Conservation Laws in Quantum Database Search.

Recently, the correspondence between the air track scenario and quantum database search algorithm was revealed. The conservation laws of linear momentum and nonlinear kinetic energy in the former case, which involve sequential elastic collisions, have their analogs in the latter case. Obviously, probability normalization combined with the Born rule serves as an analog for kinetic energy conservation. Here we explore the linear conservation laws in a generic quantum database search. Regarding the non-uniform distribution of the marked state, the uneven state is initially prepared. In this way, the Grover diffusion operator results in a linear but nonphysical conservation law. On the other hand, in the CTC-assisted database search with the vast reduction of query complexity, the nonlinear instead of linear conservation laws are found. Finally, we conjecture that there are no conservation laws in the generalized Grover’s algorithm including the imaginary number i. [ABSTRACT FROM AUTHOR]