Analog QAOA with Bayesian Optimisation on a neutral atom QPU

TL;DR

The paper demonstrates an analog QAOA implementation for MIS on a neutral-atom QPU, leveraging Rydberg blockade to encode the cost Hamiltonian and a fixed-amplitude mixing drive. It integrates Bayesian optimization to efficiently navigate the constrained parameter space under hardware noise, with SPAM-aware mitigation strategies to correct measurements. Numerical simulations and hardware experiments on Pasqal's Orion Alpha show that convergence to MIS is possible with a small number of measurements, though scaling to larger graphs requires improved noise mitigation and smarter parameter-space reduction. The work establishes a promising framework for resource-efficient quantum optimization on NISQ devices, highlighting both the potential and the practical bottlenecks of analog quantum algorithms on neutral-atom platforms.

Abstract

This study explores the implementation of the Quantum Approximate Optimisation Algorithm (QAOA) in its analog form using a neutral atom quantum processing unit to solve the Maximum Independent Set problem. The analog QAOA leverages the natural encoding of problem Hamiltonians by Rydberg atom interactions, while employing Bayesian Optimisation to navigate the quantum-classical parameter space effectively under the constraints of hardware noise and resource limitations. We evaluate the approach through a combination of simulations and experimental runs on Pasqal's first commercial quantum processing unit, Orion Alpha, demonstrating effective parameter optimisation and noise mitigation strategies, such as selective bitstring discarding and detection error corrections. Results show that a limited number of measurements still allows for a quick convergence to a solution, making it a viable solution for resource-efficient scenarios.

Figures (6)

• Figure 1: QAOA variational loop on a neutral atom quantum processor. The classical optimisation procedure, shown in the lower panel, is composed of: a cost estimation method, favouring MIS configurations; a decision-making Bayesian optimiser, navigating the parameter space with an exploitation-exploration strategy; and a sequence parametrisation step, building a new driving protocol from an initial parameter instance, to be sent to a neutral atom QPU. In the latter, shown in the upper panel, atoms are loaded, arranged into positions to reproduce the graph considered, and the quantum system is let to evolve according to the built driving protocol. Measuring the system provides one bitstring and a distribution is acquired by repeating the quantum procedure several times before being sent to the classical part. This hybrid loop runs until the QAOA converges.
• Figure 2: QAOA loops numerically simulated using Pulser. The evolution of the averaged approximation ratio $1-R$, the fidelity $F$ and the solution ratio $S_r$ (explained in the text) during optimisation are shown for various problem instances. In the first row, continuous lines show the results, varying the graph size with $N=4, 6, 8, 10$, while keeping fixed the number of shots to 1028. In the second row, dashed lines represent the results for a fixed graph of size, $N=6$, and increasing number of shots: $16, 64, 256, 1028$. The values shown are obtained averaging over 10 runs, light colour areas show the results $\pm \frac{1}{2}$ of standard deviation. Each run starts with $M=10$ training points and continues for $n_{\rm steps} = 190$ steps.
• Figure 3: Benchmark runs of the quantum dynamics with QAOA-like approach. (a) Sequences parametrised with QAOA-like approach are applied on the atomic register given in the inset. For increasing depth $p$, the control shapes of $\Omega$ and $\delta$ are displayed as sent to the atoms, i.e. distorted by the shaping device. The evolution of (b) the normalised approximation ratio $1-R_{100\%}$ and (c) the normalised truncated approximation ratio $1-R_{80\%}$ during the dynamics is obtained using noiseless numerical simulations (solid line) or numerical simulations with shot noise ($n_{\rm shots}=1000$) and detection errors ($\varepsilon=3\%$ and $\varepsilon^\prime=8\%$) (dashed). This enables to benchmark raw experimental measurements (filled dots) and SPAM corrected ones (white dots). The standard deviation (filled area-error bars) over the finite sampling with detection errors is obtained using the Jackknife resampling method Efron1981.
• Figure 4: MIS solution state obtained for the $N=15$ graph. The largest graph of $N=15$ qubits used for the experiment is plotted as an atomic register, with red qubits highlighting the MIS solution state we aim to find, corresponding to the target bitstring. The probability distribution obtained by sampling the final state produced using BO on QAOA is represented as a histogram. For each of the $2^{15}$ possible bitstrings, their probabilities $p_i$ were calculated as the ratio of the number of times they were measured to the total number of shots. The long tail of the histogram corresponds to states that were measured only once.
• Figure 5: Evolution of key metrics through the closed-loop optimisation on the $15-$qubit graph. (a) Experimental and (b) numerically simulated results compared. For each one we show during optimisation the following parameters (from left to right): the complement of the success rate $(1-R)$, fidelity $F$, correlation length $\ell$, distance between consecutive iterations $D_{i, i+1}$, and Gaussian Process Noise $\sigma$. Experimental data demonstrate gradual convergence and variations due to noise, while numerical simulations provide a controlled reference for comparison. Solid lines and markers indicate trends and discrete updates, respectively. Highlighted plateaus correspond to regions of stability in the optimisation dynamics.