Digital-analog quantum genetic algorithm using Rydberg-atom arrays

TL;DR

A quantum genetic algorithm within the DAQC framework using a Rydberg-atom emulator that employs single-qubit operations in the digital domain and a global driving interaction based on the Rydberg Hamiltonian in the analog domain is proposed.

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.

Figures (14)

• Figure 1: Schematic of the protocol: selection of candidates, crossover and mutations happens in the classical computer, while the evaluation of candidates happens in the quantum computer.
• Figure 2: Two qubit ansatz used for the H2 molecule. The ansatz is composed of RX, RY and RZ single qubit rotations and two global interacting Hamiltonians.
• Figure 3: Schematic of the crossover: two parent candidates (Candidate 1 and Candidate 2) are combined to generate two new solutions, New Candidate 3 and New Candidate 4. For the sake of simplification, the horizontal solid black line represents multiple qubits, and the different gates are applied to all of those multiple qubits.
• Figure 4: Numerical results (blue marker) of the quantum genetic algorithm with our digital-analog protocol for the $\rm H_2$ molecule. The black dashed line shows the exact Hamiltonian diagonalization. The gray shades indicate respectively errors of 10, 5, and 1%. All the points from the protocol fall within the 1% error zone.
• Figure 5: Ground state overlap (red solid line) and energy of the best solution found (blue dotted line) as a function of the number of protocol iterations for the $\rm H_2$ molecule, for an inter-atomic distance of 1.5 Å. The exact ground state energy is also shown (black dashed line).