Parametric two-qubit gates via Landau-Zener interference

AI summary

Overview

Research area: Superconducting quantum computing — specifically two-qubit gate implementations in circuit quantum electrodynamics using flux-tunable couplers.

Technical level: Intermediate (the core idea is accessible with basic quantum mechanics; the adiabatic impulse / transfer-matrix formalism and the appendices are Advanced).

Scope: The paper proposes, models, and experimentally demonstrates a two-qubit gate between superconducting qubits based on interference of consecutive Landau–Zener transitions in a flux-tunable coupler, validated on two distinct hardware platforms.

What This Paper Is About

Two-qubit gates in superconducting processors usually rely on dispersive couplers, which restrict gate speed to well below the vacuum Rabi rate and confine parametric modulation to a narrow transition-frequency window set by the qubit–coupler level structure. The authors instead operate beyond the dispersive regime: they couple two data qubits with equal strength to a flux-tunable coupler qubit and periodically modulate the coupler so that it repeatedly crosses the qubit frequencies, producing Landau–Zener interference. By tuning coupler detuning, drive amplitude, and drive frequency to a constructive-interference condition, they obtain a gate that can be activated at arbitrary drive frequencies while using the full coupling strength.

Key Contributions

1. A non-dispersive two-qubit gate mechanism based on quantum interference of consecutive Landau–Zener transitions in a flux-tunable coupler, described analytically with the adiabatic impulse (transfer-matrix) model and interpreted through a Mach-Zehnder interferometer analogy (beam splitters, path lengths, reflectivity).
2. Continuous in situ frequency tunability of the gate drive: because a corresponding pair of drive amplitude and coupler detuning satisfies the LZ resonance condition for any drive frequency, the gate can be played from baseband up to hundreds of MHz, enabling frequency multiplexing of control pulses.
3. Gate speed on the order of the full coupling strength, in contrast to dispersive schemes, with the simulated population-swap frequency starting at a maximum of √2 g and decaying algebraically as ∝ n^(−1/3) rather than exponentially.
4. Experimental demonstration on two platforms — a modular chiplet architecture of coupled generalized flux qubits and a monolithic transmon architecture — yielding an average population swap fidelity F ≈ 0.98 on the monolithic device, limited by decoherence.

Main Findings

• Gate structure: When the coupler returns to its initial state at t_swap = 1/(2Ω), the evolution acts as a two-qubit gate on the data-qubit subspace. The two forms, G₀ (coupler initially in |0⟩) and G₁ (coupler initially in |1⟩), are both locally equivalent, within single-qubit π/2 rotations, to iSWAP, a maximally entangling gate.
• Constructive interference condition: For sinusoidal modulation the condition reduces to n = ε₀/ω_d, interpretable as energy conservation for n drive photons matching the coupler–qubit detuning ε₀. Over m cycles, φ₊ = (φ₁+φ₂)/2 controls whether successive transition pairs interfere constructively, while φ₋ = (φ₂−φ₁)/2 sets the swap frequency.
• Data qubits stay at sweet spots: Only the coupler is modulated; no flux pulse is applied to the data qubits, since the effective driven two-level system is the nonlocal bright state plus the coupler, not a physical qubit.
• Modular platform results: With data qubits at ω_q/2π = 3.391 GHz and coupler detuned by ω₀/2π = −359 MHz, a 300 ns sinusoidal pulse produced interferometric population-transfer patterns matching the Mach-Zehnder model. Swapping appeared for ε_d ≥ ε₀ ≈ 2π × 0.36 GHz, and the coupler loaded only to P_c = 0.5 because it fills and empties symmetrically.
• Time-domain oscillations: At a resonance of ω_d = 2π × 50 MHz with ε_d ∈ 2π × [380, 440] MHz, coherent oscillations from qubit 1 to qubit 2 via the coupler were observed, with t_p ≈ 250 ns marking implementation of G₀.
• Coupling comparison: The modular architecture has g/2π ≈ 3 MHz, while the monolithic flux-tunable transmon device has g/2π ≈ 300 MHz, speeding up the gate by an order of magnitude.
• Arbitrary drive frequency calibration: On the monolithic device (qubits at ω_q/2π = 5.891 GHz), population swaps were calibrated across 10 MHz < ω_d/2π < 350 MHz. A gate can be calibrated for any drive frequency up to ω_d/2π < 350 MHz when at least m = 2 LZ cycles are completed; at lower frequencies m = 1 suffices.
• Drive-amplitude behavior: At ω_d = 2π × 28 MHz, the swap oscillation frequency increased with drive amplitude until A_d ≈ 1.1 V, where it went to zero due to coherent destruction of tunneling; below A_d ≈ 1 V the coupler does not reach the data-qubit resonance, and three characteristic lobes appear versus A_d.
• Benchmarking: Exponential fits of P_q2 − P_q1 = aF^{N_g} + c for m = 1 and m = 8, including a 16 ns wait between gate pulses, gave F ≈ 0.98, consistent with the measured T₂^echo = 2.2 μs (effective decoherence time quoted as T₂^eff = 2 ± 0.5 μs).
• Projected performance: Assuming qubits and couplers with two orders of magnitude larger coherence, and accounting for asymmetries, decoherence and leakage, the authors expect the LZ-interferometric gate to reach 99.9 % population swap fidelity.
• Coupler as a resource: Because the gate is non-dispersive, coupler state preparation or measurement matters; running the gate for t_swap/2 can deterministically or postselectively generate Bell states, and restricting to G₀ requires only a "cold" coupler, obtainable by means other than quantum measurement.

Methodology in Plain English

The device is a chain of three superconducting qubits coupled nearest-neighbour with equal strength: two outer data qubits tuned to the same frequency, and a central coupler whose frequency can be rapidly shifted by a flux line. The coupler is swept periodically back and forth through the data-qubit frequency. Each passage through the avoided crossing is a Landau–Zener transition, which behaves like a beam splitter for the quantum state: part of the amplitude transmits, part reflects, with a probability set by how fast the crossing is traversed. Between crossings the state accumulates phase, just as light accumulates phase travelling along an interferometer arm. The authors model this with a transfer-matrix (adiabatic impulse) approach, mapping the pulse sequence onto a chain of Mach-Zehnder interferometers, so that pulse length, frequency and amplitude correspond to number of beam splitters, path length, and reflectivity.

Experimentally, they first excite one data qubit with a π pulse and then apply a sinusoidal flux pulse to the coupler, reading out qubits and coupler simultaneously. Sweeping the modulation period and drive strength reveals the predicted interference fringes. They then fix a resonance and vary the gate duration to observe coherent swaps, and finally benchmark the swap fidelity on a monolithic transmon chip by repeating the gate an even number of times and fitting the resulting exponential decay.

Why This Matters

The work offers a two-qubit gate that combines the speed of resonant Rabi oscillations with the frequency agility of parametric gates, while leaving the data qubits unmodulated at their flux-insensitive sweet spots. This addresses a central scaling tension in superconducting hardware: fast gates need strong coupling, but strong static coupling creates always-on interactions and leakage.

• Multiplexed control: Since constructive or destructive interference can be selected per coupler by choosing amplitude and detuning, multiple couplers could be addressed simultaneously on shared drive lines, reducing control wiring in large processors.
• Chiplet interconnects: The demonstration on a modular flip-chip architecture points toward links between separately fabricated qubit chips, where coupling is limited (g/2π ≈ 3 MHz in this work).
• Hardware simplification: No flux line or drive is needed on the data qubits for the gate itself, which relaxes wiring and crosstalk constraints.
• Entanglement resources: Half-duration pulses produce Bell states deterministically or by coupler postselection, useful for state preparation and measurement-based schemes.

Industry relevance: The results are directly relevant to companies and institutes building superconducting quantum processors, particularly those pursuing modular or chiplet-based scaling and those concerned with control-signal multiplexing and wiring density. The involvement of Qruise GmbH indicates relevance to pulse-level calibration and control software.

Future Directions

• Pulse-shape optimization: The authors note that for g > ω_d full inversion can occur after a single interferometer, so even faster gates than the sinusoidal case could be reached by optimizing the pulse shape beyond a sinusoid.
• Higher-coherence hardware: The 99.9 % fidelity projection rests on qubits and couplers with two orders of magnitude larger coherence than the T₂^echo = 2.2 μs used here; realizing this is an open experimental target.
• Coupler readout and control: Because the mechanism is non-dispersive, coupler state preparation or measurement fidelity matters, and the authors note that measurement fidelities currently lag two-qubit gate fidelities; alternatives such as a "cold" coupler by non-measurement means need development.
• Frequency-multiplexed operation: Appendix I outlines the control knobs for full or zero population swap at any drive frequency; turning this into demonstrated parallel control of multiple couplers is a natural next step.
• Error budget refinement: Appendices F, G and H treat asymmetries, decoherence and leakage theoretically; experimental validation of these error channels at higher fidelity remains to be done.

Target Audience

This paper suits superconducting-qubit experimentalists and theorists working on two-qubit gate design, coupler architectures, and calibration; quantum-control engineers interested in parametric and non-dispersive driving schemes; and hardware architects evaluating modular or chiplet-based scaling strategies. Readers with graduate-level familiarity with circuit QED and Landau–Zener theory will get the most from the appendices, while the main text and the Mach-Zehnder analogy are accessible to newcomers with basic quantum mechanics.

Authors’ abstract

We propose and demonstrate gates between two superconducting qubits based on quantum interference of consecutive Landau-Zener (LZ) transitions. This gate mechanism bridges between baseband and parametric two-qubit control, enabling in situ tuning of the control frequency across a continuous interval up to hundreds of MHz. Another advantage compared to dispersive couplers is that the speed of the LZ gate is on the order of the full coupling strength. We experimentally demonstrate the gate on two platforms, a modular chiplet architecture of coupled generalized flux qubits, and on a monolithic transmon architecture. The combination of tunability and gate speed establishes the LZ gate as a unique tool for multiplexing control pulses and interconnecting superconducting chiplet architectures.