Fig. 1: A schematic diagram illustrating the p = 1 photonic counterdiabatic quantum optimization (PCQO) algorithm.
From: Photonic counterdiabatic quantum optimization algorithm
a Encoding phase: a logical problem, denoted as Hp, is encoded into F(n) or F(x) based on the problem type. The mixer Hm is introduced satisfying the non-commutativity relation, enabling the generation of the operator pool using the nested commutator method. b Processing phase: the operators from \({\mathcal{A}}=\{{A}_{\lambda }^{(2)}\}\) are exponentiated and employed as a circuit ansatz Ucd(θ) with adjustable parameters θ = {θ1, θ2, …, θQ}. Q shows the total number of parameters. The algorithm initiates with random parameter values and iteratively updates them through classical optimization, aiming to determine F(〈n〉) or F(〈x〉) until convergence is achieved. c Decoding phase: performing measurements and extracting solutions from the minimum values, \({F}_{\min }(\langle {\bf{n}}\rangle )\) or \({F}_{\min }(\langle {\bf{x}}\rangle )\), enables the representation of solutions in the form of the mean photon number 〈n〉 or the mean quadrature values 〈x〉.
