Optimal Control of Coupled Sensor-Ancilla Qubits Enables High-Precision Multiparameter Estimation

Achieving the highest possible precision in measuring multiple parameters simultaneously presents a significant challenge in quantum sensing, yet is crucial for advancing fields like medical imaging and materials science. Ayumi Kanamoto, Takuya Isogawa, and colleagues at Massachusetts Institute of Technology and The University of Tokyo, along with Haidong Yuan from The Chinese University of Hong Kong and Paola Cappellaro, demonstrate a new method for precisely controlling quantum systems to overcome this limitation.

The team numerically investigates optimal control of two interconnected quantum bits, a sensor and an ancilla, using a technique called Gradient Ascent Pulse Engineering. This approach achieves robust and highly accurate measurements across a broad range of interaction strengths and magnetic field configurations, offering a practical pathway toward building more sensitive and reliable quantum sensors, particularly for solid-state systems like nitrogen-vacancy centres in real-world experiments.

Multiparameter Quantum Sensing Beyond Classical Limits This research significantly advances quantum sensing, pushing the boundaries of measurement precision beyond what is achievable with classical techniques. Scientists focused on improving the ability to simultaneously measure multiple parameters, such as the frequency and amplitude of an oscillating magnetic field, a challenging task demanding sophisticated control strategies. A key obstacle in multiparameter estimation is the potential for incompatibility, where improving the precision of one parameter inadvertently degrades the accuracy of another.

This research addresses this challenge through precise manipulation of quantum systems, specifically solid-state spins like those found in diamond. The core of this advancement is a new optimization algorithm called Gradient-based Robust Algorithm for Parameter Estimation, or GRAPE. This algorithm effectively navigates the trade-offs between different parameters, achieving superior overall precision compared to traditional methods. Researchers implemented GRAPE using nitrogen-vacancy (NV) centers in diamond, a promising platform due to their long coherence times and ease of control. To facilitate wider adoption, the team released an open-source toolkit called Quanestimation, fostering collaboration and accelerating progress in the field. The results demonstrate performance approaching the fundamental limits of measurement precision in detecting oscillating magnetic fields, a significant achievement in quantum metrology. The methodology relies heavily on quantum control theory, designing optimal pulse sequences to manipulate the NV center. GRAPE, a gradient-based algorithm, iteratively refines control parameters to maximize measurement precision. Researchers employed numerical simulations to model the system and validate the algorithm’s performance, and experimental validation supports the claim of approaching the measurement limit. Robustness analysis confirms the algorithm’s resilience to noise and imperfections.

This research has broad implications, potentially leading to more sensitive and accurate magnetometers for biomedical imaging, materials science, geophysics, and navigation. Furthermore, the GRAPE algorithm and Quanestimation toolkit are adaptable to other quantum sensing applications, and the work contributes to the development of more sophisticated quantum control techniques.

Optimizing Entangled Qubit Control for Sensing Scientists have developed a sophisticated control scheme for a two-qubit system, maximizing precision in multiparameter sensing. The research focuses on a sensor qubit coupled to an ancilla qubit via the Ising interaction, a common configuration in systems like nitrogen-vacancy (NV) centers and their nuclear spins. A key strategy was maintaining a fixed measurement basis, recognizing that optimal measurement protocols are often unattainable in multiparameter estimation. The methodology centers on iteratively refining the control Hamiltonian using the GRAPE algorithm, maximizing an objective function directly related to estimation precision. This function quantifies the attainable precision of parameter estimation using the classical Fisher information matrix. To enhance optimization, scientists implemented a recursive protocol, starting with known solutions for weak coupling and using them as initial guesses for stronger coupling, preventing the algorithm from becoming trapped in suboptimal solutions. Computational efficiency was boosted through Numba-based JIT compilation and optimized matrix exponential calculations. The results demonstrate that the GRAPE-optimized control scheme achieves estimation precision approaching that of an interaction-free scenario, even with significant Ising coupling, and substantially outperforms naive control protocols. Recursive GRAPE Optimizes Multi-Parameter Quantum Sensing Scientists have achieved high-precision control of a two-qubit sensor system, demonstrating a robust method for simultaneously estimating multiple parameters. The research focuses on optimizing control fields to minimize uncertainty in parameter estimation, a crucial step towards realizing the full potential of quantum sensors. A key innovation was a recursive protocol, where solutions obtained for weaker interactions are used as starting points for stronger interactions, preventing the algorithm from getting trapped in suboptimal solutions. Experiments demonstrate that this approach effectively saturates the precision limit for estimating a static magnetic field, achieving a measurement precision of Tr[F⁻¹cl] = 1/(4T²) when the magnetic field strength is 1 and the angle θ and φ are both π/4. For a magnetic field strength of 1 and an evolution time T, the team achieved a 99. 9% reduction in estimation error, decreasing the value from 35. 2 to 0. 034 for an Ising interaction strength of J = 0. Furthermore, using solutions from weaker interactions as initial guesses consistently yielded higher precision, with improvements reaching approximately 25% compared to randomly generated initial values. The study extended to more complex scenarios, including estimating circularly polarized fields, demonstrating the effectiveness of the control scheme in dynamic scenarios.

Optimal Control Boosts Quantum Sensing Precision This research demonstrates a successful approach to designing optimal control protocols for multiparameter quantum sensing, achieving precision close to fundamental limits even in complex scenarios. Scientists developed a gradient-based optimization method to find control protocols for a two-qubit sensor-ancilla system interacting via an Ising term, a common feature in solid-state sensors. By strategically seeding the optimization process with solutions from simpler systems and carefully selecting initial guesses, the team achieved robust convergence and high precision across a wide range of interaction strengths and time-dependent fields. The results show significant improvements in estimation precision, with a reduction of five orders of magnitude achieved in certain configurations when compared to direct application of standard control methods. Crucially, the developed technique is well-suited for implementation on solid-state platforms such as nitrogen-vacancy centres in diamond, where interactions are unavoidable and multiparameter estimation is inherent. The method’s compatibility with digital control and ability to handle time dependence and coupling makes it immediately applicable to achieving high-precision, robust quantum magnetometry in realistic experimental settings. 👉 More information 🗞 Optimal Control of Coupled Sensor-Ancilla Qubits for Multiparameter Estimation 🧠 ArXiv: https://arxiv.org/abs/2512.11673 Tags: