Compromise-free scaling of qubit speed and coherence

Abstract

Across leading qubit platforms, a common trade-off persists: increasing coherence comes at the cost of operational speed, reflecting the notion that protecting a qubit from its noisy surroundings also limits control over it. This speed-coherence dilemma limits qubit performance across various technologies. Here, we demonstrate a hole spin qubit in a Ge/Si core/shell nanowire that triples its Rabi frequency while simultaneously quadrupling its Hahn-echo coherence time, boosting the Q-factor by over an order of magnitude. This is enabled by the direct Rashba spin-orbit interaction, emerging from heavy-hole-light-hole mixing through strong confinement in two dimensions. Tuning a gate voltage causes this interaction to peak, providing maximum drive speed and a point where the qubit is optimally protected from charge noise, allowing speed and coherence to scale together. Our proof-of-concept shows that careful dot design can overcome a long-standing limitation, offering a new approach towards building high-performance, fault-tolerant qubits.

Fig. 1. Measurement of a NW hole spin qubit at 1.5 K.

a False-color scanning electron micrograph of a representative NW-device. The Ge/Si NW is highlighted in yellow, lying on top of nine bottom gates, and is further connected to source and drain contacts from above, marked S and D. The first five bottom gates from the left were used to form a DQD, whose expected location is indicated by the yellow and pink ovals. The color code is consistently used throughout the manuscript. The scale bar corresponds to 100 nm. b Schematic of PSB. In the absence of a magnetic field and for detunings ε < ε_ST, charge transport is blocked when the system is initialized in a triplet state T(1, 1). c Measurement of bias triangles with lifted spin-blockade at B = 350 mT (x-direction) and bias of V_SD = +5 mV. The pink star marks the qubit initialization/readout spot, and the pink circle indicates the manipulation point. Inset: Same bias triangle at B = 0 mT, manifesting PSB via the suppressed current at the baseline. d Schematic of the pulse scheme applied to V_RP, consisting of the readout/initialization stage (R/I) and the manipulation stage, for which a MW burst is applied while in Coulomb blockade. e Measurement of the current as a function of f_MW and B showing characteristic EDSR at a fixed microwave burst duration. f Current as a function of microwave burst duration and magnetic field B at f_L = 2.79 GHz, showing Rabi-oscillations with a frequency f_Rabi = 130 MHz and coherence time $T_2^{\mathrm{Rabi}}=40$ ns.

Fig. 2. SOI mediated g-factor renormalization of an elongated dot.

a–c Experimental data of the qubit g-factor (solid black discs), the corresponding Rabi frequency f_Rabi (empty discs) and the estimated gtm-EDSR contribution $f_{\mathrm{Rabi}}^{\mathrm{gtm}}$ (white bars), as a function of the barrier gate voltages V_L, V_M and V_R, respectively. For each of the datasets (a–c), the values on the other two barrier gates are fixed at the value marked by the vertical dashed line. The yellow colored regions highlight the voltage ranges for which the qubit driving mechanism is dominantly iso-EDSR, whereas the brown regions show the ranges for which the contribution to the measured f_Rabi originating from gtm-EDSR, $f_{\mathrm{Rabi}}^{\mathrm{gtm}}$, is ≥15% (5% above the spread of data points, see Supplementary Information). These colors are used consistently in all other panels. The estimated $f_{\mathrm{Rabi}}^{\mathrm{gtm}}$ is represented by the white bar charts. d Schematic visualization of how the Zeeman vector ${\widehat{\mathbf{g}}}_0\cdot \mathbf{B}$ is affected when subject to an infinitesimal voltage change dV in the presence of SOI represented by ${\alpha }_{\mathrm{SO}}^{\perp }$ and a fixed magnetic field ∣B∣. Left shows pure iso-EDSR coming from displacements of the dot potential. Right shows the additional appearance of gtm-EDSR, when the dot is displaced and deformed. e Shows the extracted ∂g/∂V_RP, as a function of the voltage V_L in blue, and f as a function of V_M in red. These derivatives are used to calculate an upper bound of the g-modulated contribution to f_Rabi. g Values of the g-factor plotted versus their according f_Rabi from panels a (blue) and b (red). We exclusively show the data points for which iso-EDSR is the dominant driving mechanism (yellow regions), i.e., the gtm-EDSR contribution is ≤15% of the measured f_Rabi. We fit the data using Eq. (1), which assumes iso-EDSR (fit shown by black line with yellow highlight symbolizing iso-EDSR), yielding an intrinsic NW g-factor of g_NW ≈ 1.

Fig. 3. Compromise-free operation.

a Top: Experimental data of f_Rabi and g as a function of V_L. Bottom: Dark blue circles show coherence times $T_2^{\mathrm{Hahn}}$ obtained from fits of the time-dependent readout current measured in Hahn-echo experiments at different voltages V_L. Light blue circles show modeled coherence times taking into account $g_i^{\prime }\left(V_{\mathrm{L}}\right)$ from panels b–f using Eq. (2), yielding $S_{\mathrm{G}}=29\mathrm{nV}/\sqrt{\mathrm{Hz}}$. Vertical dashed line at V_L = 1330 mV shows sweet spot, where $T_2^{\mathrm{Hahn}}$ is maximal. This spot coincides with fastest f_Rabi within experimental errors. Error bars correspond to standard deviations that result from fitting. Inset: Pairs of f_Rabi and $T_2^{\mathrm{Hahn}}$ from V_L = 1330–1360 mV in 10 mV steps. b–f Show $g_i^{\prime }\left(V_{\mathrm{L}}\right):=\partial g/\partial V_{\mathrm{i}}\left(V_{\mathrm{L}}\right)$, as a function of different static voltages on gate V_L. Dark blue data represent values of V_L for which $g_i^{\prime }\left(V_{\mathrm{L}}\right)$ were measured. Light blue line represents linearly interpolated data needed to match the number of measured data points between $g_i^{\prime }\left(V_{\mathrm{L}}\right)$ and $T_2^{\mathrm{Hahn}}$, which was fitted in (a). Vertical dashed line marks the sweet spot at V_L = 1330 mV where all five $g_i^{\prime }\left(V_{\mathrm{L}}\right)$ reach near zero, defining the sweet spot. Horizontal dashed line marks the zero-line of the $g_i^{\prime }\left(V_{\mathrm{L}}\right)$. g The FACTOR: 2D voltage space showing $T_2^{\mathrm{Hahn}}$ as function of V_M and V_L. Filled circles represent measured coherence times $T_2^{\mathrm{Hahn}}$ extracted analogously to panel a. Data trace corresponding to the dark blue trace on panel a is referenced by the blue arrow on the 2D plot. An additional trace of $T_2^{\mathrm{Hahn}}$ as a function of V_L for fixed V_M = 630 mV is indicated by the vertical dark blue dashed line to the left end of the plot, as well as a trace of $T_2^{\mathrm{Hahn}}$ as a function of V_M for fixed V_L = 1320 mV which is indicated by the horizontal red dashed. Background is obtained by a Gaussian process interpolation serving as a guide to the eye. Black contours show a Gaussian process interpolation of measured Rabi frequencies, highlighting the overlap of maxima in $T_2^{\mathrm{Hahn}}$ and f_Rabi.