Quantum-Enhanced Sensing Enabled by Scrambling-Induced Genuine Multipartite Entanglement

TL;DR

The paper addresses the challenge of quantum-enhanced sensing in many-body systems without relying on complex entangled-state preparation or Hamiltonian engineering. It implements a universal scrambling-based metrology protocol, Butterfly Metrology, on a 4x4 lattice of 16 superconducting qubits, using forward evolution U, a local operator L_V, and backward evolution U-dagger to generate the butterfly state and encode a Ramsey-like phase that scales with system size. The phase sensing demonstration surpasses the standard quantum limit, achieving sensitivity near a factor-two of the Heisenberg limit for up to 10 qubits, with a direct link to the out-of-time-ordered correlator and the buildup of scrambling-induced genuine multipartite entanglement. The results establish scrambling as a scalable quantum resource for metrology in interacting many-body systems, connecting dynamic entanglement growth to metrological advantage and validating OTOC-based diagnostics.

Abstract

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.

Figures (4)

• Figure 1: Schematic of the butterfly metrology protocol. (a) The superconducting quantum processor. The subsets of qubits used in the experiment (6, 8, and 10 qubits with the center qubit $Q_0$) are highlighted. (b) Quantum circuit implementing the butterfly metrology protocol. (c) The protocol realizes the butterfly state, which forms a coherent superposition of two distinct branches acquiring macroscopically different phases. The resulting Ramsey-like phase accumulation of $N\phi/2$ enables quantum-enhanced sensitivity.
• Figure 2: Characterization of the OTOC and the scrambling-induced entanglement. (a) Quantum circuit for measuring the OTOC. (b) Measured $O_{j}(t)$ with $V=X$ as a function of evolution time $t$ at different qubit distance $d$ from $Q_0$. (c) The reference experiment measuring $O_{0}(t)$ with $V=I$, used to characterize non-ideal effects. (d) Dynamics of scrambling-induced entanglement quantified by the GME concurrence $C_{\mathrm{GME}}$ as a function of time $t$ for system size $N=6$ with $V=X/2$. The six-qubit density matrix is reconstructed via full quantum state tomography with a complete set of $3^6$ observables with 5000 samples for each observable measured. Insets show the reconstructed density matrices at $t=0 , 32, 56, 80$ ns.
• Figure 3: Quantum sensing of the phase $\phi$. (a) The quantum circuit for sensing the phase $\phi$. (b) Measured expectation value of $\langle \sigma_x \rangle$ as a function of the phase $\phi$ and evolution time $t$ for different system sizes $N=6, 8,$ and $10$ (from left to right). Each data set is averaged over 10 experimental runs with different sets of random $X$ gates. (c) $\langle \sigma_x \rangle$ as a function of $\phi$ at the optimal evolution time with maximal slopes for different system sizes $N$. The inset shows a enlarged area of the data near $\phi=0$.
• Figure 4: The sensitivity of the protocol. (a) The inverted sensitivity $\eta^{-1}$ as a function of evolution time $t$ for the system size $N=6,8,10$. (b) The inverted sensitivity $\eta_{\rm{norm}}^{-1}$ as a function of evolution time $t$ after the normalization process. (c) The quantity $\eta_{\rm{OTOC}}^{-1}$ as a function of evolution time $t$ is obtained from the OTOC measurement. (d) The maximal values of inverted sensitivity for different $N$. The inverted sensitivities surpass the SQL (blue solid line) for all $N$ and approach the theoretical bound of $N/2$ after the normalization porcess. The results are averaged over 10 sets of random single-qubit $X$ gates with error bars representing the standard deviation.