Generalized quantum PageRank algorithm with arbitrary phase rotations

SQUWALS: A Szegedy QUantum WALks Simulator

“…The other modification consist on transforming the reflection operator into an arbitrary phase rotation as: [14] R(𝜃)…”

“…where  is a set of marked nodes. On one hand, in order to mark node i in the first register, we have to invert the sign of the coefficients a ij ∀ j of the vector state in Equation (14). Given the matrix form Φ representing this vector, the index i in a ij refers to the columns.…”

“…Thus, it can be used over any arbitrary weighted graph. Moreover, it has been shown to be useful for problems of optimization, [8][9][10][11] classification, [12][13][14] quantum search, [15][16][17][18] and machine learning. [19] There has been research in implementing this algorithm in quantum circuits.…”

“…Furthermore, this algorithm enables the introduction of modifications as oracles, [17,18] which is not possible with the method based on the eigenvalues of the unitary operator, and complex phase extensions. [14,21] Moreover, we show how this algorithm can be implemented to simulate the recently proposed Semiclassical Szegedy walk, [22] and the quantum walk over mixed states.…”

“…Thus, it can be used over any arbitrary weighted graph. Moreover, it has been shown to be useful for problems of optimization, [ 8–11 ] classification, [ 12–14 ] quantum search, [ 15–18 ] and machine learning. [ 19 ]…”