Quantum sensing leverages quantum resources to surpass the standard quantum limit, yet many existing protocols rely on the preparation of complex entangled states and Hamiltonian engineering, posing challenges for universality and scalability. Here, we report an experimental realization of a universal protocol, known as Butterfly Metrology, proposed in [arXiv:2411.12794], demonstrating a scrambling-based approach for quantum-enhanced sensing on a superconducting quantum processor. By exploiting many-body information scrambling, we observe quantum-enhanced sensitivity to an encoded phase beyond the standard quantum limit, with a scaling consistent with a factor-of-two of the Heisenberg limit for system sizes of up to 10 qubits. Importantly, we experimentally establish a connection between the enhanced sensitivity and the dynamics of the out-of-time-order correlator (OTOC), and show that the buildup of scrambling-induced genuine multipartite entanglement underlies the observed sensitivity enhancement. Our results demonstrate a scalable and practical approach for quantum-enhanced sensing in interacting many-body quantum systems.
Quantum sensing promises measurement precision beyond classical limits, but its practical realization is often hindered by decoherence and the challenges of generating and stabilizing entanglement in large-scale systems. Here, we experimentally demonstrate a scalable, scrambling-enhanced quantum sensing protocol, referred to as butterfly metrology, implemented on a cross-shaped superconducting quantum processor. By harnessing quantum information scrambling, the protocol converts local interactions into delocalized metrologically useful correlations, enabling robust signal amplification through interference of the scrambled and polarized quantum states. We validate the time-reversal ability via Loschmidt echo measurements and quantify the information scrambling through out-of-time-ordered correlators, establishing the essential quantum resources of our protocol. Our measurements reveal that the sensing sensitivity surpasses the standard quantum limit (SQL) with increasing qubit number, reaching 3.78 in a 9-qubit configuration, compared to the SQL of 3.0. The scheme further exhibits inherent robustness to coherent control errors and probed signal noise. This work demonstrates a readily scalable path toward practical quantum sensing advantages with prevalent experimental platforms.
I discuss the time reversal of nonlinear many-body Hamiltonians and its application to the fields of quantum metrology and quantum information science. I present the experimental realization of such a protocol in an optically engineered many-body spin Hamiltonian. We used time-reversed Hamiltonian approach to achieve metrological gains well beyond the limit of the readout scheme. Moreover, with the same protocol, we experimentally elucidate the intimate relation between quantum information scrambling, out-of-time-order correlators, and metrological gain. In particular, I will highlight the robustness of time reversal protocols, and how these render many fast-scrambling and complex Hamiltonians useful for quantum-enhanced metrology.
Quantum information scrambling, the dispersal of local information into many-body degrees of freedom, provides a powerful mechanism for generating large-scale correlations and entanglement essential for quantum-enhanced metrology. However, experimentally verifying such quantum-enhanced metrology remains a demanding task. Here, we correlate thousands of spins by engineering chaotic scrambling dynamics in a solid-state nuclear spin system. By leveraging the newly developed scramblon theory, we reveal exponential scaling in both the quantum Fisher information and the signal response to a phase shift. The signal response achieves a correlation-enabled enhancement of
33(2) dB over uncorrelated spins. After accounting for signal loss due to imperfect time reversal in the readout stage, we obtain a total metrological gain of 18(1) dB with a phase sensitivity of 40(3)
μrad. Our results bridge quantum chaos with practical quantum metrology, establishing reversible scrambling dynamics as a powerful resource for precision measurements.
Quantum scrambling describes the spreading of information into many degrees of freedom in quantum systems, such that the information is no longer accessible locally but becomes distributed throughout the system. This idea can explain how quantum systems become classical and acquire a finite temperature, or how in black holes the information about the matter falling in is seemingly erased. We probe the exponential scrambling of a multiparticle system near a bistable point in phase space and utilize it for entanglement-enhanced metrology. A time-reversal protocol is used to observe a simultaneous exponential growth of both the metrological gain and the out-of-time-order correlator, thereby experimentally verifying the relation between quantum metrology and quantum information scrambling. Our results show that rapid scrambling dynamics capable of exponentially fast entanglement generation are useful for practical metrology, resulting in a 6.8(4)-decibel gain beyond the standard quantum limit.
We investigate quantum-enhanced time-reversal-based metrology using the central spin model, in which a single ancilla spin of magnitude
Scen mediates interactions between
N bath spins through a star-graph topology. We demonstrate that the SATIN (Signal Amplification Through Time-reversal Interaction) echo protocol can be implemented in this setup to achieve a Fisher information of
N2/e with the collective
⟨Jy⟩ readout, corresponding to a
4.34dB offset from the Heisenberg limit. Furthermore, we establish that this platform provides a pathway to perform the butterfly echo protocol by conjugating each evolution step with a random collective bath rotation, thereby achieving axis-agnostic Heisenberg-scaled sensing. Crucially, with a small
N−independent number of random steps, the butterfly echo reaches a Fisher information of
N2/4 (
6dB below the Heisenberg limit) for any unknown encoding axis, with the plateau gain tracking the Haar limit. Finally, we demonstrate that the central-spin magnitude
Scen provides a powerful knob to reduce the optimal protocol timescale without altering the metrological ceiling or the circuit depth required to reach isotropy. The proposed scheme is relevant to cavity QED and NMR quantum processors, where the central spin architecture arises naturally.