency-Tunable Superconducting Qubits

We demonstrate diabatic two-qubit gates with Pauli error rates down to $4.3(2)\times {10}^{-3}$ in as fast as 18 ns using frequency-tunable superconducting qubits. This is achieved by synchronizing the entangling parameters with minima in the leakage channel. The synchronization shows a landscape in gate parameter space that agrees with model predictions and facilitates robust tune-up. We test both iswap-like and cphase gates with cross-entropy benchmarking. The presented approach can be extended to multibody operations as well.

Figure 1

(a) Circuit diagram of two transmon qubits coupled through a small capacitance, giving rise to a frequency-dependent coupling strength. (b) Schematic representation of the iswap gate. (1) Qubits at rest (idle), separated by a large detuning. (2) $A$’s qubits are rapidly detuned to the interaction frequency, qubit $B$’s ${\omega }_{10}$ transition sweeps by $A$’s ${\omega }_{21}$ transition, potentially incurring leakage from $|11⟩$ to $|20⟩$. (3) Qubits at the interaction frequency undergo an iswap operation; both qubits’ $|2⟩$ states hybridize. Resonant Rabi oscillations occur between $|10⟩$ and $|01⟩$ while weaker off-resonant Rabi oscillations occur between $|11⟩$ and $|{\psi }_b⟩$. (c) The frequency dependence of the coupling $g$ makes the synchronization of the exchange between $|01⟩$ and $|10⟩$ and preservation of the occupation of $|11⟩$ occur at specific frequencies. Red lines denote the swap-and-back condition between $|11⟩$ and $|{\psi }_b⟩$, blue denotes a full swap between $|01⟩$ and $|10⟩$.

Figure 2

Achieving a swap and leakage error rate of below ${10}^{-3}$. (a) The pulse sequence consists of a rounded trapezoid that is applied on both qubit frequency control lines simultaneously to bring them to the interaction frequency. The inset highlights the small overshoot. Hold time is 15.2 ns. Qubits idle detuned by 1 GHz to minimize interactions. (b) During the hold period, swap (blue) and leakage channels (red) are realized. $|01⟩$ and $|10⟩$ are resonant, and $|11⟩$ and $|{\psi }_b⟩$ are near resonance. (c) By tuning the hold duration one can achieve synchronization of minimal swap and leakage error. Data not corrected for measurement visibility.

Figure 3

Mapping synchronization. Swap (blue) and leakage (red) error probabilities as a function of interaction frequency (${\omega }_i$), overshoot frequency (${\mathrm{\Delta }}_i$), and hold times. Color legend is top left. Model results in (a), (c), and (e), and experimental results in (b), (d), and (f). Experimental results are not corrected for measurement error. Bright white areas indicate the parameter values for which the minima of leakage and swap error synchronize.

Figure 4

Gate benchmarking. (a) Swap and leakage error for iswap-like and (b) leakage error for cphase vs ${\mathrm{\Delta }}_i$ and hold time. The white circle denotes parameters used for (c). Color legend from Fig. 3. (c) XEB cycle fidelity vs cycles using 100 random circuits. Inset: The qubits start in the ground state, XEB cycles are applied from the specific circuit, with each cycle comprised of single-qubit gates (red) and a two-qubit gate (green), appended by a final round of single qubit gates and measurement. This is repeated 1200 times for statistics per circuit. (d) Decay of $\sqrt{P}$ (square root of rescaled purity [14]) and accumulation of leakage during XEB. Single-qubit XEB is in the Supplemental Material [14]. We extract Pauli gate errors of $4.3(2)\times {10}^{-3}$ for the iswap-like and $5.8(2)\times {10}^{-3}$ for the cphase gates, with contributions from control and decoherence of $1.8(4)\times {10}^{-3}$ and $4.1(4)\times {10}^{-3}$, respectively.