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

One of the major problems of most 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. Therefore, finding a way to make the best of today’s quantum hardware has become a critical issue. In this work, we propose an algorithm, called large-system sampling approximation (LSSA), to solve Ising problems with sizes up to N gb 2 N gb by an N gb -qubit gate-based quantum computer, and with sizes up to N an 2 N gb by a hybrid computational architecture of an N an -qubit quantum annealer and an N gb 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. After optimizing the VQE amplitude contributions, the approximated ground-state configuration, which is the approximated solution of a corresponding quadratic unconstrained binary optimization (QUBO) problem, will be determined. We apply the level-1 approximation of LSSA to solving fully-connected random Ising problems up to 160 variables using a 5-qubit gate-based quantum computer, and solving portfolio optimization problems up to 4096 variables using a 100-qubit quantum annealer and a 7-qubit gate-based quantum computer. Moreover, LSSA can be further extended to a deeper level of approximation. We demonstrate the use of the level-2 approximation of LSSA to solve the portfolio optimization problems up to 5120 ( N gb 2 2 N gb ) variables with pretty good performance by using just a 5-qubit ( N gb -qubit) gate-based quantum computer. 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.