High dimensional counterdiabatic quantum computing

The digital version of adiabatic quantum computing enhanced by counterdiabatic driving, known as digitized counterdiabatic quantum computing, has emerged as a paradigm that opens the door to fast and low-depth algorithms. In this work, we explore the extension of this paradigm to high-dimensional systems. Specifically, we consider qutrits in the context of quadratic problems, obtaining the qutrit Hamiltonian codifications and the counterdiabatic drivings. Our findings show that qutrits can improve the solution quality up to 90 times compared to the qubit counterpart. We tested our proposal on 1000 random instances of the multiway number partitioning, max 3-cut, and portfolio optimization problems, demonstrating that, in general, without prior knowledge, it is better to use qutrits and, apparently, high-dimensional systems in general instead of qubits. Finally, considering the state-of-the-art quantum platforms, we show the experimental feasibility of our high-dimensional counterdiabatic quantum algorithms at least in a fully digital form. This work paves the way for the efficient codification of optimization problems in high-dimensional spaces and their efficient implementation using counterdiabatic quantum computing.