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arXiv:2605.04203

GHZ is All You Need: Quantum Sensing with VISTA

Oskar Novak, Christos N. Gagatsos, Narayanan Rengaswamy

quant-phSubmitted May 5, 2026• Announced May 7, 2026• 0 citations
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Abstract

Quantum metrology holds the potential to enhance magnetic field sensing beyond current limits. However, in the presence of realistic noise, this advantage degrades to the Standard Quantum Limit. While recent algorithmic and variational techniques attempt to recover this scaling, they are hindered by stringent control requirements on the probe state that are infeasible in the near term, or by barren plateaus and interpretability issues inherent to black-box variational quantum circuits. Here, we introduce Variational Inference and Sensing with Twin Ansätze (VISTA), a closed-loop protocol that combines passive sensing, or where the probe state is left to evolve without any active control, with physics-informed variational optimization. In the VISTA framework, a probe state evolves under a Lindbladian master-equation, and is compared, via the Swap test, to a parameterized ``quantum twin", a shallow quantum circuit designed to mimic the underlying pure-state or Lindbladian master-equation dynamics. By restricting the optimization space to the physical parameters of interest, VISTA circumvents barren plateaus. We demonstrate that by coupling the protocol with a classical optimizer and high shot counts, VISTA can temporarily achieve near-Heisenberg scaling for moderately noisy qubits over a finite range of system sizes. Furthermore, we introduce a Quasi-Normalization technique that sharpens the loss gradients, enabling simultaneous extraction of both the coherent signal $θ$ and the environmental noise rate $γ$ with low absolute error. Finally, we extend VISTA to the multi-parameter vector metrology regime, enabling simultaneous parameter extraction from a transverse-magnetic-field Hamiltonian. By eliminating the need for complex, open-loop control and processing, VISTA offers a highly practical, resource-efficient framework for near- to intermediate-term quantum sensors.

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12 Pages, 14 Figures

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Quantum metrology holds the potential to enhance magnetic field sensing beyond current limits. However, in the presence of realistic noise, this advantage degrades to the Standard Quantum Limit. While recent algorithmic and variational techniques attempt to recover this scaling, they are hindered by stringent control requirements on the probe state that are infeasible in the near term, or by barren plateaus and interpretability issues inherent to black-box variational quantum circuits. Here, we introduce Variational Inference and Sensing with Twin Ansätze (VISTA), a closed-loop protocol that combines passive sensing, or where the probe state is left to evolve without any active control, with physics-informed variational optimization. In the VISTA framework, a probe state evolves under a Lindbladian master-equation, and is compared, via the Swap test, to a parameterized ``quantum twin", a shallow quantum circuit designed to mimic the underlying pure-state or Lindbladian master-equation dynamics. By restricting the optimization space to the physical parameters of interest, VISTA circumvents barren plateaus. We demonstrate that by coupling the protocol with a classical optimizer and high shot counts, VISTA can temporarily achieve near-Heisenberg scaling for moderately noisy qubits over a finite range of system sizes. Furthermore, we introduce a Quasi-Normalization technique that sharpens the loss gradients, enabling simultaneous extraction of both the coherent signal θθθ and the environmental noise rate γγγ with low absolute error. Finally, we extend VISTA to the multi-parameter vector metrology regime, enabling simultaneous parameter extraction from a transverse-magnetic-field Hamiltonian. By eliminating the need for complex, open-loop control and processing, VISTA offers a highly practical, resource-efficient framework for near- to intermediate-term quantum sensors.
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 harnesses the unique properties of quantum systems to enable precision measurements of physical quantities such as time, magnetic and electric fields, acceleration, and gravitational gradients well beyond the limits of classical sensors. However, identifying suitable sensing probes and measurement schemes can be a classically intractable task, as it requires optimizing over Hilbert spaces of high dimension. In variational quantum sensing, a probe quantum system is generated via a parameterized quantum circuit (PQC), exposed to an unknown physical parameter through a quantum channel, and measured to collect classical data. PQCs and measurements are typically optimized using offline strategies based on frequentist learning criteria. This paper introduces an adaptive protocol that uses Bayesian inference to optimize the sensing policy via the maximization of the active information gain. The proposed variational methodology is tailored for non-asymptotic regimes where a single probe can be deployed in each time step, and is extended to support the fusion of estimates from multiple quantum sensing agents.
Entangled quantum probes can achieve Heisenberg-limited measurement precision, but this advantage is typically destroyed by noise. We address this issue by introducing a framework that we call encoded quantum signal processing, which unifies quantum error detection and quantum signal processing into an effective single-qubit framework, and provides a paradigm for constructing logical sensors that are robust to noise while remaining sensitive to the signal of interest. We show that encoding sensor qubits into a repetition code and using syndrome measurements as a signal-processing primitive restores Heisenberg scaling under realistic noise, without applying recovery operations. We prove that product-state sensing with syndrome post-processing is fundamentally limited to standard quantum limit (SQL) scaling, and develop four protocols that overcome this barrier through entanglement or sequential signal amplification, achieving Heisenberg-limited precision with exponential error suppression in code distance. For spatially inhomogeneous fields, Bayesian marginalization preserves Heisenberg scaling provided noise decreases sufficiently with system size. The underlying mechanism, which we formalize as encoded quantum signal processing, reduces multi-qubit metrology to an effective single-qubit problem where syndrome measurement implements nonlinear signal transformations. Numerical simulations validate the theoretical predictions: syndrome-based inference achieves near-Heisenberg scaling at noise levels where bare probes approach the SQL, and a concatenated protocol maintains this scaling under joint transverse noise and longitudinal inhomogeneities.
QSNs (QSNs) incorporate quantum sensing and quantum communication to achieve Heisenberg precision and unconditional security by leveraging quantum properties such as superposition and entanglement. However, the QSNs deploying noisy intermediate-scale quantum (NISQ) devices face near-term practical challenges. In this paper, we employ variational quantum sensing (VQS) to optimize sensing configurations in noisy environments for the physical quantity of interest, e.g., magnetic-field sensing for navigation, localization, or detection. The VQS algorithm is variationally and evolutionarily optimized using a genetic algorithm for tailoring a variational or parameterized quantum circuit (PQC) structure that effectively mitigates quantum noise effects. This genetic VQS algorithm designs the PQC structure possessing the capability to create a variational probe state that metrologically outperforms the maximally entangled or product quantum state under bit-flip, dephasing, and amplitude-damping quantum noise for both single-parameter and multiparameter NISQ sensing, specifically as quantified by the quantum Fisher information. Furthermore, the quantum anonymous broadcast (QAB) shares the sensing information in the VQS network, ensuring anonymity and untraceability of sensing data. The broadcast bit error probability (BEP) is further analyzed for the QAB protocol under quantum noise, showing its robustness—i.e., error-free resilience—against bit-flip noise as well as the low-noise BEP behavior. This work provides a scalable framework for integrated quantum anonymous sensing and communication, particularly in a variational and untraceable manner.
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.
Estimating multiple unknown parameters simultaneously is essential for practical quantum sensing. However, it faces a fundamental challenge: the optimal strategy for estimating one parameter is often incompatible with that for another, making it impossible to simultaneously achieve the ultimate precision limits for all parameters. Here we develop a general and efficient computational framework that jointly optimizes probe states, control operations, and measurements across different strategy families, including parallel, sequential, and those with indefinite causal order. Our approach provides exact semidefinite-program formulations for several precision bounds, including the Holevo, Nagaoka-Hayashi, and quantum Cramér-Rao bounds. We demonstrate the capabilities of the framework in multiparameter magnetometry and frequency estimation, identifying optimal protocols within each class and revealing a strict hierarchy among the achievable performances of different classes in the multiparameter regime. The framework also directly incorporates resource constraints, such as energy budgets, enabling systematic investigation of experimentally realistic sensing scenarios. Furthermore, we develop a finite-memory optimization method for sequential strategies with restricted ancillary-memory dimension. By decomposing the protocol into initial probe preparation and intermediate control operations, this method provides a practical route to designing resource-constrained sequential sensing schemes. Our work establishes a versatile computational tool for determining fundamental precision limits and designing optimal quantum-sensing protocols in complex multiparameter settings.