Experimental Quantum Hamiltonian Learning (1703.05402v1)

Abstract: Efficiently characterising quantum systems, verifying operations of quantum devices and validating underpinning physical models, are central challenges for the development of quantum technologies and for our continued understanding of foundational physics. Machine-learning enhanced by quantum simulators has been proposed as a route to improve the computational cost of performing these studies. Here we interface two different quantum systems through a classical channel - a silicon-photonics quantum simulator and an electron spin in a diamond nitrogen-vacancy centre - and use the former to learn the latter's Hamiltonian via Bayesian inference. We learn the salient Hamiltonian parameter with an uncertainty of approximately $10^{-5}$. Furthermore, an observed saturation in the learning algorithm suggests deficiencies in the underlying Hamiltonian model, which we exploit to further improve the model itself. We go on to implement an interactive version of the protocol and experimentally show its ability to characterise the operation of the quantum photonic device. This work demonstrates powerful new quantum-enhanced techniques for investigating foundational physical models and characterising quantum technologies.

• The paper demonstrates a novel quantum Hamiltonian learning approach by integrating silicon-photonics with Bayesian inference.
• The paper achieves NV spin dynamics parameter estimation with a precision uncertainty around 10⁻⁵, noting algorithm saturation that suggests model refinements.
• The paper introduces an interactive protocol (IQLE) that boosts error resilience and scalability for calibrating complex quantum devices.

An Evaluation of Experimental Quantum Hamiltonian Learning

The paper "Experimental Quantum Hamiltonian Learning" presents an important stride in employing quantum-enhanced techniques to comprehend the dynamical properties of quantum systems through Hamiltonian learning. The authors propose and demonstrate a method that integrates a programmable silicon-photonics quantum simulator with Bayesian inference to ascertain the Hamiltonian parameters governing the dynamics of an electron spin in a nitrogen-vacancy (NV) center. This work is pivotal in expanding our capacity to accurately characterize quantum technologies and validate fundamental physical models, which is indispensable for the progression of quantum technologies and our understanding of quantum mechanics.

The primary focus of this paper is developing and applying Quantum Hamiltonian Learning (QHL), a novel approach that bestows efficiency in quantum system characterization and model validation. The authors utilized a silicon-photonics quantum simulator, interfacing it with the NV center electron spin through a classical computational channel. Their methodology allowed them to estimate the Hamiltonian parameter with an uncertainty in the vicinity of $10^{-5}$. Notably, the experiment revealed a saturation in the learning algorithm, indicative of possible oversights or simplifications in the initial Hamiltonian model. This observation propelled further refinement of the model, exemplifying the iterative process of model validation and enhancement inherent to the scientific method.

An interesting aspect of this research is the development of an interactive QHL protocol, extending the method's applicability to the characterization of quantum devices beyond single-parameter models to more complex quantum gates. By advancing beyond static simulation to interactive means, the authors significantly enlarge the scope for QHL's application in verifying and optimizing quantum technologies.

Furthermore, the paper elaborates on the intricacies of implementing Quantum Likelihood Estimation (QLE) and Interactive Quantum Likelihood Estimation (IQLE). In QLE, the prior distribution of parameters is iteratively updated based on likelihood computations derived from the simulator. In contrast, IQLE involves a bidirectional quantum channel that facilitates time-reversed transformations via trusted hardware to infer parameters efficiently. This novel approach offers heightened resilience to errors and scalability, portraying substantial promise for practical implementation across various quantum platforms.

The authors reported specific outcomes from the experimental applications of QLE. Within 50 steps, QLE learned the Rabi frequency of the NV spin dynamics with commendable precision when compared to traditional measurement techniques. Moreover, the self-verification of the quantum photonic device via IQLE marked another significant achievement, highlighting the robustness and potential of quantum-enhanced Bayesian inference for device calibration and validation.

The implications of this paper span both theoretical and practical domains. Theoretically, it accentuates the synergy of quantum and classical processing to overcome computational barriers in validating quantum models. Practically, the experimentation opens pathways for deploying quantum simulators to guarantee the accuracy of quantum devices, a necessity as these technologies scale in complexity and application.

In looking toward future developments, extending QHL's methodology to multi-qubit systems and varied quantum platforms could provide deeper insights into the modeling of complex quantum dynamics. As quantum hardware continues to progress, the techniques pioneered in this paper could become foundational in achieving efficient, scalable quantum technology characterization.

In conclusion, this paper integrates sophisticated techniques in quantum simulation and classical inference to present a robust and efficient framework for quantum Hamiltonian learning. It paves avenues for enhanced device calibration methods and provides substantial groundwork for the universal application of quantum-enhanced learning tools in quantum technology and foundational physics investigations.