Direct entanglement ansatz learning (DEAL) with ZNE on error-prone superconducting qubits

Abstract: Quantum combinatorial optimization algorithms typically face challenges due to complex optimization landscapes featuring numerous local minima, exponentially scaling latent spaces, and susceptibility to quantum hardware noise. In this study, we introduce Direct Entanglement Ansatz Learning (DEAL), wherein we employ a direct mapping from quadratic unconstrained binary problem parameters to quantum ansatz angles for cost and mixer hamiltonians, which improves the convergence rate towards the optimal solution. Our approach exploits a quantum entanglement-based ansatz to effectively explore intricate latent spaces and zero noise extrapolation (ZNE) to greatly mitigate the randomness caused by crosstalk and coherence errors. Our experimental evaluation demonstrates that DEAL increases the success rate by up to 14% compared to the classic quantum approximation optimization algorithm while also controlling the error variance. In addition, we demonstrate the capability of DEAL to provide near optimum ground energy solutions for travelling salesman, knapsack, and maxcut problems, which facilitates novel paradigms for solving relevant NP-hard problems and extends the practical applicability of quantum optimization using noisy quantum hardware.