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arXiv:2505.04958

Enhancing the Dynamic Range of Quantum Sensing via Quantum Circuit Learning

Kawaguchi, Hideaki, Yuichiro Mori, Takahiko Satoh, Yuichiro Matsuzaki

Published May 8, 2025• 0 citations
arXivHTMLPDF

Abstract

Quantum metrology is a promising application of quantum technologies, enabling the precise measurement of weak external fields at a local scale. In typical quantum sensing protocols, a qubit interacts with an external field, and the amplitude of the field is estimated by analyzing the expectation value of a measured observable. Sensitivity can, in principle, be enhanced by increasing the number of qubits within a fixed volume, thereby maintaining spatial resolution. However, at high qubit densities, inter-qubit interactions induce complex many-body dynamics, resulting in multiple oscillations in the expectation value of the observable even for small field amplitudes. This ambiguity reduces the dynamic range of the sensing protocol. We propose a method to overcome the limitation in quantum metrology by adopting a quantum circuit learning framework using a parameterized quantum circuit to approximate a target function by optimizing the circuit parameters. In our method, after the qubits interact with the external field, we apply a sequence of parameterized quantum gates and measure a suitable observable. By optimizing the gate parameters, the expectation value is trained to exhibit a monotonic response within a target range of field amplitudes, thereby eliminating multiple oscillations and enhancing the dynamic range. This method offers a strategy for improving quantum sensing performance in dense qubit systems.

DOI
10.48550/arxiv.2505.04958

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Quantum metrology is a promising application of quantum technologies, enabling the precise measurement of weak external fields at a local scale. In typical quantum sensing protocols, a qubit interacts with an external field, and the amplitude of the field is estimated by analyzing the expectation value of a measured observable. Sensitivity can, in principle, be enhanced by increasing the number of qubits within a fixed volume, thereby maintaining spatial resolution. However, at high qubit densities, inter-qubit interactions induce complex many-body dynamics, resulting in multiple oscillations in the expectation value of the observable even for small field amplitudes. This ambiguity reduces the dynamic range of the sensing protocol. We propose a method to overcome the limitation in quantum metrology by adopting a quantum circuit learning framework using a parameterized quantum circuit to approximate a target function by optimizing the circuit parameters. In our method, after the qubits interact with the external field, we apply a sequence of parameterized quantum gates and measure a suitable observable. By optimizing the gate parameters, the expectation value is trained to exhibit a monotonic response within a target range of field amplitudes, thereby eliminating multiple oscillations and enhancing the dynamic range. This method offers a strategy for improving quantum sensing performance in dense qubit systems.
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.
In the rapidly evolving field of quantum computing, optimizing quantum circuits for specific tasks is crucial for enhancing performance and efficiency. More recently, quantum sensing has become a distinct and rapidly growing branch of research within the area of quantum science and technology. The field is expected to provide new opportunities, especially regarding high sensitivity and precision. Entanglement is one of the key factors in achieving high sensitivity and measurement precision [3]. This paper presents a novel approach utilizing quantum machine learning techniques to optimize entanglement distribution in quantum sensor circuits. By leveraging reinforcement learning within a quantum environment, we aim to optimize the entanglement layout to maximize Quantum Fisher Information (QFI) and entanglement entropy, which are key indicators of a quantum system's sensitivity and coherence, while minimizing circuit depth and gate counts. Our implementation, based on Qiskit, integrates noise models and error mitigation strategies to simulate realistic quantum environments. The results demonstrate significant improvements in circuit performance and sensitivity, highlighting the potential of machine learning in quantum circuit optimization by measuring high QFI and entropy in the range of 0.84-1.0 with depth and gate count reduction by 20-86%.
The rapid advancements in quantum computing (QC) and machine learning (ML) have sparked significant interest, driving extensive exploration of quantum machine learning (QML) algorithms to address a wide range of complex challenges. The development of high-performance QML models requires expert-level expertise, presenting a key challenge to the widespread adoption of QML. Critical obstacles include the design of effective data encoding strategies and parameterized quantum circuits, both of which are vital for the performance of QML models. Furthermore, the measurement process is often neglected-most existing QML models employ predefined measurement schemes that may not align with the specific requirements of the targeted problem. We propose an innovative framework that renders the observable of a quantum system-specifically, the Hermitian matrix-trainable. This approach employs an end-to-end differentiable learning framework, enabling simultaneous optimization of the neural network used to program the parameterized observables and the standard quantum circuit parameters. Notably, the quantum observable parameters are dynamically programmed by the neural network, allowing the observables to adapt in real time based on the input data stream. Through numerical simulations, we demonstrate that the proposed method effectively programs observables dynamically within variational quantum circuits, achieving superior results compared to existing approaches. Notably, it delivers enhanced performance metrics, such as higher classification accuracy, thereby significantly improving the overall effectiveness of QML models.
Variational quantum sensing offers a promising route to high-precision parameter estimation, but its performance depends strongly on the circuit architectures used for probe preparation and measurement. Existing approaches typically optimize continuous parameters within predefined ansätze, restricting the accessible design space and limiting adaptation to sensing tasks and hardware constraints. Here, we introduce \textsc{AutoQSense}, a reinforcement-learning framework that searches circuit architectures using Fisher-information-based objectives. For few-qubit systems, a single agent sequentially constructs preparation and measurement circuits. For larger systems, a distributed formulation assigns local circuit design to subsystem agents and inter-block entanglement to a budgeted agent. Numerical results show that the learned architectures recover known benchmark strategies, adapt to dephasing noise, and outperform fixed hardware-efficient ansätze while using fewer entangling gates. These results establish \textsc{AutoQSense} as a resource-aware approach to adaptive and hardware-compatible quantum sensing.
Estimating properties of quantum states, such as fidelities, molecular energies, and correlation functions, is a fundamental task in quantum information science. Due to the limitation of practical quantum devices, including limited circuit depth and connectivity, estimating even linear properties encounters high sample complexity. To address this inefficiency, we propose a framework that optimizes sample complexity for estimating the expectation value of any observable using a shallow parameterized quantum circuit. Within this framework, we introduce two decomposition algorithms, a tensor network approach and a greedy projection approach that decompose the target observable into a linear combination of multiple observables, each of which can be diagonalized with the shallow circuit. Using this decomposition, we then apply an importance sampling algorithm to estimate the expectation value of the target observable. We numerically demonstrate the performance of our algorithm by estimating the expectation values of some specific Hamiltonians and inner product of a Slater determinant with a pure state, highlighting advantages compared to some conventional methods. Additionally, we derive the fundamental lower bound for the sample complexity required to estimate a target observable using a given shallow quantum circuit, thereby enhancing our understanding of the capabilities of shallow circuits in quantum learning tasks.
We introduce an end-to-end optimization strategy for quantum machine learning that directly targets performance under finite measurement resources, where learning objectives are defined directly at the level of task performance. The method is applied on a Bayesian quantum metrology task since it provides a natural testbed with known fundamental limits and scaling with system size. The sampling-aware hybrid algorithm achieves a single-shot risk within 1 dB of the -20 dB Bayesian limit using 32 qubits. We extend the Bayesian framework from parameter estimation to global function inference, where the task is to infer a target function of the sensor input drawn from an arbitrary prior, and we demonstrate a clear computational-sensing advantage for direct functional inference over indirect reconstruction. We relate the corresponding Bayesian risk to the Capacity metric and argue that the Resolvable Expressive Capacity provides a natural measure of the space of functions accessible in a single shot. The resulting eigentask analysis identifies noise-robust feature combinations that yield compact estimators with improved accuracy and reduced optimization cost in resource-limited or real-time on-device settings. Going beyond the irreducible statistical uncertainty associated with finite measurement records, we study implementation-induced distortions of the sensor response focusing on representative imperfections arising from readout errors and static coherent gate disorder. We show that when these imperfections are stationary across training and inference, end-to-end optimization can adapt the quantum circuit and classical estimator to the implemented hardware response, preserving high inference performance over a broad range of imperfection strengths.