Hamiltonian Engineering with Multicolor Drives for Fast Entangling Gates and Quantum Crosstalk Cancellation

Quantum computers built with superconducting artificial atoms already stretch the limits of their classical counterparts. While the lowest energy states of these artificial atoms serve as the qubit basis, the higher levels are responsible for both a host of attractive gate schemes as well as generating undesired interactions. In particular, when coupling these atoms to generate entanglement, the higher levels cause shifts in the computational levels that lead to unwanted $ZZ$ quantum crosstalk. Here, we present a novel technique to manipulate the energy levels and mitigate this crosstalk with simultaneous off-resonant drives on coupled qubits. This breaks a fundamental deadlock between qubit-qubit coupling and crosstalk. In a fixed-frequency transmon architecture with strong coupling and crosstalk cancellation, additional cross-resonance drives enable a 90 ns CNOT with a gate error of $(0.19\pm 0.02)\%$, while a second set of off-resonant drives enables a novel CZ gate. Furthermore, we show a definitive improvement in circuit performance with crosstalk cancellation over seven qubits, demonstrating the scalability of the technique. This Letter paves the way for superconducting hardware with faster gates and greatly improved multiqubit circuit fidelities.

Figure 1

(a) Modulation of the $ZZ$ interaction strength ${\tilde{\nu }}_{ZZ}$ as the Rabi amplitude of the Stark tones is swept (ratio ${\mathrm{\Omega }}_1/{\mathrm{\Omega }}_0=0.5$) for fixed frequency ${\nu }_d=5.075\mathrm{GHz}$ and phase difference $\varphi =\pi$. The inset shows a circuit representation of the primary two-qubit device discussed in this Letter. (b) The corresponding excursions of the computational levels, calculated numerically, to generate the ${\tilde{\nu }}_{ZZ}$ shown in (a). (c) Modulation of the $ZZ$ interaction strength ${\tilde{\nu }}_{ZZ}$ as the phase difference between the Stark tones is swept, for fixed frequency ${\nu }_d=5.075\mathrm{GHz}$ and and drive amplitudes ${\mathrm{\Omega }}_1=0.5{\mathrm{\Omega }}_0=20\mathrm{MHz}$. Experimental data (black circles) is compared to numerical (blue line) and perturbative (red line) calculations using the device parameters of Table 1 in (a) and (c). (d) The corresponding excursions of the computational levels, calculated numerically, to generate the ${\tilde{\nu }}_{ZZ}$ shown in (c).

Figure 2

(a) Simultaneous randomized benchmarking (RB) of 50 ns single qubit gates in the absence of static $ZZ$ cancellation (blue) leads to an average EPG of $6.6\times {10}^{-3}$. After static $ZZ$ cancellation with a pair of CW Stark tones at ${\nu }_d=5.1\mathrm{GHz}$, the EPG dramatically improves to $7.1\times {10}^{-4}$ (red). Bold symbols represent mean of the individual seeds (represented by light symbols), and dotted lines are exponential fits to the decay of the excited state probability $P_1$. (b) Phase calibration of the CW Stark tones to ${\tilde{\nu }}_{ZZ}\sim 0$. (c) Strength of $ZX$ interaction ${\tilde{\nu }}_{ZX}$ versus cross-resonance drive amplitude ${\mathrm{\Omega }}_{\mathrm{CR}}$ with (red) and without (blue) static $ZZ$ cancellation. Here, Q1 is the control qubit and Q0 is the target qubit. Bold circles represent experimentally measured rates, using Hamiltonian tomography. Dotted lines are perturbative estimates, see Supplemental Material. (d) EPG measured by interleaved RB, for direct CNOT gates constructed from cross-resonance, after $ZZ$ cancellation, as a function of CNOT gate time. The blue dotted line represent the coherence limit to gate error from estimated using standard $T_1$ and $T_2$ measurements before every RB run. (e) Post-$ZZ$ cancellation interleaved RB of a 90 ns direct CNOT gate reveals a best EPG of $1.86\times {10}^{-3}$, with an EPG upper bound of $4.0\times {10}^{-3}$.

Figure 3

(a) Post $ZZ$ cancellation 2D sweep of ${\nu }_{ZZ}$ with pulsed Stark frequency ${\nu }_{\mathrm{gate}}$ and amplitude, with the ratio of the two amplitudes fixed to ${\mathrm{\Omega }}_0={\mathrm{\Omega }}_1$, and phase calibrated to maximum contrast. The CW tones to cancel $ZZ$ use the same parameters discussed in Fig 2, with ${\nu }_d=5.1\mathrm{GHz}$. (b) Interleaved RB of a calibrated CZ gate based on siZZle reveals an EPG of $5\times {10}^{-3}$, with an EPG upper bound of $7.6\times {10}^{-3}$.

Figure 4

(Top) A device schematic of the line of 7 qubits, with a combination of hardware and control approaches to $ZZ$ modulation. The device employs multipath couplers composed of a direct capacitive coupling and a $\lambda /4$ bus resonator. (Bottom) Average heavy output probability (HOP) for the same set of 200 random quantum volume (QV) circuits, at different levels of ${\tilde{\nu }}_{ZZ}$. We observe an improvement in HOP from $0.5810\pm 0.0027$ to $0.5996\pm 0.0023$ as the average ${\tilde{\nu }}_{ZZ}$ is tuned from the bare value $\sim 40\mathrm{kHz}$ to $\sim 0\mathrm{kHz}$. Error bars represent standard error of the mean. The maximum and minimum ${\tilde{\nu }}_{ZZ}$ data points are tuned by setting the pairwise phase difference between the siZZle tones to $\varphi \sim 0$ and $\varphi \sim \pi$, respectively. The middle data point is measured in the absence of siZZle. (Inset) Scatter of individual circuit HOPs for the native (bare) device versus post-$ZZ$ cancellation.