Quantum metrology promises to surpass classical precision limits by leveraging quantum resources such as entanglement. Maximally entangled Greenberger-Horne-Zeilinger (GHZ) states are theoretically optimal probes for quantum metrology. However, they are fragile to environmental noise, severely limiting their practical utility. To overcome this limitation, we propose and experimentally realize a noise-adaptive quantum metrology scheme that autonomously identifies optimal probes without any prior information of the noise. This is achieved by combining a variational quantum circuit that optimizes available resources with an efficient strategy for evaluating the sensing performance. Using a seven-qubit nuclear spin sensor, we identify optimal probe states that achieve precision improvements up to 0.698 dB over GHZ states when sensing a fixed magnetic field. Furthermore, we show that the learned probe state exhibits cross-parameter robustness, maintaining superior performance over a broad range of magnetic field frequencies. The proposed scheme is model-free, hardware-efficient, and scalable, providing a practical route to noise-resilient quantum metrology on near-term quantum devices.
Quantum metrology promises to surpass classical precision limits by leveraging quantum resources such as entanglement. Maximally entangled Greenberger-Horne-Zeilinger (GHZ) states are theoretically optimal probes for quantum metrology. However, they are fragile to environmental noise, severely limiting their practical utility. To overcome this limitation, we propose and experimentally realize a noise-adaptive quantum metrology scheme that autonomously identifies optimal probes without any prior information of the noise. This is achieved by combining a variational quantum circuit that optimizes available resources with an efficient strategy for evaluating the sensing performance. Using a seven-qubit nuclear spin sensor, we identify optimal probe states that achieve precision improvements up to 0.698 dB over GHZ states when sensing a fixed magnetic field. Furthermore, we show that the learned probe state exhibits cross-parameter robustness, maintaining superior performance over a broad range of magnetic field frequencies. The proposed scheme is model-free, hardware-efficient, and scalable, providing a practical route to noise-resilient quantum metrology on near-term quantum devices.
Quantum sensing is an important application of emerging quantum technologies. We explore whether a hybrid system of quantum sensors and quantum circuits can surpass the classical limit of sensing. In particular, we use optimization techniques to search for encoder and decoder circuits that scalably improve sensitivity under given application and noise characteristics.Our approach uses a variational algorithm that can learn a quantum sensing circuit based on platform-specific control capacity, noise, and signal distribution. The quantum circuit is composed of an encoder which prepares the optimal sensing state and a decoder which gives an output distribution containing information of the signal. We optimize the full circuit to maximize the Signal-to-Noise Ratio (SNR). Furthermore, this learning algorithm can be run on real hardware scalably by using the "parameter-shift" rule which enables gradient evaluation on noisy quantum circuits, avoiding the exponential cost of quantum system simulation. We demonstrate up to 13.12x SNR improvement over existing fixed protocol (GHZ), and 3.19x Classical Fisher Information (CFI) improvement over the classical limit on 15 qubits using IBM quantum computer. More notably, our algorithm overcomes the decreasing performance of existing entanglement-based protocols with increased system sizes.
Phase sensing with entangled multi-qubit states in the presence of noise is a central theme of modern quantum metrology. The present work investigates Dicke state superposition probes for quantum phase sensing under parameter encoding generated by one- and two-body interaction Hamiltonians. Under linear collective-spin encoding, near-optimal Dicke superposition states are shown to exhibit significantly enhanced robustness against phase damping noise compared with Greenberger--Horne--Zeilinger (GHZ), W-superposition, and balanced Dicke states, while maintaining favorable metrological performance under realistic decoherence channels. For two-body interactions, optimal probe states maximizing the quantum Fisher information are identified. Their noise resilience and metrological scaling behaviour under phase damping, amplitude damping, and global depolarizing channels are analyzed. The associated near-optimal Dicke superposition states are found to exhibit improved resilience to phase damping, for the system sizes considered. These results establish tailored near-optimal Dicke state superposition probes as versatile and noise-resilient resources for Heisenberg and super-Heisenberg quantum phase sensing governed by one- and two-body interactions.
For single-parameter sensing, Greenberger-Horne-Zeilinger (GHZ) probes achieve optimal quantum-enhanced precision across the unknown parameter range, solely relying on parameter-independent separable measurement strategies for all values of the unknown parameter. However, in the multiparameter setting, a single GHZ probe not only fails to achieve quantum advantage but also the corresponding optimal measurement becomes complex and dependent on the unknown parameters. Here, we provide a recipe for multiparameter sensing with GHZ probes using quantum error correction techniques by treating all but one unknown parameters as noise, whose effects can be corrected. This strategy restores the core advantage of single parameter GHZ-based quantum sensing, namely reaching optimally quantum-enhanced precision for all unknown parameter values while keeping the measurements separable and fixed. Specifically, given one shielded ancilla qubit per GHZ probe, our protocol extracts optimal possible precision for any probe size. While this optimal precision is shot-noise limited for a single GHZ probe, we recover the Heisenberg scaling through use of multiple complementary GHZ probes. We demonstrate the effectiveness of the protocol with Bayesian estimation.
By leveraging quantum effects, such as superposition and entanglement, quantum metrology promises higher precision than classical strategies. It is, however, a challenging task to achieve the higher precision on practical systems. This is mainly due to difficulties in engineering nonclassical states and performing nontrivial measurements on the system, especially when the number of particles is large. Here we propose a variational scheme with the Loschmidt echo for quantum metrology. By utilizing hardware-efficient ansatzes in the design of variational quantum circuits, the quantum Fisher information (QFI) of the probe state can be extracted from the experimentally measured Loschmidt echo in a scalable manner. This QFI is then used to guide the online optimization of the preparation of the probe state. We experimentally implement the scheme on an ensemble of 10-spin quantum processors and achieve a 12.4-dB enhancement of the measurement precision over the uncorrelated states, which is close to the theoretical limit. The scheme can also be employed on various other noisy intermediate-scale quantum devices, which provides a promising protocol to demonstrate quantum advantages.
Quantum metrology plays a fundamental role in many scientific areas. However, the complexity of engineering entangled probes and the external noise raise technological barriers for realizing the expected precision of the to-be-estimated parameter with given resources. Here, we address this problem by introducing adjustable controls into the encoding process and then utilizing a hybrid quantum-classical approach to automatically optimize the controls online. Our scheme does not require any complex or intractable off-line design, and it can inherently correct certain unitary errors during the learning procedure. We also report the first experimental demonstration of this promising scheme for the task of finding optimal probes for frequency estimation on a nuclear magnetic resonance (NMR) processor. The proposed scheme paves the way to experimentally auto-search optimal protocol for improving the metrology precision.
Modern quantum systems have two facets: they are resources we would like to harness, and they contain physics we would like to probe. This thesis studies both through several case studies in quantum metrology and computing, unified by the interplay between entanglement, noise, and dissipation. We first probe entanglement in an optomechanical setting, where a mechanical oscillator is continuously driven and monitored by a light field. Assuming Gaussian dynamics and arbitrary, possibly non-Markovian noise, we derive necessary and sufficient conditions for entanglement. For a vacuum input, the entangling-disentangling transition is set by the environmental noise alone and is independent of the optomechanical coupling strength. Furthermore, frequency-dependent squeezing cannot entangle a system that is separable when driven by vacuum. In the Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO), we find that the present level of classical noise, dominated by low-frequency seismic noise, makes significant stationary entanglement unlikely. We then turn to quantum frequency estimation and present two schemes. The first scheme harnesses entanglement as a metrological resource, approaching Heisenberg-limited precision up to a constant factor using blocks of Greenberger-Horne-Zeilinger (GHZ) states prepared with logarithmic-depth circuits and read out with local, adaptive measurements. The second scheme addresses the precision-bandwidth trade-off through a weak-measurement Ramsey protocol that recovers the classical precision limit over an extended dynamic range. Finally, we harness dissipation by introducing the 0-n Fock qubit, a noise-biased bosonic encoding stabilized by frequency-selective dissipation, with bit-flip errors exponentially suppressed in n (the highest Fock level). Used as a bias-preserving ancilla for cat-qubit architectures, it enables noise-biased controlled-X gates and low logical error rates with experimentally realistic parameters. Together, these results explore the regimes where entanglement and quantum advantage can survive noise, and show how measurement and dissipation can be engineered to protect them.