Demonstration of a parametrically activated entangling gate protected from flux noise

In state-of-the-art quantum computing platforms, including superconducting qubits and trapped ions, imperfections in the two-qubit entangling gates are the dominant contributions of error to systemwide performance. Recently, a novel two-qubit parametric gate was proposed and demonstrated with superconducting transmon qubits. This gate is activated through rf modulation of the transmon frequency and can be operated at an amplitude where the performance is first-order insensitive to flux noise. In this work we experimentally validate the existence of this ac sweet spot and demonstrate its dependence on white-noise power from room-temperature electronics. With these factors in place, we observe entangling-gate fidelity with coherence-limited performance. An ensemble of repeated observations has a median fidelity of 98.8%, with roughly 10% of observations above 99%.

Figure 1

Device diagram. (a) Circuit diagram of the device under test. Our planar architecture features four frequency tunable transmons (orange) with a fixed capacitive coupling to four fixed frequency transmons (blue), each capacitively coupled to its own quarter-wavelength coplanar waveguide resonator (red) for readout. Single qubit control is implemented by driving microwave pulses through each qubit's resonator. Frequency tunable transmons each have their own inductively coupled flux bias line. All control lines (dotted lines) are in the same plane as circuit elements and external control is brought in from contact pads (purple for rf, orange for flux) at the edge of the chip, where individual wirebonds connect to a copper PCB. The two qubits used in this experiment (Q6, Q7) are denoted by the dashed red square. Coherence times and CZ fidelities of qubits and edges in the four-qubit subsystem defined by the neighbors of the tunable qubit are presented in Table 1. The coupling geometry and Hamiltonian of the chip represent a subcomponent (dashed green) of the tileable lattice design shown in (b). (c) A photograph of the fabricated device.

Figure 2

Coherence under modulation. We compare the coherence properties when modulating the flux with two different instruments: a National Instruments USRP (in blue) and a custom built flux delivery module (in orange). We present (a) the average power spectral density of each instrument measured with a pulsed output signal representative of typical gate parameters. We measure (b) the difference between the qubit's parking frequency and the time-averaged frequency under modulation as a function of the applied amplitude as well as (c),(d) the coherence properties of the qubit under modulation. In both the $T_1$ and $T_2^{*}$ experiments in (c) and (d), we replace the free evolution time of the experiment with a time-varying modulated flux pulse at a fixed frequency. We do not expect a $T_1$ dependence from this modulation, but we use the measured relaxation to calculate the pure dephasing time $T_{\varphi }$. We report all modulation amplitudes in units of the flux quantum by finding the linear scaling factor consistent with a minimum $\delta {\omega }_T$ at a modulation amplitude of $0.6{\mathrm{\Phi }}_0$.

Figure 3

Parametric gate calibration. (a) Excited-state population of the fixed qubit, Q7, when preparing the $|11\rangle$ (fixed-tunable) state and driving the $|11\rangle \leftrightarrow |02\rangle$ transition near the ac sweet spot. This results in a characteristic “chevron” pattern as we vary the frequency and duration of the flux pulse. To calibrate the gate, we fit slices of fixed pulse frequency and varying duration, like those shown in (b), to find the pulse duration that most closely returns the system to the $|11\rangle$ state.

Figure 4

Repeated benchmarking. (a) We estimate the empirical cumulative distribution function (ECDF) from repeated observations of gate infidelity as measured by interleaved randomized benchmarking over a period of 8 h (90% confidence region for the ECDF shown). We report a gate fidelity $>99\%$ for $\sim 10\%$ of the recorded fidelities, with the highest recorded fidelity at $99.2\pm 0.15\%$ over this period shown in (b). For these RB sequences, we extract decay rates of $p_{\mathrm{ref}}=0.960\pm 0.086$ and $p_{\mathrm{int}}=0.950\pm 0.091$, from which we can estimate the mean (across all $11520$ different two-qubit Clifford group operations [31]) average gate infidelity to be $\approx 97\%$.

Figure 5

Overview of the experimental setup. This diagram details the control electronics, wiring, and filtering for the two qubits involved in the experiment (Q6 and Q7). The single qubit control pulses and readout pulses for one qubit are generated separately on two daughter cards of one USRP software defined radio. These signals are combined at room temperature and sent down one line in the dilution refrigerator (yellow). The readout signal (blue) is first amplified by a high electron mobility transistor (HEMT), followed by two room temperature amplifiers, before being received by the USRP receive port. Both dc and ac signals for flux delivery (green) are generated by custom Rigetti AWGs. All control lines go through various stages of attenuation and filtering in the dilution refrigerator.

Figure 6

Gate set tomography. The reconstructed CZ Pauli transfer matrix.

Figure 7

Time series for iRB infidelity for CZ. Error bars correspond to 90% confidence intervals, and gray (empty) data points correspond to iRB experiments that were excluded due to failing the stability hypothesis test (i.e., decay rates were not stable for the duration of the experiments). The time span for the measurement corresponds to 8 h.