Fast logic with slow qubits: microwave-activated controlled-Z gate on low-frequency fluxoniums

Abstract

We demonstrate a controlled-Z gate between capacitively coupled fluxonium qubits with transition frequencies 72.3 MHz and 136.3 MHz. The gate is activated by a 61.6 ns long pulse at the frequency between non-computational transitions |10 −|20 and |11 −|21 , during which the qubits complete only 4 and 8 Larmor periods, respectively. The measured gate error of (8 ± 1) × 10 −3 is limited by decoherence in the non-computational subspace, which will likely improve in the next generation devices. Although our qubits are about fifty times slower than transmons, the two-qubit gate is faster than microwave-activated gates on transmons, and the gate error is on par with the lowest reported. Architectural advantages of low-frequency fluxoniums include long qubit coherence time, weak hybridization in the computational subspace, suppressed residual ZZ-coupling rate (here 46 kHz), and absence of either excessive parameter matching or complex pulse shaping requirements.

Arbitrary controlled-phase gate on fluxonium qubits using differential ac-Stark shifts

“…Most importantly, while certain circuit parameter combinations would further mitigate the errors, the CP gate requires no special parameter combinations and hence would be tolerant to fabrication variability. For example, the qubit frequency could be as low as 100 MHz, as in our earlier demonstration of the CZ-gate [27], but it can also be around 200 − 500 MHz (main device here) or even 700 − 1.3 GHz (second device here).…”

“…1a) and the measurement setup are similar to those previously reported in Ref. [27]. We conventionally label the coupled energy eigenstates as |kl , where the k and l indices are the uncoupled eigenstates of qubits A and B, respectively.…”

“…Using procedures similar to those described in Ref. [27], we optimized the gate pulses and obtained a CZ gate fidelity of 0.989 ± 0.001 at f d = 4.545 GHz and 0.991 ± 0.001 at f d = 6.665 GHz. Next, we characterize the CP gate at φ = π using the cross-entropy (XEB) benchmarking technique, which is applicable to non-Clifford operations, and also evades the SPAM errors [5,12,29].…”

“…We use the same readout and initialization procedures described in Ref. [27]. The device is embedded into a rectangular copper cavity resonator with a resonance frequency f C = 7.538 GHz and linewidth κ/2π = 5 MHz, thermally anchored to the base plate of a dilution refrigerator at 14 mK.…”

“…We consider fluxoniums that are coupled by a fixed capacitance, which is compatible with transmon-based processors, and biased at the half-integer flux quantum, practically eliminating the flux-noise decoherence channel. Previously, we have demonstrated a controlled-Z (CZ) gate in such a system by applying a near-resonant drive to the transition between first and second excited states of one of the qubits [27]. In that experiment, the ZZterm was naturally suppressed by the special choice of relatively low qubit frequencies (about 100 MHz).…”