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High-fidelity, high-scalability two-qubit gate scheme for superconducting qubits
Yuan Xu, Ji Chu, Jiahao Yuan, Jiawei Qiu, Yuxuan Zhou, Libo Zhang, Xinsheng Tan, Yang Yu, Song Liu, Jian Li, Fei Yan, Dapeng Yu
TL;DR
As quantum processors scale, preserving two-qubit gate quality while keeping gates easy to scale remains a challenge. This work demonstrates a fixed-frequency-qubit, tunable-coupler adiabatic CZ scheme, achieving 99.5% fidelity in 30 ns.
Problem
Scalable quantum processing requires high-fidelity two-qubit gates, yet gate performance can deteriorate as more qubits and control lines are integrated.
Source: p. 1Method
The authors experimentally demonstrate an adiabatic CZ scheme using fixed-frequency qubits and a tunable coupler to adjust effective longitudinal coupling.
Source: pp. 1–2Results
99.5% fidelity was achieved for a 30 ns adiabatic CZ gate, with errors limited mostly by decoherence.
Source: p. 1Takeaways & Limitations
The scheme's intrinsic crosstalk robustness and simple calibration are presented as promising for improved scalability in practice.
Source: p. 1
Abstract
from arXiv · showhide
High-quality two-qubit gate operations are crucial for scalable quantum information processing. Often, the gate fidelity is compromised when the system becomes more integrated. Therefore, a low-error-rate, easy-to-scale two-qubit gate scheme is highly desirable. Here, we experimentally demonstrate a new two-qubit gate scheme that exploits fixed-frequency qubits and a tunable coupler in a superconducting quantum circuit. The scheme requires less control lines, reduces crosstalk effect, simplifies calibration procedures, yet produces a controlled-Z gate in 30ns with a high fidelity of 99.5%, derived from the interleaved randomized benchmarking method. Error analysis shows that gate errors are mostly coherence limited. Our demonstration paves the way for large-scale implementation of high-fidelity quantum operations.
I. THE DEVICE · A. Device parameters and experimental setup
The device was fabricated from aluminum on sapphire and operated in a dilution refrigerator at about 10 mK, with standard circuit-QED measurements.
A. Device parameters and experimental setup
- The aluminum-on-sapphire device’s relevant parameters are summarized in Table S1.Source: A. Device parameters and experimental… · p. 8, Table S1 · p. 8
- The device was mounted in a dilution refrigerator at a base temperature of about 10 mK.Source: A. Device parameters and experimental… · p. 8
- Fridge wiring and measurement circuitry are shown in Fig. S1.Source: A. Device parameters and experimental… · p. 8, Figure S1 · p. 8
- The experiments used standard circuit-QED measurements.Source: A. Device parameters and experimental… · p. 8
B. Z crosstalk
Biasing Q1 at its maximum frequency makes it insensitive to flux variation, adding robustness to crosstalk and supporting its treatment as a fixed-frequency qubit.
B. Z crosstalk
- About 8% Q1–coupler Z-line crosstalk was characterized from frequency responses to control lines and compensated; at maximum frequency, Q1 is flux-insensitive.Q1’s flux bias was set to zero throughout the experiment to use it as a fixed-frequency qubit.Source: B. Z crosstalk · p. 9
C. Coupler spectrum
A coupler-state-dependent frequency shift of Q2 enables measurement of the coupler spectrum. Two avoided crossings in the spectrum correspond to coupling between the coupler and the two qubits.
C. Coupler spectrum
- Two avoided crossings in the measured coupler spectrum reveal coupler–qubit coupling strengths g1c and g2c, extracted from their smallest gaps.The coupler is pulse-biased while a microwave drive is applied through Q1’s XY control line; Q2’s state-dependent frequency shift is read out by probing R2 after a selective π-pulse.Source: Figure S2 · p. 9, C. Coupler spectrum · p. 9
- About 10 MHz of spectral width suggests a coupler T2 of a few tens of nanoseconds, but this rough estimate is broadened by the drive.The passage cautions that the spectral width is only a rough indicator of coherence because the drive broadens it.Source: C. Coupler spectrum · p. 9
- A few hundred nanoseconds of qubit coherence could be limited by extra low-frequency noise from the coupler-pulsing AWG, distinct from device-local noise.Separate tests identify control-instrument instability as a factor to distinguish from the device’s local noise.Source: C. Coupler spectrum · p. 9
II. ENHANCED ADIABATICITY
Modulating the tunable coupler enhances adiabaticity relative to the conventional fixed-coupling scheme, with a substantially smaller non-adiabaticity factor during the pulse. Simulations also show that pulse shaping can reduce non-adiabatic error at 30 ns.
II. ENHANCED ADIABATICITY
- The comparison evaluates β, which quantifies unwanted transitions, for tunable-qubit frequency modulation in a fixed-coupling architecture versus tunable-coupler frequency modulation; rapid-gate ramps are typically about 100 MHz/ns.The ramping speed can be varied with different pulse waveforms.Source: §II · p. 10
- The tunable-coupler scheme makes the peak β during the pulse nearly two orders of magnitude smaller than the conventional scheme, enabling faster, lower-leakage adiabatic controlled-phase gates.The comparison identifies a flat β-response region after the coupler is tuned across the higher-frequency Q1, suggesting intrinsic robustness to control-parameter instability and pulse distortion.Source: §II · p. 10, Figure S3 · p. 10
- At τgate = 30 ns, the experimental cosine pulse simulated 0.18% non-adiabatic error, while an alternative pulse like the original fast adiabatic CZ gate reduced it below 0.01%.The authors note this indicates potential as qubits become more coherent and signal distortion is better remedied.Source: §II · p. 11, Figure S4 · p. 11
III. ERROR ANALYSIS · A. Single-qubit gate randomized benchmarking
Simultaneous single-qubit randomized benchmarking measured average gate infidelities of 0.16% for Q1 and 0.10% for Q2.
A. Single-qubit gate randomized benchmarking
- 0.16% for Q1 and 0.10% for Q2 were the average single-qubit gate infidelities in simultaneous randomized benchmarking.Fig. S5 shows sequence-fidelity decay for the reference and interleaved X/2 cases.Source: A. Single-qubit gate randomized… · p. 12, Figure S5 · p. 12
B. Two-qubit gate randomized benchmarking
The section describes conventional and CZ-interleaved two-qubit randomized benchmarking and explains why leakage can produce nonstandard decay offsets in the measured traces.
B. Two-qubit gate randomized benchmarking
- The reference RB applies random two-qubit Clifford sequences followed by a recovery gate, while the interleaved experiment inserts a CZ gate into each Clifford cycle.Results are averaged over 100 random samples.Source: B. Two-qubit gate randomized… · p. 12
- Exponential fits to the reference and interleaved decay curves yield decay constants and error rates per Clifford, from which CZ error and fidelity are extracted.The CZ error is calculated from the ratio of the interleaved and reference decay constants.Source: B. Two-qubit gate randomized… · p. 12
- When leakage and return rates are comparable, two-qubit RB traces have different offsets and do not decay to 0.25, as observed experimentally.The leakage-aware model tracks computational-subspace population as Clifford gates are applied.Source: B. Two-qubit gate randomized… · p. 12
C. Frequency-dependence of coherence times
During the CZ gate, effective coherence times are lower than idling times, with Q1’s dephasing especially shortened by its stronger interaction with the less-coherent coupler.
C. Frequency-dependence of coherence times
- T1 and Tφ were measured across coupler frequencies, and effective gate times were calculated by integrating error rates weighted by the actual half-period cosine pulse shape.The measurements are shown in Fig. S6 and used to generate Fig. 3(b) in the main text.Source: C. Frequency-dependence of coherence… · p. 12, Figure S6 · p. 13
- Effective/idling T1 times were 6.54µ/10.33µs for Q1 and 9.48µs/11.88µs for Q2; effective/idling Tφ times were 0.49µs/8.86µs and 7.21µs/17.63µs, respectively.Both effective T1 and Tφ times were lower than their idling counterparts.Source: C. Frequency-dependence of coherence… · p. 12
- During the CZ pulse, higher-frequency Q1 had T eff φ,Q1 ≈0.5 µs, attributed to stronger interaction with the less-coherent coupler.Source: C. Frequency-dependence of coherence… · p. 12
D. Pulse-induced error
The CZ pulse induces state-dependent transitional errors relative to identity operations, with measured excess beyond T1 attribution interpreted as non-adiabatic error.
D. Pulse-induced error
- Transition rates quantify errors added by the CZ pulse relative to identity, including energy relaxation during the gate and pulse-induced non-adiabatic transitions.The experiment measured all four initial joint eigen-states; for |00⟩, the pulse-induced error was extracted from the difference between fitted slopes, while other states used exponential-decay fits and r = 1−pCZ/pId.Source: D. Pulse-induced error · p. 13
- Per-gate pulse-induced errors were 0.005%, 0.185%, 0.196%, and 0.316% for |00⟩, |01⟩, |10⟩, and |11⟩, respectively.The average difference between these transition rates and the T1 contribution was (0.06 ±0.06)%, identified as non-adiabatic error; repeated CZ pulses may suppress it through interference.Source: D. Pulse-induced error · p. 13