Digital-analog quantum genetic algorithm using Rydberg-atom arrays

TL;DR

This paper introduces a digital-analog quantum genetic algorithm using Rydberg-atom arrays, demonstrating high-accuracy energy estimations for molecules with promising efficiency and fidelity in the noisy intermediate-scale quantum era.

Contribution

It proposes a novel quantum genetic algorithm within the DAQC framework utilizing Rydberg-atom arrays, combining digital and analog operations for improved quantum computation.

Findings

Achieved less than 1% error in energy estimations for molecular Hamiltonians.

State overlaps nearing 1 indicate high accuracy of the algorithm.

Computation times range from minutes to days depending on circuit size.

Abstract

Digital-analog quantum computing (DAQC) combines digital gates with analog operations, offering an alternative paradigm for universal quantum computation. This approach leverages the higher fidelities of analog operations and the flexibility of local single-qubit gates. In this paper, we propose a quantum genetic algorithm within the DAQC framework using a Rydberg-atom emulator. The algorithm employs single-qubit operations in the digital domain and a global driving interaction based on the Rydberg Hamiltonian in the analog domain. We evaluate the algorithm performance by estimating the ground-state energy of Hamiltonians, with a focus on molecules such as $\rm H_2$, $\rm LiH$, and $\rm BeH_2$. Our results show energy estimations with less than 1% error and state overlaps nearing 1, with computation times ranging from a few minutes for $\rm H_2$ (2-qubit circuits) to one to two days for $\rm LiH$ and $\rm BeH_2$ (6-qubit circuits). The gate fidelities of global analog operations further underscore DAQC as a promising quantum computing strategy in the noisy intermediate-scale quantum era.