Quantum system control is broadly classified into coherent and incoherent control. Coherent control utilizes control Hamiltonians for deterministic time evolution, while incoherent control relies on non-deterministic measurement outcomes. The quantum Zeno effect, a phenomenon where frequent measurements freeze system dynamics, occupies a boundary between these approaches. Measurements partition the Hilbert space into subspaces with distinct eigenvalues, generating Zeno dynamics within each subspace. While transitions between subspaces are suppressed, evolution within a subspace remains coherent. Prior theoretical work suggested the potential of Zeno dynamics to transform trivial quantum systems (with only local control) into universally controllable systems within the Zeno subspace, proposing various state-entangling schemes. This letter presents an explicit construction of such universal control and its experimental demonstration in a circuit QED system. Specifically, it demonstrates an N-Control-phase gate on N qubits (with one qutrit acting as a control), termed a Zeno gate, between two effectively non-interacting transmon qubits. Unlike other measurement-based methods, this approach offers coherent, deterministic dynamics and universality. The experimental system, despite possessing resonator-induced interaction (RIP), actively cancels these to isolate the Zeno effect. The goal is to showcase how universality can be switched on and off simply by observing a single level within the quantum system. The Zeno dynamics leverage local operations and non-local projections. A 2π rotation on one transition imparts a geometric phase of π, and rapid projections block transitions between Zeno subspaces, enabling phase accumulation only for specific states. An appropriate non-local projector conditions this phase on the state of both qubits, resulting in entanglement. This resembles Rydberg blockade in neutral atoms, where a non-local state is inaccessible, but differs in using incoherent measurements (instead of coherent interactions) for the block.

The paper references several key works in quantum control and the quantum Zeno effect. It cites research on continuous joint measurement and entanglement of qubits, deterministic remote entanglement generation with active quantum feedback, continuous quantum non-demolition feedback, and faster qubit projection using quantum feedback. Studies on deterministic entanglement of superconducting qubits through parity measurement and feedback, reversal of weak quantum state measurements, and continuous quantum non-demolition measurement are also mentioned. The authors acknowledge previous work on quantum Zeno dynamics and its mathematical and physical aspects, theoretical proposals on using Zeno dynamics for universal control and entanglement, and the circuit quantum electrodynamics framework. Additionally, the literature review implicitly covers existing entangling schemes based on Rydberg blockade and the resonator-induced phase gate (RIP-gate) in circuit QED. The paper builds upon these existing studies to experimentally demonstrate a novel approach to universal quantum control using the Zeno effect.

The experiment uses a circuit QED system comprising two transmon qubits dispersively coupled to a superconducting 3D cavity. The system is designed to minimize qubit-qubit interactions while optimizing the implementation of the non-local measurement. The transmon qubits have far-detuned transition frequencies and anharmonicities. One transmon acts as a qutrit. The cavity mode frequency and linewidth are specified. The transmon-cavity dispersive couplings are characterized. The residual direct qutrit-qubit interaction is measured using Ramsey interferometry and shown to be negligible. The dispersive Hamiltonian describes the system-cavity interaction, resulting in cavity resonance frequencies that depend on the qutrit-qubit state. Probing the cavity resonance frequency enables state deduction. Continuous measurement of the projector P is achieved by driving the cavity at the resonance frequency when the system is in |f⟩ (Zeno drive). The output signal is amplified using a flux-pumped Josephson Parametric Amplifier (JPA), enabling sequential amplification of different frequencies (Zeno drive and readout). The Zeno blocking probability is characterized as a function of drive amplitude and Rabi frequency. The experiment compares results with numerical simulations based on the master equation for a full qutrit-qubit-cavity system, and deviations are discussed in relation to the Markovian and non-Markovian regimes. To negate residual effects on states other than the one intended to be blocked by the Zeno drive, a symmetric drive is applied to the cavity. This cancels the phase accumulation caused by the Zeno drive, preventing entanglement from RIP-gate mechanisms. The combined effect of Zeno drive and symmetric drive is modeled using a driven system Hamiltonian. The Zeno gate is implemented by applying the drives, initializing the system in a specific state, applying the Rabi drive to the qutrit transition, and finally performing state tomography. The time evolution of the system is analyzed. The fidelity and concurrence of the final state are calculated as a function of Zeno drive amplitude. Post-selection based on the JPA signal is implemented to improve gate fidelity and concurrence.

The experiment successfully demonstrates a Zeno gate between two effectively non-interacting transmon qubits. The Zeno effect is used to create entanglement without direct qubit-qubit interaction. The Zeno blocking probability is experimentally characterized and shows good agreement with numerical simulations, although deviations are observed in the non-Markovian regime. The residual effects of the Zeno drive are successfully canceled using a symmetric drive. The experimental results show a clear generation of entanglement, confirmed by the acquired π phase and calculated concurrence. While the experimental fidelity is higher than simulated values, the discrepancy is attributed to the imperfect mapping of the qutrit level |f⟩ in the tomography process. Post-selection based on the JPA signal enhances the gate fidelity and concurrence. The data shows a clear increase in both as the percentage of excluded trials (based on JPA signal) increases. These results provide a proof-of-concept for using the Zeno effect to create universal quantum control in non-interacting systems. The experiments are performed at a Rabi frequency faster than the system decoherence time to maximize fidelity despite reduced Zeno blocking effectiveness. The limitation in observing the Zeno effect even with reduced effectiveness is attributed to the limited blocking ability in the non-Markovian regime.

The findings address the research question by experimentally demonstrating the feasibility of using the Zeno effect to achieve universal quantum control in a system without direct interactions between the qubits. The success of canceling resonator-induced interactions isolates the contribution of the Zeno effect to the observed entanglement. The results have significant implications for quantum computing and quantum information processing. The ability to generate entanglement and universal control using only measurements expands the toolkit for quantum control and opens up possibilities for designing quantum systems with minimal or no direct interactions. The demonstration of high fidelity (although probabilistically) and high concurrence in the generated entangled state shows the effectiveness of the approach. The observed deviations from the theoretical model in the non-Markovian regime highlight the importance of accurately modeling the system dynamics and measurement process. This research contributes to our fundamental understanding of the quantum Zeno effect and its applications in quantum technologies.

This paper successfully demonstrates universal quantum control using only the Zeno effect in a system of effectively non-interacting qubits. The experimental implementation of a Zeno gate between two transmon qubits, with active cancellation of resonator-induced interactions, showcases the potential of measurement-based coherent control. Future research could focus on extending this approach to larger numbers of qubits, exploring different qubit platforms, and developing more robust and higher-fidelity Zeno-based quantum gates. Improving the accuracy of the theoretical model in the non-Markovian regime is also a promising avenue for future work.

The main limitation is the probabilistic nature of the gate due to the finite measurement rate, which causes escapes from the Zeno subspace. The experimental setup uses actively canceled resonator-induced interaction, which may not be feasible in all systems. The fidelity of the gate is affected by imperfections in the tomography process, particularly the mapping of the |f⟩ state. The experiment operates in a regime where the Zeno effect is less pronounced (non-Markovian) which reduces the effectiveness of blocking transitions and impacts the fidelity of the Zeno gate.