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arXiv:2312.13870

Variational quantum algorithm for enhanced continuous variable optical phase sensing

Jens Arnbak Holbøll Nielsen, Mateusz Kiciński, Tummas Napoleon Arge, Kannan Vijayadharan, Jonathan Foldager, Johannes Borregaard, Johannes Jakob Meyer, Jonas Schou Neergaard-Nielsen, Tobias Gehring, Ulrik L. Andersen

Published Dec 21, 2023• 0 citations
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Abstract

Variational quantum algorithms (VQAs) are hybrid quantum-classical approaches used for tackling a wide range of problems on noisy intermediate-scale quantum (NISQ) devices. Testing these algorithms on relevant hardware is crucial to investigate the effect of noise and imperfections and to assess their practical value. Here, we implement a variational algorithm designed for optimized parameter estimation on a continuous variable platform based on squeezed light, a key component for high-precision optical phase estimation. We investigate the ability of the algorithm to identify the optimal metrology process, including the optimization of the probe state and measurement strategy for small-angle optical phase sensing. Two different optimization strategies are employed, the first being a gradient descent optimizer using Gaussian parameter shift rules to estimate the gradient of the cost function directly from the measurements. The second strategy involves a gradient-free Bayesian optimizer, fine-tuning the system using the same cost function and trained on the data acquired through the gradient-dependent algorithm. We find that both algorithms can steer the experiment towards the optimal metrology process. However, they find minima not predicted by our theoretical model, demonstrating the strength of variational algorithms in modelling complex noise environments, a non-trivial task.

DOI
10.48550/arxiv.2312.13870

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In recent years, variational quantum algorithms (VQA) have been receiving a great deal of attention, demonstrating their applicability in a wide range of tasks and implementable even in the noisy quantum processors currently available [1]. A VQA is a hybrid quantum-classical algorithm where a problem is encoded in a cost function that can be efficiently evaluated on a parametric quantum device and the minimum represents the desired solution. A classical optimizer can then be used to tune the parameters of the quantum device in order to minimize the loss function and find the optimal solution (Fig. 1). In the field of quantum computing, one of the main promising platforms is based on the use of single photons and integrated photonic circuits since photons are a natural choice for transferring information and have different degree of freedom that can be to encode the information. Moreover the use of integrated photonic allow the realization of compact and table complex interferometers with a high number of control parameters. Even if there are few applications [2], [3], VQA with photonic platforms remains a relatively unexplored subject. One of the main problems is the application of the classical optimizer to the photonic platform since most of the algorithms are based on the estimation of the gradient of the cost function with the finite difference method but that can not be applied to a noisy apparatus.
Variational quantum algorithms (VQAs) offer a promising path toward using near-term quantum hardware for applications in academic and industrial research. These algorithms aim to find approximate solutions to quantum problems by optimizing a parametrized quantum circuit using a classical optimization algorithm. A successful VQA requires fast and reliable classical optimization algorithms. Understanding and optimizing how off-the-shelf optimization methods perform in this context is important for the future of the field. In this work, we study the performance of four commonly used gradient-free optimization methods [sequential least-squares quadratic programming, constrained optimization by linear approximations, the covariance matrix adaptation evolutionary strategy (CMA-ES), and the simultaneous perturbation stochastic approximation (SPSA)] to find ground-state energies of a range of small chemistry and material science problems. We test a telescoping sampling scheme (where the accuracy of the cost-function estimate provided to the optimizer is increased as the optimization converges) for all methods, demonstrating mixed results across our range of optimizers and problems chosen. We further hyperparameter tune two of the four optimizers (CMA-ES and SPSA) across a large range of models and demonstrate that with appropriate hyperparameter tuning, CMA-ES is competitive with and sometimes outperforms SPSA (which is not observed in the absence of hyperparameter tuning). Finally, we investigate the ability of an optimizer to beat the ``sampling-noise floor'' given by the sampling noise of each cost-function estimate provided to the optimizer. Our results demonstrate the necessity for tailoring and hyperparameter tuning known optimization techniques for inherently noisy variational quantum algorithms and that the variational landscape that one finds in a VQA is highly problem and system dependent. This provides guidance for future implementations of these algorithms in experiments.
Abstract Variational quantum metrology represents a powerful tool to optimize estimation strategies, resulting particularly beneficial for multiparameter estimation problems that often suffer from limitations due to the curse of dimensionality and computational complexity. To overcome these challenges, we develop a variational approach able to efficiently optimize a quantum multiphase sensor. Leveraging the reconfigurability of an integrated photonic device, we implement a hybrid quantum-classical feedback loop able to enhance the estimation performances. The quantum circuit evaluations are used to compute the system partial derivatives by applying the parameter-shift rule, and thus reconstruct experimentally the Fisher information matrix. This in turn is adopted as the cost function of a classical learning algorithm run to optimize the measurement settings. Our experimental results showcase significant improvements in estimation accuracy and noise robustness, highlighting the potential of variational techniques for practical applications in quantum sensing and more generally in quantum information processing using photonic circuits.