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 propose an algorithm, called large-system sampling approximation (LSSA), to solve Ising problems with sizes up to N_gb2^N_gb by an N_gb-qubit gate-based chip, and with sizes up to N_an2^N_gb by a hybrid computational architecture of an N_an-qubit quantum annealer and an N_gb-qubit gate-based chip. 

LSSA algorithm solves the subsystem problems by either gate-based quantum chips 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). After optimizing the VQE amplitude contributions, the approximated ground-state, which is the approximated solution of a corresponding quadratic unconstrained binary optimization (QUBO) problem, will be determined. 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.