Designing quantum experiments with a genetic algorithm

Abstract

We introduce a genetic algorithm that designs quantum optics experiments for engineering quantum states with specific properties. Our algorithm is powerful and flexible, and can easily be modified to find methods of engineering states for a range of applications. Here we focus on quantum metrology. First, we consider the noise-free case, and use the algorithm to find quantum states with a large quantum Fisher information (QFI). We find methods, which only involve experimental elements that are available with current or near-future technology, for engineering quantum states with up to a 100-fold improvement over the best classical state, and a 20-fold improvement over the optimal Gaussian state. Such states are a superposition of the vacuum with a large number of photons (around 80), and can hence be seen as Schrödinger-cat-like states. We then apply the two most dominant noise sources in our setting -photon loss and imperfect heralding -and use the algorithm to find quantum states that still improve over the optimal Gaussian state with realistic levels of noise. This will open up experimental and technological work in using exotic non-Gaussian states for quantum-enhanced phase measurements. Finally, we use the Bayesian mean square error to look beyond the regime of validity of the QFI, finding quantum states with precision enhancements over the alternatives even when the experiment operates in the regime of limited data.PACS numbers:

Using states with a large photon number variance to increase quantum Fisher information in single-mode phase estimation

“…For the case that the photon number distribution is unbounded, on the other hand, we have discussed several particular photon number statistics which show Heisenberg scaling and sub-Heisenberg scaling without requiring nonlinear effects. The states discussed in this work have rarely been experimentally realized [39], but state-of-the-art quantum state engineering technique would enable the generation of an arbitrary photon number superposition via quantum circuit optimization [42][43][44]. In the scenario when a priori probability distribution of the parameter is unknown and the number of measurements is limited, those states may not be useful since they are still Heisenberg-scaling limited with n = N N tot , the total average number of photons being used.…”

“…Note that H 0&M in the order of 10 5 can be theoretically attained by increasing M even when N is fixed. The 0&M state has been realized up to = M 18 in the harmonic motion of a single trapped ion [39], and the states with higher M can also be realized in quantum optical circuits with current technology [42][43][44].…”

“…It would require the development of quantum technology geared towards engineering states with photon number statistics on demand. Recently, an arbitrary photon number statistics has been shown to be producible with current technology through quantum optical circuits being optimized for a target photon number statistics [40][41][42][43]. Having the ability to prepare such quantum states unlocks their use for various purposes in quantum applications [44].…”

Bayesian multiparameter quantum metrology with limited data

“…More concretely, if we recall that¯ mse ≈ 0.168 in such scenario, and noticing that¯ prior = π 2 /48 ≈ 0.206, then a single shot can improve our knowledge about (θ 1 , θ 2 ) by 18% with respect to the prior uncertainty, having defined the improvement as (¯ prior −¯ mse )/¯ prior multiplied by 100%. Further examples of this notion of improvement can be found in [68].…”

A hybrid machine learning algorithm for designing quantum experiments

“…To assess the suitability of a given state, we require a fitness function that takes as input a quantum state and outputs a number -the fitness value -that quantifies whether the state has the properties we desire or not. Our previous works largely focused on quantum metrology, where our algorithm found quantum states with substantial improvements over the alternatives in the literature [4,14]. While in [4,14] the fitness function assessed the phase-measuring capabilities of the states, in this paper instead we look at producing a range of useful and interesting states (introduced below) to a high fidelity, and hence we use as our fitness function the fidelity to our target states.The search space for our genetic algorithm is huge, which means that typically the algorithm has to simulate and evaluate a vast number of quantum optics experiments in order to finally find strong solutions.…”