Matrix-product-state simulation of an extended Brüschweiler bulk-ensemble database search

Abstract

Br\uschweiler's database search in a spin Liouville space can be efficiently simulated on a conventional computer without error as long as the simulation cost of the internal circuit of an oracle function is polynomial, unlike the fact that in true NMR experiments, it suffers from an exponential decrease in the variation of a signal intensity. With the simulation method using the matrix-product-state proposed by Vidal [G. Vidal, Phys. Rev. Lett. 91, 147902 (2003)], we perform such a simulation. We also show the extensions of the algorithm without utilizing the $J$-coupling or $DD$-coupling splitting of frequency peaks in observation: searching can be completed with a single query in polynomial postoracle circuit complexities in an extension; multiple solutions of an oracle can be found in another extension whose query complexity is linear in the key length and in the number of solutions (this extension is to find all of marked keys). These extended algorithms are also simulated with the same simulation method.