Hybrid Gate-Based and Annealing Quantum Computing for Large-Size Ising Problems

One of the major problems of quantum computing applications is that the required number of qubits to solve a practical problem is much larger than that of today's quantum hardware. In this work, we introduce the large-system sampling approximation (LSSA) algorithm to solve Ising problems with sizes up to Ngb2Ngb by an Ngb-qubit gate-based quantum computer, and problems with sizes up to Nan2Ngb by a hybrid computational architecture of an Nan-qubit quantum annealer and an Ngb-qubit gate-based quantum computer. By dividing the full-system problem into smaller subsystem problems, the LSSA algorithm then solves the subsystem problems by either gate-based quantum computers or quantum annealers, and optimizes the amplitude contributions of the solutions of the different subsystems with the full-problem Hamiltonian by the variational quantum eigensolver (VQE) on a gate-based quantum computer to determine the approximated ground-state configuration. LSSA has polynomial time complexity and can be further extended to a deeper level of approximation with computational overhead that grows linearly with the problem size. The effects of different subsystem sizes, numbers of subsystems, and full problem sizes on the performance of LSSA are investigated on both simulators and real hardware. The completely new computational concept of the hybrid gate-based and annealing quantum computing architecture opens a promising possibility to investigate large-size Ising problems and combinatorial optimization problems, making practical applications by quantum computing possible in the near future.