Mitigating crosstalk errors for simultaneous single-qubit gates on a superconducting quantum processor

Abstract

Single-qubit gates on superconducting quantum processors are typically implemented using microwave pulses applied through dedicated control lines. However, these microwave pulses may also drive other qubits due to crosstalk arising from capacitive coupling and wavefunction overlap in systems with closely spaced transition frequencies. Crosstalk and frequency crowding increase errors during simultaneous single-qubit operations relative to isolated gates, thus forming a major bottleneck for scaling superconducting quantum processors. In this work, we combine model-based qubit frequency optimization with pulse shaping to demonstrate crosstalk error mitigation in single-qubit gates on a 49-qubit superconducting quantum processor. We introduce and experimentally verify an analytical model of simultaneous single-qubit gate error caused by microwave crosstalk that depends on a given pulse shape. By employing a model-based optimization strategy of qubit frequencies, we minimize the crosstalk-induced error across the processor and achieve a mean simultaneous single-qubit gate fidelity of 99.96% for a 16-ns gate duration, approaching the mean individual gate fidelity. To further reduce the simultaneous error and required qubit frequency bandwidth on high-crosstalk qubit pairs, we introduce a crosstalk transition suppression (CTS) pulse shaping technique that minimizes the spectral energy around transitions inducing leakage and crosstalk errors. Finally, we combine CTS with model-based frequency optimization across the device and experimentally show a systematic reduction in the required qubit frequency bandwidth for high-fidelity simultaneous gates, supported by simulations of systems with up to 1000 qubits. By alleviating constraints on qubit frequency bandwidth for parallel single-qubit operations, this work represents an important step for scaling towards larger quantum processors.

Figures (26)

• Figure 1: Device overview and crosstalk statistics.(a) Schematic of the IQM crystal device. Transmon qubits (blue) are connected through tunable couplers (cyan). The gray arrows indicate qubit control lines (beginning of the arrow) which have more than -30dB crosstalk to another qubit (end of the arrows, respectively). The components without a dot in the center are not functional in this device, see \ref{['sec: MW crosstalk and 1qb gate error']}. (b) Partial circuit diagram of a group of qubits indicated in (a) to illustrate the effect of microwave drive crosstalk. A qubit $j$ can be driven through its own control line causing Rabi oscillations with rate $\Omega_{jj}$ (black pulse), while a nearby qubit $k$ oscillates due to crosstalk with a smaller rate $\Omega_{kj}$ (grey pulses). Each qubit is frequency tunable using individual flux lines (Z control, pink) and controllable using drive lines (XY control, brown) - tunable couplers are not shown here. (c) Histogram of the crosstalk elements $\{C_{kj}\}$ of the 49 qubits used in this work.
• Figure 2: The effect of microwave drive crosstalk on single-qubit gate error.(a) Schematic drawing of the relevant energy levels for a pair of transmon qubits, named target qubit T and control qubit C, shown in blue and grey respectively. Transition frequencies to the first ($f_{01}^\mathrm{T}$, $f_{01}^\mathrm{C}$) and from the first to the second excited state ($f_{12}^\mathrm{T}$, $f_{12}^\mathrm{C}$) are indicated for the target and control qubit, respectively. During operation, the target qubit is driven by both its own drive at frequency $f_\mathrm{d}^\mathrm{T}= f_{01}^\mathrm{T}$ and by the control qubit drive at detuned frequency $f_\mathrm{d}^\mathrm{C}=f_{01}^\mathrm{T}-\Delta/(2\pi)$ with an amplitude scaled by the crosstalk. (b) Clifford sequences used for measuring the individual and simultaneous $X_{\pi/2}$ error on the target and control, denoted by $\varepsilon_\mathrm{ind}^\mathrm{T}$, $\varepsilon_\mathrm{sim}^\mathrm{T}$, $\varepsilon_\mathrm{sim}^\mathrm{C}$ respectively, for the data in (c, d). (c) The crosstalk-induced gate error on the target qubit exhibits a double-peaked dependence on the control-target detuning $f_\mathrm{d}^\mathrm{C}-f_{01}^\mathrm{T}$, due to the resonance of $f_\mathrm{d}^\mathrm{C}$ with $f^\mathrm{T}_{01}$ (blue marker) or $f^\mathrm{T}_{12}$ (yellow marker) indicated in (a) for a pair of qubits with $C_\mathrm{TC}=-10dB$. The peak centered at $f^\mathrm{T}_{12}$ is dominated by leakage error (yellow dashed line). Solid lines show the theoretical prediction with no fit parameters. (d) The crosstalk-induced error on the target qubit is proportional to the crosstalk. The experimental data at zero detuning ($\Delta=0)$ and analytical model are displayed as red dots and solid lines, respectively. The effective crosstalk $C_\mathrm{TC,eff}$ is swept experimentally by scaling down the control pulse amplitude $a_\mathrm{C}$ to emulate a lower crosstalk (see inset and the main text). (e) The measured average crosstalk $\overline{C}(r)$ (blue diamonds, see main text) as a function of the qubit-qubit physical distance $r$. Each data point indicates the average crosstalk across target qubits from control qubits in an annulus of radius $r$ and width $dr$ (see inset). The dashed line indicates an exponential fit to the first six data points above the measurement limit (grey shaded region). (f) The worst-case (fully resonant) simultaneous error saturates with distance due to the scaling of crosstalk with the on-chip lateral distance. The measured simultaneous $X_{\pi/2}$ error is shown for each target qubit (transparent red lines), when sweeping the number of included control qubits driven resonantly ($\{f_\mathrm{d}^\mathrm{C}\} = f_{01}^\mathrm{T}$) in simultaneous RB at an increasing distance $r$. Red dots indicate the error averaged over all 49 target qubits $\overline{\varepsilon}_\mathrm{sim}^\mathrm{T}$. Overlayed is the prediction of the resonant theory for the measured $\overline{C}(r)$ from (e), using the same discrete lattice (black solid steps) or an analytical integral assuming a continuous density (grey dashed line).
• Figure 3: Optimization of simultaneous operation of the full device using conventional pulse shapes.(a) Schematic unit cell of four qubits in the device, where the qubits are set in two frequency groups $f_A$ and $f_B$, detuned by $f_A-f_B = |\alpha|/2 \approx 90MHz$, referred to as the reference configuration (called AB). (b) Correlation between the measured and predicted added simultaneous error ($\Delta\varepsilon_\mathrm{sim}=\varepsilon_\mathrm{sim}-\varepsilon_\mathrm{ind}$) across the full chip in the AB configuration shown in (a). The dashed grey line indicates the two values being equal. Values below $10^{-4}$ are not shown as the uncertainty of individual gate error dominates the difference. (c) Schematic of the optimization algorithm (see text). (d) Illustration of the error landscape and qubit frequency update shown in (c). Top row: $\varepsilon_{\mathrm{self}}$, which is the error on this qubit due to the drive pulses of all other qubits (see inset illustration). Middle row: $\varepsilon_{\mathrm{others}}$, which is the error that the drive pulse of this qubit would cause on others if it was updated to have that frequency. Bottom row: the combined $\varepsilon_{\mathrm{total}}$, which is used to determine the updated qubit frequency. (e) Spread of qubit frequencies for the reference (AB) and optimized (CT) configuration. (f) Comparison of the fully simultaneous single-qubit gate fidelity in the AB (red) and CT (dark blue) configuration. Top panel: cumulative density function across the QPU, full lines indicate $\varepsilon_\mathrm{sim}$ while dashed lines indicate $\varepsilon_\mathrm{ind}$. Markers indicate mean values for $\varepsilon_\mathrm{ind}$, $\varepsilon_\mathrm{sim}$ with the same color, and the values for $\varepsilon_\mathrm{sim}$ are written above the panel. Bottom panel: 12-hour interleaved measurement of the average $\varepsilon_\mathrm{sim}$ for both configurations, shaded area indicates the minimum and maximum error for the CT configuration. (g) Comparison of RB traces from the data in (f) for a qubit where the simultaneous fidelity in the reference configuration was severely affected by crosstalk (magenta marker in (b)), while in the CT configuration $\varepsilon_\mathrm{sim}$ is close to $\varepsilon_\mathrm{ind}$. Error bars indicate one standard deviation over different Clifford sequences.
• Figure 4: Crosstalk transition suppression using higher-derivative DRAG and off-resonant drive pulses. (a) In-phase ($s_I^\mathrm{C}$, solid) and quadrature ($s_Q^\mathrm{C}$, dashed) envelopes of resonant 20-ns cosine DRAG (red here and later) and higher-derivative (HD) DRAG pulses (light blue here and later) applied to the control qubit. (b) Comparison of the energy spectral density $S(f)$ for the pulse envelopes in (a). Dashed gray lines correspond to the transition frequencies $f_{01}^\mathrm{T}$, $f_{12}^\mathrm{T}$, and $f_{12}^\mathrm{C}$ suppressed by HD DRAG to mitigate crosstalk and leakage. A simultaneous drive pulse on the target qubit (inset) leads to a Rabi splitting of its $|0\rangle \leftrightarrow |1\rangle$ transition, which effectively broadens the transition frequencies $f_{01}^\mathrm{T}$ and $f_{12}^\mathrm{T}$ (shaded gray regions). (c) Energy spectral density $S(f)$ for the resonant HD DRAG pulse and an off-resonant HD DRAG pulse (dark blue here and later) detuned by $\Delta f_\mathrm{d}^\mathrm{C}=-20MHz$ with respect to the qubit frequency $f_{01}^\mathrm{C}$. The off-resonant pulse reduces the energy spectral density around the nearest harmful transition frequency $f_{01}^\mathrm{T}$ across the frequency range corresponding to the Rabi splitting (shaded gray regions). (d) Simulated trajectory of the state of the control qubit and the target qubit during simultaneous $X_{\pi/2}$ gates for varying off-resonant drive detunings $\Delta f_\mathrm{d}^\mathrm{C}$ of the control qubit (shades of red). A virtual $Z$ rotation can correct phase errors of the control qubit unless the drive detuning is too large (dark red trajectory). (e) Measured excited state probability of the control qubit in a Rabi experiment using a cosine DRAG pulse as a function of normalized pulse amplitude $a_I^\mathrm{C}$ and drive detuning, with the drive detunings of (d) indicated with horizontal solid lines. A 20-ns $X_{\pi/2}$ gate can be implemented along the contour with $P_{|1\rangle}^\mathrm{C} = 0.5$ for drive detunings up to $|\Delta f_\mathrm{d}^\mathrm{C}| \lesssim 30MHz$ (dashed lines). (f) Analytical (lines) and numerically simulated (markers) gate error of a 20-ns $X_\theta$ gate on the target qubit as a function of the target qubit rotation angle $\theta^\mathrm{T}$, with a simultaneous $X_{\pi/2}$ gate applied to the control qubit (inset) using the pulse shapes in (a)-(c). Dashed lines illustrate an approximation of the gate error due to an ac Stark shift of the target qubit induced by the drive pulse of the control qubit in the limit $\theta^\mathrm{T} \rightarrow 0$. In all panels, we assume $f_{01}^\mathrm{C} - f_{01}^\mathrm{T} = -60MHz$ and a crosstalk of $-13.9dB$.
• Figure 5: Experimental demonstration of crosstalk transition suppression (CTS) for a high-crosstalk pair. (a) We compare the error of simultaneous 20-ns $X_{\pi/2}$ gates measured from leakage RB with CTS on or off. For CTS on (blue here and later), we combine off-resonant driving and HD DRAG pulses on the control qubit. For CTS off (dark red here and later), we apply resonant cosine DRAG pulses on both qubits. As a baseline, we measure the individual gate error of the target qubit (light red here and later) using a cosine DRAG pulse. (b) Impact of off-resonant driving on measured simultaneous $X_{\pi/2}$ error of the target qubit $\varepsilon_\mathrm{sim}^\mathrm{T}$ (markers) for the two pulse shapes. Solid lines show the analytical gate error model of Eq. \ref{['eq:mt_eps_av random phase']}. Gray square markers denote the measured simultaneous gate error of the control qubit $\varepsilon_\mathrm{sim}^\mathrm{C}$ using an off-resonant HD DRAG pulse. The inset shows a diagram of the relevant transition frequencies together with the drive detuning $\Delta f_\mathrm{d}^\mathrm{C} = f_\mathrm{d}^\mathrm{C} - f_{01}^\mathrm{C}$ shifting the drive frequency away from the nearest harmful transition $f_{01}^\mathrm{T}$. The black marker on the x axis marks the magnitude of the drive detuning $\Delta f_\mathrm{d, default}^\mathrm{C}$ used by default in (c). (c) Comparison of the experimental $X_{\pi/2}$ error of the target qubit $\varepsilon^\mathrm{T}$ for CTS on and off as a function of qubit-qubit detuning $f_{01}^\mathrm{C}- f_{01}^\mathrm{T}$. We denote analytical models of gate error and leakage as solid and dashed lines, respectively. For a 20-ns $X_{\pi/2}$ gate, the HD DRAG calibration may fail within $\pm30MHz$ of the resonance conditions $f_{01}^\mathrm{C} =f_{01}^\mathrm{T}$ and $f_{01}^\mathrm{C} =f_{12}^\mathrm{T}$ (shaded blue regions). The marker on the x axis denotes the qubit-qubit detuning used in (b). The data in panels (b) and (c) is measured for the highest-crosstalk pair $\mathrm{Q}_5$--$\mathrm{Q}_{11}$ of our device ($C_{5, 11} = -13.9dB$, see \ref{['ap: frequency dependence of crosstalk']}). In panels (b) and (c), the error bars represent 1$\sigma$ uncertainty of the mean based on 3-6 repeated leakage RB experiments.