Noise-Resilient Quantum Metrology with Quantum Computing

TL;DR

This work tackles practical quantum metrology by addressing two core bottlenecks: loading classical data into quantum processors and resilience to realistic noise. It introduces a noise-resilient QM+QC framework that directly processes quantum data from sensors on a quantum computer, using variational quantum algorithms to implement quantum principal component analysis and iterative optimization to purify the noisy state. Experiments with NV centers and numerical simulations of distributed superconducting processors show substantial gains: accuracy improvements by over 200x under strong noise and a 13.27 dB boost in the quantum Fisher information, approaching the Heisenberg limit. The results indicate a feasible pathway to deploy near-term quantum computers for realistic, noisy metrology tasks, bypassing classical data-loading overheads and enhancing both fidelity and precision.

Abstract

Quantum computing has made remarkable strides in recent years, as demonstrated by quantum supremacy experiments and the realization of high-fidelity, fault-tolerant gates. However, a major obstacle persists: practical real-world applications remain scarce, largely due to the inefficiency of loading classical data into quantum processors. Here, we propose an alternative strategy that shifts the focus from classical data encoding to directly processing quantum data. We target quantum metrology, a practical quantum technology whose precision is often constrained by realistic noise. We develop an experimentally feasible scheme in which a quantum computer optimizes information acquired from quantum metrology, thereby enhancing performance in noisy quantum metrology tasks and overcoming the classical-data-loading bottleneck. We demonstrate this approach through experimental implementation with nitrogen-vacancy centers in diamond and numerical simulations using models of distributed superconducting quantum processors. Our results show that this method improves the accuracy of sensing estimates and significantly boosts sensitivity, as quantified by the quantum Fisher information, thus offering a new pathway to harness near-term quantum computers for realistic quantum metrology.

Figures (4)

• Figure 1: Concept and theoretical framework of the QM+QC method.a, Conceptual illustration of accuracy and precision in statistics, represented by dartboard charts showing various combinations of accuracy and precision. b, Schematic of the QM+QC framework. The quantum sensor is initialized in a probe state $|\psi_0\rangle$, evolves under noisy sensing superoperator $\tilde{\mathcal{U}}_\phi$ to yield a mixed state $\tilde{\rho}_{t}$, which is then transferred to a quantum computer for optimization. The optimized state becomes closer to the ideal target, thus improving both accuracy and precision. c, Accuracy enhancement ($\Delta F$) achieved by the QM+QC method compared with standard QM. Accuracy is characterized by the fidelity between the measured and ideal states; the gray dashed line marks $\Delta F = 0$. Error probability is $1-P_0$ and noise strength is $1-\mathrm{Tr}[\rho_t \tilde{N}(\rho_t)]$. d, Comparison of QFI for a 6-qubit GHZ state with and without optimization, showing a 13 dB improvement in QFI at $P_{0} = 0.5$.
• Figure 2: Experimental setup of the NV-center platform and implementation of the QM+QC protocol.a, Experimental setup and schematic structure of the NV center in diamond. Black spheres represent carbon atoms, the blue sphere denotes the nitrogen atom, and the dashed circle marks the vacancy. The yellow curve indicates the microwave waveguide. b, Energy-level diagram of the NV center. Green laser excitation initializes the electron spin, and red fluorescence from the excited- to ground-state transition enables spin-state readout. The ground triplet state $m_s= 0,\pm 1$ exhibits a 2.87 GHz zero-field splitting, and an applied magnetic field lifts the $m_s= \pm 1$ degeneracy. c, Pulse sequence of the Ramsey and qPCA experiments. A 2000 ns laser pulse polarizes the spin into $|0\rangle$ state; two microwave $\pi/2$ pulses separated by $\tau$ encode magnetic-field information. For the qPCA sequence, additional parameterized microwave pulses $U(\bm{\theta})$ are applied and optimized; after convergence, the inverse operation $U^{\dagger}(\bm{\theta})$ retrieves the optimized sensing result. d, Ramsey fringes measured under noise. Blue dots represent experimental data fitted by the solid blue curve, while the gray dashed line shows the ideal Ramsey signal.
• Figure 3: Experimental results of the QM+QC protocol on NV centers.a, Convergence of the measured magnetic field during iterative optimization. Blue diamonds show the optimized results approaching the target field $B_{0} = 0.25$ Gauss (red line). b, Magnetic-field sensing under different noise strengths ($\sigma$). Red and blue dots denote results from conventional Ramsey metrology (QM) and the QM+QC protocol, respectively. The red dashed line represents numerical simulation. c, Sensing results at various phases $\phi$ under $\sigma = 30\%$. QM+QC yields robust accuracy independent of evolution time, whereas the Ramsey method performs well only near the optimal phase $\phi = \pi/2$. d, APE for QM and QM+QC at various $\sigma$ and $\phi$, showing over 200-fold improvement in accuracy with the QM+QC method.
• Figure 4: QM+QC approach using distributed superconducting chips.a, Modular superconducting schematic comprising two four-qubit chips interconnected by a low-loss aluminum coaxial cable. One module acts as the quantum sensor, the other as the quantum computer. b, Evolution of state fidelity during PQC optimization for 2-, 3-, and 4-qubit GHZ probes. c, APE versus noise strength. QM+QC maintains APE $<0.6\%$, while conventional QM shows significant deviation at high noise levels. d, QFI as a function of noise strength for evolution times $\tau = 20 \sim 100$ ns. The QM+QC results are shown for $\tau = 100$ ns (thin solid line), lying almost indistinguishably close to the Heisenberg limit (dashed line). e, QFI of the QM+QC method when the sensing results are transmitted through a noisy quantum channel modeled by amplitude-damping noise with loss rates $\Gamma = 3\% \sim 15\%$. f, QFI comparison between QM and QM+QC when the transmission fidelity is $92\%$ ($\Gamma = 4.15\%$), The inset shows the QFI enhancement $\mathcal{F}_{\text{QM+QC}} - \mathcal{F}_{\text{QM}}$ as a function of noise strength and channel loss, highlighting consistent improvement across realistic operating conditions.