Demonstration of universal control between non-interacting qubits using the Quantum Zeno effect

The study investigates how the quantum Zeno effect—frequent or continuous measurement that partitions Hilbert space into subspaces—can be used to achieve coherent, deterministic control within these Zeno subspaces. Prior theory indicates Zeno dynamics can enable universal control even in systems with only local operations and no direct interactions. The authors present an explicit construction that uses strong measurements to conditionally impart a geometric phase, effectively turning a single-qutrit drive into a multiqubit entangling control-phase gate. They aim to demonstrate such a Zeno gate between two effectively non-interacting transmon qubits in a circuit QED architecture, highlighting that universality can be switched on or off via measurement of a single auxiliary level.

Zeno dynamics have been theoretically shown to enable universal control within measurement-defined subspaces and to support entangling schemes (e.g., Refs. 9–13). Prior measurement-based entanglement methods in superconducting circuits often rely on parity measurements and feedback (Refs. 5,16,17) but differ by being non-deterministic or not providing universal control. The present approach resembles neutral-atom entangling operations using Rydberg blockade (Refs. 20–22) in that a non-local state is inaccessible, but here the blockade arises from incoherent measurements rather than strong coherent interactions. Foundational and modeling work on Zeno physics in circuit QED, including quantum trajectories and strong-measurement regimes, informs the design and interpretation (Refs. 27–29), while recent theory unifies Zeno dynamics across mechanisms and coupling limits (Refs. 24,25).

System: Two transmon devices dispersively coupled to a superconducting 3D cavity (ωc/2π = 7.32 GHz, κ/2π = 0.15 MHz). Transmon frequencies: ωg1e1/2π = 3.28 GHz, ωg2e2/2π = 6.24 GHz, anharmonicities α1/2π = −175 MHz, α2/2π = −225 MHz. Dispersive shifts: χ1/2π = −4.25 MHz, χ2/2π = −4.35 MHz; qutrit f-state shift χf/2π ≈ −10 MHz. Residual ZZ interaction measured ≈ 30 kHz, negligible on gate timescales. Concept: Use a qutrit-qubit system where the qutrit’s |f⟩ serves as an auxiliary level. Apply an |e⟩↔|f⟩ Rabi drive at rate ΩR while continuously measuring the projector P = 1 − |f e…e⟩⟨f e…e| (two-qubit case: P = 1 − |f e⟩⟨f e|) via a cavity tone resonant with the cavity frequency corresponding to the undesired state. Rapid measurement partitions Hilbert space; transitions out of the Zeno subspace are suppressed, while coherent evolution within the subspace imparts a geometric phase from a 2π rotation on |e⟩→|f⟩→|e⟩. Over a duration t = 2π/ΩR, the |e g⟩ component accrues a π phase, effecting a control-phase gate up to local operations. The scheme generalizes to an N-control-phase using one qutrit and N−1 qubits by appropriate choice of P. Modeling: Continuous measurement at rate Γ is modeled by a Lindblad master equation: ρ̇ = −i[H,ρ] + Γ D[P]ρ, where H includes the |e⟩↔|f⟩ Rabi term and dispersive interactions. In the Markovian limit (ΩR ≪ κ), Γ ≈ 4ε^2/κ with cavity drive amplitude ε. Gate error in the diamond norm is bounded as ≤ 3θ ΩR/Γ (per Supplementary Note 1). Beyond the Markovian regime (ΩR ≳ κ), non-Markovian effects reduce blocking efficiency; full system simulations (qutrit–qubit–cavity) are used. Measurement implementation: The cavity is probed at ωfe = ωgg + χf + χ2 (the resonance when the system is in |f e⟩) to realize the Zeno measurement. The output is amplified by a flux-pumped JPA; tones are sequenced to first amplify the Zeno-drive band and then the readout band. A second “symmetric” cavity drive at ωsym = ωc + χ1 − χ2 cancels conditional phase accumulation (RIP-gate) arising from finite κ and off-resonant cavity displacement, isolating Zeno-only entanglement. Procedure: Initialize the two-transmon system in |+⟩|+⟩ with |+⟩ = (|g⟩+|e⟩)/√2. Apply simultaneous Zeno and symmetric cavity drives. Rabi-drive the qutrit |e⟩↔|f⟩ transition at the Stark-shifted frequency for a duration t = 2π/ΩR (typical ΩR/2π = 1 MHz). Perform full state tomography using a set of pulses mapping observables to |gg⟩⟨gg| measurements, reconstructing density matrices via maximum likelihood estimation. Characterizations: Zeno blocking probability is measured by preparing |gg⟩, applying a Rabi pulse on |g⟩↔|e⟩ for t = π/(2ΩR) with a Zeno drive at ωeg, and recording the probability to remain in |gg⟩ versus ε and ΩR. Concurrence and state fidelity relative to the ideal entangled state are extracted from reconstructed density matrices. Post-selection on the JPA signal (detecting escapes from the Zeno subspace) is used to demonstrate probabilistic performance improvements.

- Demonstrated a Zeno-enabled control-phase gate between two effectively non-interacting transmon qubits by imparting a conditional geometric phase via continuous measurement of a non-local projector while driving a single qutrit transition. - Verified Zeno blocking: The probability to prevent transitions increases with measurement drive amplitude ε and decreases with Rabi rate ΩR. Deviations from the simple Markovian model (ΩR ≪ κ) were observed at experimental operating points (e.g., ΩR/2π up to 1 MHz vs κ/2π = 0.15 MHz), consistent with reduced blocking in the non-Markovian regime and full-system simulations. - Implemented a symmetric cavity drive to cancel dispersive, measurement-induced conditional phases (RIP-gate), isolating entanglement generated solely by Zeno dynamics. - Achieved entanglement: For evolution to t ≈ 1 μs (ΩR/2π = 1 MHz), the |eg⟩ component acquired a π phase, and the final two-qubit state exhibited nonzero concurrence. Fidelity and concurrence versus ε showed an initial increase with ε (stronger Zeno block), followed by reduction at higher ε due to increased measurement-induced dephasing from finite κ. - Post-selection using the JPA-detected escape signal improved both state fidelity and concurrence as a function of excluded trials (shown for ε/2π = 2 MHz). Error-detection fidelity was ~75% (limited by short gate-time readout and enhanced relaxation from |f⟩), while single-shot readout fidelity was ~93%. - System coherence times: qutrit T1 ≈ 52 μs, T2 ≈ 12.9 μs (T2* ≈ 22.2 μs, T2echo ≈ 5.8 μs); qubit T1 ≈ 18.9 μs, T2 ≈ 15.7 μs. Gate operated with ΩR/2π = 1 MHz to keep gate time short relative to decoherence.

The results show that strong, continuous, non-local measurement can endow an otherwise non-interacting system with universal control by enforcing coherent Zeno dynamics within a measurement-defined subspace. The demonstrated two-qubit gate arises from a conditional geometric phase acquired only within the Zeno subspace and is deterministic and coherent, distinct from probabilistic, measurement-based state-preparation schemes. The approach generalizes to an N-control-phase gate using a single qutrit coupled with multiple qubits through the same cavity, with scalability limited by frequency crowding and residual interqubit couplings. Performance is governed by the competition between Zeno blocking (enhanced by larger ε) and measurement-induced dephasing (set by κ and finite detunings); operating deeper in the dispersive regime (|χ| ≫ κ) would improve fidelity by allowing larger χ with reduced dephasing and reduced unintended entangling phases. Although the RIP-gate can yield higher performance in this specific hardware, active cancellation enabled observation of Zeno-only coherent control, highlighting the principle that universality can be switched on by measurement alone.

The work provides a proof-of-concept that the quantum Zeno effect can convert trivial, non-interacting dynamics into universal control by combining local drives with strong, continuous, non-local projections. A two-qubit entangling control-phase operation was demonstrated in a circuit QED platform using a single qutrit’s auxiliary level and continuous measurement, with entanglement verified via state tomography and trends in fidelity and concurrence mapped versus measurement strength and post-selection. Future directions include: moving deeper into the |χ| ≫ κ regime to reduce dephasing and enhance blocking; improving measurement chains and detection fidelity to reduce escapes and enable lower-loss post-selection or feedforward; extending to multi-qubit Zeno gates sharing a common resonator; and exploring platforms with even weaker native interactions where Zeno-enabled control is the primary coherent mechanism.

- Finite measurement rate and cavity linewidth (κ) induce dephasing and limit blocking efficiency, especially outside the Markovian regime (ΩR ≳ κ). - Residual dispersive phase accumulation (RIP-gate) requires careful cancellation via a symmetric drive; imperfect cancellation can reduce fidelity. - Main gate infidelity arises from escapes from the Zeno subspace; detection fidelity of escapes (~75%) limits the benefit of post-selection despite high single-shot readout fidelity (~93%). - Tomography inaccuracies due to population of |f⟩ and cavity-induced Stark shifts during escape events can mis-map states, slightly biasing fidelity estimates. - Scalability is constrained by frequency crowding and residual interqubit couplings when multiple qubits share a cavity. - Practical limits on achievable dispersive coupling χ (tens of MHz) in current circuit QED hardware cap the extent to which |χ|/κ can be increased.