Symmetry-enhanced counterdiabatic quantum algorithm for qudits

Qubit-based variational quantum algorithms have undergone rapid development in recent years but still face several challenges. Here, we introduce a symmetry-based enhancement to digitized counterdiabatic quantum algorithms, applicable for qudits of any dimension. This approach offers three types of compression compared to conventional variational circuits. First, compression in the circuit depth is achieved by counterdiabatic protocols. Second, information about the problem is compressed by replacing qubits with qudits, allowing for a more efficient representation of the problem. Finally, the number of parameters is reduced by employing the symmetries of the system. We illustrate this approach by tackling a graph-based optimization problem -3-, a highly entangled state preparation, the qutrit <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>W</a:mi></a:math> state, and a two-body only antiferromagnetic Ising problem. As our numerical results show, we achieve a better convergence with a lower circuit depth and less measurement overhead, albeit with some identified limitations for which we propose a work-around. This work leads to a better design of shallow variational quantum circuits, improving the feasibility of their implementation on near-term qudit devices.