Tek Dönüşlü Dinamik Araştırma Durumu ile Manyetik Alanı Algılama: Kuantum Fisher Bilgileri Yoluyla Algılama Hassasiyeti Üzerinde Kontrol

Year 2023, , 29 - 33, 28.02.2023

Sergey Borisenok

https://doi.org/10.31590/ejosat.1249710

Abstract

Kuantum sensörleri, modern bilimin birçok dalında önemli bir rol oynar ve kuantum cihazları için büyüyen pazarın büyük bir bölümünü işgal eder. Kuantum sensörleri, kuantum öğelerini tespit etmek ve analiz etmek için kübitleri ve analoglarını kullanır. Bazı sensörler, genellikle evrimini sözde Bloch küresi üzerinde gerçekleştiren bir sistem olarak sunulan tek bir kübite dayalı olabilir. Algılama sürecinin etkinliğini değerlendirmek için farklı kriterler kullanılır. En popüler olanlardan biri, Fisher bilgilerine dayanan Kuantum Fisher Bilgi Matrisidir (KFBM). KFBM öğelerinin büyüklükleri, algılama hassasiyeti ile güçlü bir şekilde ilişkilidir. Klasik Cramér teoreminin bir benzeri olarak, V = 1/NF'ye eşit olan V varyansı için kuantum Cramér-Rao bağı tanımlanabilir; burada F, karşılık gelen kuantum Fisher bilgi öğesidir ve N, tekrarlanan duyusal ölçümlerin sayısını temsil etmektedir. Bu çalışmada, harici manyetik alanları algılamak için tek bir geri bildirim odaklı kübit tipi eleman için kuantum Fisher bilgi tabanlı yaklaşımımızı geliştirmekteyiz. Algoritmamızın verimliliğini göstermekte ve olası iyileştirmelerini tartışmaktayız. Burada geliştirilen yaklaşım, toplu döndürme sistemleri ve çoklu kübit tabanlı sensörler gibi diğer algılama şemalarına kolayca genişletilebilmektedir. KFBM bileşenlerinin maksimize edilmesi için araştırma durumu vektörünü sürmek üzere alternatif kontrol algoritmaları uygulanabilir. Kontrol algoritmasına özgü yapılacak seçim belirlenen deneysel düzenek tarafından tanımlanır.

Keywords

Kuantum biti, Bloch küresi, Cramer-Rao sınırı, Kuantum algılama, İleri besleme kontrolü

Supporting Institution

Abdullah Gül Üniversitesi

Project Number

BAP FBA-2023-176

Thanks

This work was supported by the Research Fund of Abdullah Gül University; Project Number: BAP FBA-2023-176 “Geribesleme kontrol algoritmaları ile kubit tabanlı sensörlerin verimliliğinin artırılması”.

Sensing Magnetic Field with Single-Spin Dynamical Probe State: Control over Sensing Precision via Quantum Fisher Information

Abstract

Quantum sensors play an important role in many branches of modern science, and they occupy a huge segment of the growing market for quantum devices. Quantum sensors use qubits and their analogs as detecting and analyzing quantum elements. Some sensors can be based on a single qubit, which is often presented as a system making its evolution on the so-called Bloch sphere. Different criteria are used to evaluate the efficiency of the sensing process. One of the most popular is the Quantum Fisher Information Matrix (QFIM) based on Fisher information. The magnitudes of the QFIM elements are strongly related to the precision of the sensing. As an analog of the classical Cramér theorem, one can define the quantum Cramér-Rao bound for the variance V, which is equal to V = 1/NF where F is the corresponding quantum Fisher information element, and N stands for the number of repeated sensory measurements. In this work, we develop our quantum Fisher information-based approach for a single feedback-driven qubit-type element for sensing external magnetic fields. We demonstrate the efficiency of our algorithm and discuss its further possible improvement. The approach developed here can be easily extended to other sensing schemes: collective spin systems and multi-qubit-based sensors. Alternative control algorithms can be applied to drive the probe state vector for maximization of the QFIM components. The particular choice of the control algorithm is defined by the specific experimental set-up.

Keywords

Quantum bit, Bloch sphere, Cramer-Rao bound, Quantum sensing, Feedforward control

Project Number

BAP FBA-2023-176

References

• Amari, S., Nagaoka, H. (2000). Methods of Information Geometry, Providence, USA: American Mathematical Society.
• Bloch, F. (1946). Nuclear induction, Physical Review, 70, 460-474.
• Borisenok, S. (2018). Control over performance of qubit-based sensors, Cybernetics and Physics, 7(3), 93-95.
• Braunstein, L. V., Caves, C. M. (1994). Statistical distance and the geometry of quantum states, Physical Review Letters, 72, 3439-3443.
• Cramér, H. (1946). Mathematical Methods of Statistics, Princeton Mathematical Series, Princeton, USA: Princeton University Press.
• Crawford, S. E., Shugayev, R. A., Paudel, H. P., Lu, P., Syamlal, M., Ohodnicki, P. R., Chorpening, B., Gentry, R., Duan, Y. (2021). Quantum sensing for energy applications: Review and perspective, Advanced Quantum Technologies, 4(8), 2100049.
• Degen C. L., Reinhard, F., Cappellaro, P. (2017). Quantum sensing, Review of Modern Physics, 89, 035002.
• Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics, Philosophical Transactions of the Royal Society of London, Series A, 222, 309-368.
• Fradkov, A. L. (2007). Cybernetical Physics. From Control of Chaos to Quantum Control, Berlin, Heidelberg, Germany: Springer.
• Jing, X. X., Liu, J., Xiong, H. N., Wang, X. (2015). Maximal quantum Fisher information for general su(2) parametrization processes, Physical Review A, 92, 012312.
• Kolesnikov, A. A. (2014). Introduction of synergetic control, 2014 American Control Conference, Portland, USA, 3013-3016.
• Koppenhöfer, M., Groszkowski, P., Lau, H., Clerk, A. A. (2022). Dissipative superradiant spin amplifier for enhanced quantum sensing, PRX Quantum, 3, 030330.
• Laurenza, R., Lupo, C., Spedalieri, G., Braunstein, S. L., Pirandola, S. (2018). Channel simulation in quantum metrology, Quantum Measurements and Quantum Metrology, 5, 1-12.
• Liu, J., Jing, X., Wang, X. (2015). Quantum metrology with unitary parametrization processes, Scientific Reports, 5, 8565.
• Liu, J., Yuan, H., Lu, X., Wang, X. (2019). Quantum Fisher information matrix and multiparameter estimation, Journal of Physics A: Mathematical and Theoretical, 53(2), 023001.
• Nielsen, F. (2013). Cramer-Rao lower bound and information geometry, In: R. Bhatia, C. S. Rajan, A. I. Singh, Eds, Connected at Infinity II. Texts and Readings in Mathematics, vol 67. Gurgaon, India: Hindustan Book Agency.
• Nielsen, M. A., Chuang, I. L. (2004). Quantum Computation and Quantum Information, Cambridge, UK: Cambridge University.
• Pang, S., Brun, T. A. (2014). Quantum metrology for a general Hamiltonian parameter, Physical Review A, 90, 022117.
• Pechen, A. N., Borisenok, S., Fradkov, A. L. (2022). Energy control in a quantum oscillator using coherent control and engineered environment, Chaos, Solitons & Fractals, 164, 112687.
• Poggiali, F., Cappellaro, P., Fabbri, N. (2018). Optimal control for one-qubit quantum sensing, Physical Review X, 8, 021059.
• ReportLinker. (2022). The Global Quantum Sensors Market size is expected to reach $619.8 million by 2028, rising at a market growth of 16.4% CAGR during the forecast period. [Online]. Available: https://www.globenewswire.com/news-release/2022/11/22/2561070/0/en/The-Global-Quantum-Sensors-Market-size-is-expected-to-reach-619-8-million-by-2028-rising-at-a-market-growth-of-16-4-CAGR-during-the-forecast-period.html
• Wu, W., Shi, C. (2021). Criticality-enhanced quantum sensor at finite temperature, Physical Review A, 104, 022612.
• Yuan, H. (2016). Sequential feedback scheme outperforms the parallel scheme for Hamiltonian parameter estimation, Physical Review Letters, 117, 160801.
• Zhong, W., Sun, Z., Ma, J., Wang, X., Nori, F. (2013). Fisher information under decoherence in Bloch representation, Physical Review A, 87, 022337.