Combinatorial optimization enhanced by shallow quantum circuits with 104 superconducting qubits

A pivotal task for quantum computing is to speed up solving problems that are both classically intractable and practically valuable. Among these, combinatorial optimization problems have attracted tremendous attention due to their broad applicability and natural fitness to Ising Hamiltonians. Here we propose a quantum sampling strategy, based on which we design an algorithm for accelerating solving the ground states of Ising model, a class of NP-hard problems in combinatorial optimization. The algorithm employs a hybrid quantum-classical workflow, with a shallow-circuit quantum sampling subroutine dedicated to navigating the energy landscape. Using up to 104 superconducting qubits, we demonstrate that this algorithm outputs favorable solutions against even a highly-optimized classical simulated annealing (SA) algorithm. Furthermore, we illustrate the path toward quantum speedup based on the time-to-solution metric against SA running on a single-core CPU with just 100 qubits. Our results indicate a promising alternative to classical heuristics for combinatorial optimization, a paradigm where quantum advantage might become possible on near-term superconducting quantum processors with thousands of qubits and without the assistance of error correction.