Optimal control of a quantum sensor - A fast algorithm based on an analytic solution
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2024-07-04 |
| Journal | SciPost Physics |
| Authors | Santiago HernĂĄndez-GĂłmez, Federico Balducci, Giovanni Fasiolo, Paola Cappellaro, Nicole Fabbri |
| Institutions | University of Trieste, The Abdus Salam International Centre for Theoretical Physics (ICTP) |
| Citations | 7 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis research presents a novel, fast algorithm for optimizing the control sequence of spin-qubit quantum sensors, significantly enhancing their sensitivity to time-varying AC fields while suppressing dephasing noise.
- Core Value Proposition: The method provides a quasi-optimal pulsed control sequence (Dynamical Decoupling, DD) that maximizes the sensorâs sensitivity (smallest detectable signal, η) much faster and more effectively than standard protocols.
- Optimization Strategy: The complex continuous optimization problem is mapped onto finding the ground state of a classical Ising spin chain, allowing for analytic approximation.
- Hybrid Algorithm: A fast analytic solution (Spherical Model, SM) provides a high-quality initial guess, which is rapidly refined using a few steps of Simulated Annealing (SA).
- Performance Gain: The SM+SA protocol achieves sensitivities approaching 80-85% of the theoretical lower bound, outperforming generalized Carr-Purcell (gCP) sequences by a factor of 1.5 to 3.
- Computational Efficiency: The optimal sequence is generated extremely quickly (approx. 0.02 s for 500 spins) on a low-power Raspberry Pi microcomputer, enabling real-time adaptive sensing applications.
- Experimental Validation: Demonstrated sensitivity improvement using a Nitrogen-Vacancy (NV) center in bulk diamond, successfully filtering the 13C nuclear spin bath noise while detecting complex multi-chromatic target signals.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Sensor Platform | NV Center in Bulk Diamond | N/A | Single spin-qubit magnetometer. |
| Qubit Basis | ms = 0 â ms = +1 | N/A | Ground state electron spin levels. |
| Bias Magnetic Field (B) | 403.2(2) | G | Used for Zeeman splitting and spin quantization. |
| Noise Source | 13C Nuclear Spin Bath | N/A | Primary dephasing noise source (classical stochastic field). |
| Noise Spectral Density (NSD) Center | 0.4316(2) | MHz | 13C Larmor frequency (ÎœL). |
| NSD Standard Deviation (Ï/2Ï) | 4.2(2) | kHz | Bandwidth of the Gaussian noise spectrum. |
| Spin-Lattice Relaxation Time (T1) | ~1 | ms | Upper limit for sensing time T (Room Temp). |
| Sensitivity Bound Achieved | 80-85 | % | Fraction of the theoretical Spherical Model (SM) bound (ηSM). |
| Optimization Time (SM+SA) | ~0.02 | s | Time required to find optimal sequence (N=500 spins) on Raspberry Pi. |
| Time Discretization Interval (Ît) | 160 | ns | Smallest separation between Ï-pulses in experiments. |
| Sensitivity Improvement | 1.5 to 3 | Times | Improvement factor over generalized Carr-Purcell (gCP) protocol (numerical average). |
Key Methodologies
Section titled âKey MethodologiesâThe optimization protocol relies on a hybrid approach combining analytic modeling from statistical physics with numerical refinement:
- Cost Function Mapping: The dimensionless logarithmic sensitivity (Δ) is defined as the cost function. Upon time discretization, this function is mathematically recast as the Hamiltonian of a classical Ising spin system (H = Δ), where the spin configuration (si = ±1) defines the DD pulse sequence.
- Spherical Approximation (SM): The strict Ising constraint (si = ±1) is relaxed to a continuous spherical constraint (ÎŁ si2 = N). This âSpherical Modelâ allows for an analytic solution, yielding a continuous quasi-optimal modulation function y(t) and a theoretical lower bound (ηSM) for the sensitivity.
- Initial Guess Generation: The continuous SM solution y(t) is projected onto the discrete hypercube using the sign function (si = sign(yi)). This sequence, termed sign(SM), serves as a highly effective starting configuration for the numerical search.
- Simulated Annealing (SA) Refinement: A fast SA algorithm is executed, starting from the sign(SM) sequence. The SA focuses on flipping only the spins at the domain walls (where the sign changes), quickly converging to the optimal DD sequence that minimizes the Ising Hamiltonian (Δ).
- Experimental Setup: Experiments utilize a single NV center in bulk diamond. The qubit is initialized and read out optically (532 nm green light, 637 nm photoluminescence) and coherently controlled using microwave (MW) pulses.
- Target Signal and Noise: The target signal b(t) is a superposition of monochromatic waves (e.g., 3- or 7-chromatic). The noise S(Ï) is characterized beforehand, centered at the 13C Larmor frequency.
- Sensitivity Determination: Sensitivity η is measured by performing Ramsey interferometry experiments and analyzing the oscillation of the spin coherence P(T, b) as a function of the target field amplitude b.
Commercial Applications
Section titled âCommercial ApplicationsâThe development of fast, optimized quantum control sequences has direct implications for several high-tech sectors:
- Quantum Sensing and Metrology:
- Development of next-generation, high-sensitivity magnetometers, particularly those based on solid-state spin qubits (like NV centers).
- Improved detection of weak AC signals in noisy environments, crucial for fundamental physics and materials science research.
- Miniaturized Quantum Devices:
- Enabling the miniaturization of control electronics by shifting complex optimization tasks from high-power dedicated hardware to low-power embedded systems (e.g., Raspberry Pi).
- Facilitating the deployment of portable, field-ready quantum sensors.
- High-Resolution Spectroscopy:
- Enhancing the signal-to-noise ratio in magnetic resonance spectroscopy (MRS) and nuclear magnetic resonance (NMR) using nanoscale sensors.
- Applications in characterizing small spin ensembles or single molecules in chemistry and biology.
- Adaptive Control Systems:
- Implementation of adaptive sensing protocols where the optimal DD sequence is recalculated in real-time to track changes in the target signal spectrum or the environmental noise profile.
- Bio-Sensing and Medical Diagnostics:
- Sensing weak magnetic fields generated by biological processes (e.g., neuronal activity or action potentials) with high spatial and temporal resolution.
View Original Abstract
Quantum sensors can show unprecedented sensitivities, provided they are controlled in a very specific, optimal way. Here, we consider a spin sensor of time-varying fields in the presence of dephasing noise, and we show that the problem of finding the pulsed control field that optimizes the sensitivity (i.e., the smallest detectable signal) can be mapped to the determination of the ground state of a spin chain. We find an approximate but analytic solution of this problem, which provides a lower bound for the sensitivity and a pulsed control very close to optimal, which we further use as initial guess for realizing a fast simulated annealing algorithm. We experimentally demonstrate the sensitivity improvement for a spin-qubit magnetometer based on a nitrogen-vacancy center in diamond.