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arXiv:2206.14681 · Quantum Science and Technology

Optimal quantum control via genetic algorithms for quantum state engineering in driven-resonator mediated networks

Jonathon Brown, Mauro Paternostro, Alessandro Ferraro

Published Jan 13, 2023• 15 citations
arXivHTMLPDF

Abstract

Abstract We employ a machine learning-enabled approach to quantum state engineering based on evolutionary algorithms. In particular, we focus on superconducting platforms and consider a network of qubits—encoded in the states of artificial atoms with no direct coupling—interacting via a common single-mode driven microwave resonator. The qubit-resonator couplings are assumed to be in the resonant regime and tunable in time. A genetic algorithm is used in order to find the functional time-dependence of the couplings that optimise the fidelity between the evolved state and a variety of targets, including three-qubit GHZ and Dicke states and four-qubit graph states. We observe high quantum fidelities (above 0.96 in the worst case setting of a system of effective dimension 96), fast preparation times, and resilience to noise, despite the algorithm being trained in the ideal noise-free setting. These results show that the genetic algorithms represent an effective approach to control quantum systems of large dimensions.

DOI
10.1088/2058-9565/acb2f2

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Abstract We investigate the optimization of graph topologies for quantum sensing networks designed to estimate weak magnetic fields. The sensors are modeled as spin systems governed by a transverse-field Ising Hamiltonian in thermal equilibrium at low temperatures. Using a genetic algorithm (GA), we evolve network topologies to maximize a perturbative spectral sensitivity measure, which serves as the fitness function for the GA. For the best-performing graphs, we compute the corresponding quantum Fisher information (QFI) to assess the ultimate bounds on estimation precision. To enable efficient scaling, we use the GA-generated data to train a deep neural network, allowing extrapolation to larger graph sizes where direct computation becomes prohibitive. Our results show that while both the fitness function and QFI initially increase with system size, the QFI exhibits a clear non-monotonic behavior—saturating and eventually declining beyond a critical graph size. This reflects the loss of superlinear scaling of the QFI, as the narrowing of the energy gap signals a crossover to classical scaling of the QFI with system size. The effect is reminiscent of the microeconomic law of diminishing returns: beyond an optimal graph size, further increases yield reduced sensing performance. This saturation and decline in precision are particularly pronounced under Kac scaling, where both the QFI and spin squeezing plateau or degrade with increasing system size. We also attribute observed even–odd oscillations in the spectral sensitivity measure and QFI to quantum interference effects in spin phase space, as confirmed by our phase-space analysis. These findings highlight the critical role of optimizing interaction topology—rather than simply increasing network size—and demonstrate the potential of hybrid evolutionary and learning-based approaches for designing high-performance quantum sensors.