Leveraging qudits: high-dimensional Grover adaptive search algorithm for solving quadratic and higher-order unconstrained binary optimization problems

Abstract The Grover Adaptive Search (GAS) is an innovative approach offering solutions to optimization problems thanks to quadratic speedup enabled by the Grover Search Algorithm. However, the need for more qubits, depending on the number of variables in optimization problems, creates problems in providing optimal solutions. The central premise of this study is the principle that d -dimension is more efficient than 2-dimension could lead to more advantageous results when the GAS algorithm is adapted to d -dimension. To that end, this study adapts the GAS algorithm to the d -dimension drawing on quantum computing in the d -dimension, allowing computing using fewer quantum resources, namely, qudits. The proposed algorithm is validated against the Quadratic and Higher-Order Unconstrained Binary Optimization (QUBO-HUBO). This study concludes the d -dimensional GAS algorithm achieves solutions using fewer qudits for these problems in the QUBO and the HUBO. This study underscores the progress achieved in the advancement of high-dimensional quantum computing.