Ultrafast Single Qubit Gates through Multi-Photon Transition Removal

TL;DR

This work targets leakage in ultrafast single-qubit gates caused by multilevel structures in superconducting qubits. It introduces the R2D pulse shaping method, a double-recursive Derivative Removal by Adiabatic Gate that suppresses multi-photon transitions, and accompanies it with the amplified leakage error (ALE) technique to quantify leakage down to $\sim 10^{-6}$. Experiments on a transmon qubit demonstrate total leakage $<2.0\times 10^{-5}$ and gate fidelities $>99.98\%$ for X and X/2 gates at $t_p=6.8$ ns, with the dominant remaining errors arising from higher-order transitions and decoherence; normalized driven strength reaches $\Omega/\Delta=0.33$, a record for single-qubit control. The approach is benchmarked via RB, LRB, and PRB, and the methods generalize to other qubit modalities and potentially to fast two-qubit gates, enabling ultrafast, high-fidelity quantum operations.

Abstract

One of the main enablers in quantum computing is having qubit control that is precise and fast. However, qubits typically have multilevel structures making them prone to unwanted transitions from fast gates. This leakage out of the computational subspace is especially detrimental to algorithms as it has been observed to cause long-lived errors, such as in quantum error correction. This forces a choice between either achieving fast gates or having low leakage. Previous works focus on suppressing leakage by mitigating the first to second excited state transition, overlooking multi-photon transitions, and achieving faster gates with further reductions in leakage has remained elusive. Here, we demonstrate single qubit gates with a total leakage error consistently below $2.0\times10^{-5}$, and obtain fidelities above $99.98\%$ for pulse durations down to 6.8 ns for both $X$ and $X/2$ gates. This is achieved by removing direct transitions beyond nearest-neighbor levels using a double recursive implementation of the Derivative Removal by Adiabatic Gate (DRAG) method, which we name the R2D method. Moreover, we find that at such short gate durations and strong driving strengths the main error source is from these higher order transitions. This is all shown in the widely-used superconducting transmon qubit, which has a weakly anharmonic level structure and suffers from higher order transitions significantly. We also introduce an approach for amplifying leakage error that can precisely quantify leakage rates below $10^{-6}$. The presented approach can be readily applied to other qubit types as well.

Figures (14)

• Figure 1: Schematic of qubit level structures and pulse shapes for fast gates. (a) Schematic representation of qubit energy levels in the qubit eigenbasis (left) and in the dressed eigenbasis under Schrieffer-Wolff transformation (right). The colored arrows show the unwanted leakage transitions. (b) An example R2D pulse for $t_p=7$ ns. The magnitude spectrum of both $\Omega = \Omega_R+i\Omega_I$ (gray) and $\Omega_R^2$ (blue) are plotted. The solid lines highlight the unwanted transition frequencies to $|2\rangle$ (red) and $|3\rangle$ (purple). The inset shows the normalized time domain pulse for both $\Omega$ and $\Omega_R^2$, and the dashed line shows $\Omega_I$. (c) The same magnitude spectrum of $\Omega$ and $\Omega_R^2$ as in (b), highlighting the frequencies of the unwanted single- and multi-photon transitions.
• Figure 2: Amplified leakage error experiments. (a) The schematic of the ALE pulse sequence. We repeatedly apply $N$ times a $X$ operation followed by a VZ with angle $\theta$. The sequence ends with measurements of the leakage population. (b) The $|2\rangle$ leakage population as a function of $\theta$ and $N$. The line plot on top shows the maximum leakage population for each $\theta$. (c) Same as (b) but plotted with $|3\rangle$ leakage population. (d)(e) The same data as in (b)(c) but with a magnified window around one of the amplification phases (dashed lines). The clear chevron pattern indicates a coherent oscillation of the leakage population.
• Figure 3: Extracting leakage error from leakage randomized benchmarking and amplified leakage error. (a)(b)(c) Leakage error rates of an X gate at $t_p=7$ ns extracted from LRB (circle) and ALE (square) for leakage state $|2\rangle$ (red) and $|3\rangle$ (purple) as a function of parameter $\alpha_{12}$ (a), $\alpha_{02}$ (b), and $\alpha_{13}$ (c). The optimal parameter set $(\alpha_{12}^{opt},\alpha_{02}^{opt},\alpha_{13}^{opt})$ is obtained through an in-situ optimization. The raw traces of the marked data points in (c) are shown. (d) Raw traces used to extract leakage errors marked in (c) for both states using LRB. Only the interleaved curves are shown. Solid lines are fit curves. (e)(f) Raw traces used to extract leakage errors marked in (c) for $|2\rangle$ (e) and $|3\rangle$ (f) using ALE. Solid lines are fit curves.
• Figure 4: Gate benchmarks with varying pulse lengths. Gate performance with pulse durations $t_p\in [6.6,9]$ ns. X gate is on the left, and X/2 gate is on the right. (a)(b) Error rates extracted from RB (green), PRB (black), LRB for $|2\rangle$ (red), and LRB for $|3\rangle$ (purple). Solid lines are simulation results. (c)(d) Different contributions to total gate error, including decoherence error (dark magenta), leakage error (blue), and coherent control error (orange). (e)(f) Parameter sets of optimal gates from in-situ calibrations (symbols) and simulations (dashed lines).
• Figure S1: Raw IQ points from the single shot experiment where qubit is prepared in the $|0\rangle$ (blue), $|1\rangle$ (orange), $|2\rangle$ (green), and $|3\rangle$ (red) states. We show 5000 out of $2^{17}$ preparations for each state. The black points are the fitted state centers, the circles have the radii corresponding to two (solid line) and three (dashed line) standard deviations of the data.