Quantum Sensing: Real-time Frequency Estimation With OPX+

In the rapidly advancing field of quantum technology, the pursuit of refined and more sensitive measurement systems is relentless. Recent advancements aim to surpass the standard quantum limit (SQL) and approach the Heisenberg limit (HL) using quantum algorithms. One such algorithm is the phase estimation algorithm (PEA), known for its capability to achieve high sensitivities with single-shot readout (SSR) sensors. However, applying adaptive PEA to non-SSR sensors, which typically have lower contrast measurements, poses unique challenges.

A pivotal paper published in Quantum Science and Technology in May 2023, by I. Zohar et al.[1], highlights a groundbreaking approach to quantum sensing. Quantum Machines is proud to be at the forefront of these developments with its innovative processor-based OPX quantum control platform, enabling such advanced protocols. This blog post delves into the significant enhancements brought about by integrating OPX into quantum measurement systems, focusing on its application in real-time frequency estimation of a qubit without single-shot-readout.

The Role of OPX in Advanced Quantum Sensing

The study conducted by the team led by Prof. Amit Finkler at the Weizmann Institute of Science, together with collaborators in Edinburgh and Stuttgart, explores an intricate quantum sensing technique using the nitrogen-vacancy (NV) center in diamond as a sensor. This study explores a non-adaptive PEA method using a binomial distribution technique to improve accuracy in real-time frequency estimation.  

This method is particularly challenging because it does not rely on single-shot-readout (SSR), which is commonly used in high-contrast quantum measurements. Instead, the research introduces a non-adaptive phase estimation algorithm (PEA) that employs a binomial distribution method to achieve higher accuracy and sensitivity in environments where SSR is not feasible (Figure 1). To further shorten the sensing time, they proposed an adaptive algorithm that controls the readout phase by showing through numerical simulation that adding the adaptive protocol can further improve the accuracy in a future real-time experiment. 

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Quantum Machines’ OPX becomes as a game-changer

OPX is utilized to execute real-time calculations essential for the phase estimation algorithm. OPX’s capability to orchestrate complex pulse sequences, manage photon readout, and perform Bayesian updates in real time is crucial. It dramatically reduces the computational overhead and speeds up the process, thereby enhancing the efficiency and effectiveness of quantum sensing experiments. 

Figure 1: Graphical illustration of the adaptive phase estimation algorithm comprising four steps: (1) A pulse sequence suitable for the estimation of the unknown parameter, given the nature of the interaction between the sensor and the parameter. This pulse sequence will be applied with exponentially growing sensing times. The state of the sensor is measured after every sensing time. (2) Calculating the probability function for the state of the sensor given the unknown parameter. (3) Using Bayes’ Theorem to update the probability function for the parameter. (4) Calculating the optimal variables for extracting maximal information from the next iteration. After Mk iterations for each sensing time, the final distribution will be the estimate of the unknown parameter. Credits: Figure 2.c Zohar et al.[1]

Demonstrating Improved Sensitivity and Precision

The experiment detailed in the paper employs OPX to compare the traditional majority-voting method against the newly introduced binomial distribution approach in estimating magnetic fields at ambient conditions. In the study, the NV center in diamond is used as a non-SSR sensor. This quantum system is utilized for its sensitivity to magnetic fields via the Zeeman effect. The adaptive PEA algorithm involves the following steps: 

1. Pulse Sequence Application: A suitable pulse sequence is applied based on the interaction between the sensor and the target parameter, using exponentially growing sensing times. 
2. Probability Function Calculation: The probability function for the sensor state, given the unknown parameter, is calculated. 
3. Bayesian Update: Bayesian inference is used to update the probability function for the unknown parameter. 
4. Optimal Variable Calculation: Optimal variables for extracting maximum information in the next iteration are determined. 

The results are compelling. The binomial distribution method demonstrated superior accuracy and sensitivity over the majority-voting approach. is evident in reduced mean square errors and improved measurement fidelity, all achieved within shorter sensing times. For instance, an MSE of approximately 0.6 MHz was achieved with the binomial method at R=2500R=2500 and a total sensing time of 0.75 s, while the majority-voting method required almost twice the sensing time to reach a similar MSE (Figure 2). 

Figure 2: Error (sqrt of variance) vs. total measurement time (iterations) using binomial distribution (blue) and majority voting (orange) for 2500 cycle repetitions. Data is from 500 random detunings. Credits: Figure 2.c Zohar et al.[1]

Transformative Advances in Quantum Sensing: The Future Powered by Quantum Machines

The study by Zohar et al. demonstrates the effectiveness of the binomial distribution approach in non-SSR quantum sensing, showing a significant reduction in MSE and enhanced sensitivity compared to traditional methods. Additionally, the proposed adaptive protocol offers further improvements in measurement accuracy and efficiency, underscoring the crucial role of sophisticated control systems like OPX. 

The success of this research is a clear indicator of OPX potential to revolutionize the field of quantum technology. The ability of OPX to measure, process and adapt and control pulses in real-time (much more than Boolean play/don’t play decisions) underscores its value in a wide array of quantum applications, from magnetic field sensing to more complex quantum computing tasks. 

Quantum Machines’ commitment to the development of cutting-edge quantum control technology not only propels current quantum research forward but also paves the way for future breakthroughs poised to revolutionize our technological landscape. 

Looking ahead, Quantum Machines continues to innovate, ensuring that OPX remains at the forefront of quantum technology with continuous firmware updates, and the brand-new OPX1000 control platform, which scales OPX capabilities to new heights. 

Your trusted quantum control partner – accelerate your research and development with us. 

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Contact us or request a demo to learn more about OPX+ and its scaled-up version OPX1000 to better understand how these unique processor-based controllers can accelerate your research. 

References

[1] I Zohar, B Haylock, Y Romach, M J Arshad, N Halay, N Drucker, R Stöhr, A Denisenko, Y Cohen, C Bonato, & A Finkler (2023). Real-time frequency estimation of a qubit without single-shot-readout. Quantum Science and Technology, 8(3), 035017.