Emergent-Coupling-Based Ansatz Evaluated on a Superconducting Quantum Processor

Abstract

The performance of the variational quantum eigensolver depends critically on the choice of ansatz. In this work, we experimentally evaluate the emergent-coupling-based ansatz (ECBA), a physically motivated variational ansatz for disordered systems. The ECBA is based on a renormalization (semi-)group approach to determine the dominant effective couplings and construct an asymptotically correct ground state. A variational layer based on the location and strength of the effective couplings then corrects the limitations of the renormalization group approach while preserving shallow circuits that capture the essential long-range entanglement structure and balance local correlations. We implement the ECBA on superconducting quantum processors and benchmark it on disordered Heisenberg chain models. Using classically pre-optimized parameters and error mitigation techniques, we study systems of up to 30 qubits and observe a relative experimental energy accuracy of 96.41% for the largest system. Furthermore, we find that the ECBA can be efficiently embedded on hardware with two-dimensional square-lattice connectivity. We compare to commonly used hardware efficient ansätze and observe that the ECBA achieves significantly higher accuracy at a similar gate count.