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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
Fast, low-leakage controlled-phase gates require adiabaticity despite rapid coupler-frequency ramps. The paper analyzes the effective coupling and non-adiabaticity of tunable-coupler pulses, finding reduced non-adiabaticity and simulated 30 ns operation with errors below 0.01% for an alternative pulse shape.
Problem
Rapid controlled-phase gates must balance gate speed against non-adiabatic leakage.
Method
The study calculates effective ZZ coupling and a non-adiabaticity factor versus coupler frequency for different pulse schemes.
Results
30 ns gate time yields a simulated non-adiabatic error rate of 0.18% with the experimental cosine pulse and below 0.01% with an alternative pulse shape.
Takeaways & Limitations
A tunable coupler can provide a flatter non-adiabaticity response and support faster, lower-leakage adiabatic controlled-phase gates.
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.
Supplementary Material for “High-fidelity, high-scalability two-qubit gate scheme for superconducting qubits”
The supplementary material identifies the authors and their institutional affiliations.
- The paper lists Yuan Xu and coauthors, including Ji Chu, Jiahao Yuan, Jiawei Qiu, and others.
- The authors are affiliated with the Southern University of Science and Technology and its quantum-science laboratories in Shenzhen, China.
A. Device parameters and experimental setup
The experiment uses a fabricated superconducting circuit operated in a dilution refrigerator, with device parameters summarized separately and wiring documented schematically.
- The device is fabricated with aluminum on a sapphire substrate and operated at a base temperature of about 10 mK.
- Fridge wiring and measurement circuitry are shown in Fig. S1.
- Table S1 summarizes the device parameters.
B. Z crosstalk
The experiment compensates Z-control-line crosstalk while operating Q1 as an effectively fixed-frequency qubit.
- Q1 is held at zero flux bias throughout the experiment to operate it as a fixed-frequency qubit.
- Z-control-line crosstalk between Q1 and the coupler is characterized and compensated, with coefficients of about 8%.
- At maximum frequency, Q1 becomes insensitive to flux variation, adding robustness to residual control-line crosstalk.
C. Coupler spectrum
The coupler spectrum is measured through Q2’s coupler-state-dependent frequency shift, while the coupler’s spectral width provides only a rough coherence estimate.
- Q2’s coupler-state-dependent frequency shift enables measurement of the coupler spectrum.
- The two avoided crossings reveal the qubit–coupler couplings, whose strengths are extracted from their gaps.
- The measured spectrum uses a pulse-biased coupler driven through Q1’s XY control line, with transitions appearing at resonant drive frequencies.
- A spectral width of about 10 MHz corresponds to a rough coupler T2 estimate of a few tens of nanoseconds.
II. ENHANCED ADIABATICITY
The tunable-coupler scheme enhances adiabaticity by reducing non-adiabatic transitions during rapid controlled-phase gates. Simulations indicate that optimized pulse shaping can further suppress these errors at 30 ns.
- Enhanced adiabaticity: The adiabaticity analysis compares tunable-qubit and tunable-coupler protocols by summing unwanted population transfers across possible states.βnm quantifies unwanted transitions, while the coupler frequency ramp rate depends on the pulse waveform.
- Enhanced adiabaticity: β f is nearly two-orders-of-magnitude smaller with a tunable coupler than in the conventional tunable-qubit scheme in the relevant interaction region.The comparison uses simulated ZZ coupling and β f versus frequency detuning.
- Enhanced adiabaticity: The tunable-coupler scheme’s strongest β during the pulse is nearly two-orders-of-magnitude smaller than in the conventional scheme, enabling faster, lower-leakage adiabatic controlled-phase gates.The analysis also identifies a flat response region in the coupler-based scheme.
- Enhanced adiabaticity: 0.18% non-adiabatic error is obtained in simulation for the experimental cosine pulse at τgate = 30 ns.An alternative optimized pulse shape reduces simulated non-adiabatic errors below 0.01% at the same gate time.
- Enhanced adiabaticity: Below 0.01% non-adiabatic error is simulated at 30 ns using an alternative optimized pulse shape.The simulation includes a 400 MHz Gaussian filter reshaping the pulse; the reported dip near 30 ns for the Slepian case is unexplained.
A. Single-qubit gate randomized benchmarking
Simultaneous single-qubit randomized benchmarking measures the performance of gates on both qubits. The reported average infidelities are below the two-qubit gate error scale.
- A. Single-qubit gate randomized benchmarking: 0.16% average single-qubit gate infidelity is measured for Q1 in simultaneous randomized benchmarking.The experiment uses standard single-qubit randomized benchmarking on both qubits simultaneously.
- A. Single-qubit gate randomized benchmarking: 0.10% average single-qubit gate infidelity is measured for Q2 in simultaneous randomized benchmarking.The results are presented as sequence-fidelity decays for the reference and interleaved X/2 cases.
- A. Single-qubit gate randomized benchmarking: The experiment applies standard randomized benchmarking to both qubits simultaneously.The plotted quantity is sequence fidelity versus the number of Clifford gates.
B. Two-qubit gate randomized benchmarking
Two-qubit Clifford randomized benchmarking compares reference sequences with sequences interleaved by the calibrated CZ gate. A leakage-aware model is required because leakage changes the decay offsets.
- B. Two-qubit gate randomized benchmarking: The reference experiment applies random two-qubit Clifford sequences followed by a recovery gate, while the interleaved experiment inserts one CZ per Clifford cycle.The results are averaged over 100 random samples.
- B. Two-qubit gate randomized benchmarking: The CZ gate error is extracted as rCZ = 3/4(1−pint/pref), and the CZ fidelity as FCZ = 1−rCZ.The decay constants are obtained by fitting F = Ap^m+B to reference and interleaved traces.
- B. Two-qubit gate randomized benchmarking: When leakage is comparable to depolarized errors, the randomized-benchmarking analysis uses a model with leakage and return rates.The computational-subspace population follows ΔPs/Δm = −rleakagePs + rreturn(1−Ps).
- B. Two-qubit gate randomized benchmarking: Two-qubit randomized-benchmarking traces do not decay to 0.25 and have different offsets when leakage and return rates are comparable.This behavior is clearly observed in the experimental data.
C. Frequency-dependence of coherence times
Coherence times vary strongly with coupler frequency and are reduced during the CZ pulse relative to idling. The higher-frequency qubit Q1 experiences particularly strong pulse-induced dephasing.
- C. Frequency-dependence of coherence times: Effective/idling Tφ times are 0.49µs/8.86µs for Q1 and 7.21µs/17.63µs for Q2.Effective times integrate relaxation and dephasing error rates over coupler frequencies weighted by the pulse shape.
- C. Frequency-dependence of coherence times: Effective T1 and Tφ are lower during the CZ gate than during idling.The coherence measurements are taken as functions of coupler frequency and used to generate the gate error analysis.
- C. Frequency-dependence of coherence times: Tφ,Q1 ≈ 0.5 µs, reflecting drastically faster dephasing for the higher-frequency qubit during the CZ pulse.The passage attributes this to stronger interaction with the less coherent coupler.
- C. Frequency-dependence of coherence times: Figure S6 plots energy-relaxation and Gaussian-pure-dephasing times versus coupler frequency, marking the frequency corresponding to maximum pulse amplitude.The figure relates coherence behavior to the gate pulse trajectory.
D. Pulse-induced error
The analysis separates CZ-pulse-induced transitional errors from energy-relaxation contributions and estimates the remaining non-adiabatic component. Measured errors per joint state range from 0.005% to 0.316%.
- The |00⟩ response should remain flat because the adiabatic CZ gate has almost no effect on that state.A slight measured rise may reflect conversion of residual excited-state populations to the ground state.
- The error rate is extracted as r = 1−pCZ/pId by comparing CZ-pulse and identity-operation population decay.
- 0.005%, 0.185%, 0.196%, and 0.316% are the extracted CZ-pulse-induced errors per gate for the four joint states.These transitional errors include additional energy relaxation during the gate and unwanted transitions from non-adiabatic effects.
- The average difference between transitional error rates and T1 contributions is (0.06 ±0.06)%, attributed to non-adiabatic errors.This value is below simulation results, possibly because repeated CZ pulses interfere and suppress non-adiabatic errors.