Vibrational molecular quantum computing: Basis set independence and theoretical realization of the Deutsch–Jozsa algorithm

Abstract

The phase of quantum gates is one key issue for the implementation of quantum algorithms. In this paper we first investigate the phase evolution of global molecular quantum gates, which are realized by optimally shaped femtosecond laser pulses. The specific laser fields are calculated using the multitarget optimal control algorithm, our modification of the optimal control theory relevant for application in quantum computing. As qubit system we use vibrational modes of polyatomic molecules, here the two IR-active modes of acetylene. Exemplarily, we present our results for a Pi gate, which shows a strong dependence on the phase, leading to a significant decrease in quantum yield. To correct for this unwanted behavior we include pressure on the quantum phase in our multitarget approach. In addition the accuracy of these phase corrected global quantum gates is enhanced. Furthermore we could show that in our molecular approach phase corrected quantum gates and basis set independence are directly linked. Basis set independence is also another property highly required for the performance of quantum algorithms. By realizing the Deutsch-Jozsa algorithm in our two qubit molecular model system, we demonstrate the good performance of our phase corrected and basis set independent quantum gates.

Implementation of simple logic gates on gold–ammonia bonding patterns in different charge states

“…Encoding classical bits into bonds is somewhat analogous to the approach known as vibrational quantum computing [35][36][37][38] in the sense that it requires addressable bonds (which each corresponds to a vibrational mode) as the inputs to the logic gate. The difference is that in our approach, the changes of the bonding patterns due to an external perturbation (charge alternation or optical excitation) implement the logic gate, not the transitions within the vibrational manifold induced by external IR laser pulses as is the case in vibrational quantum computing.…”

Quantum Computing and Optimal Control Theory

“…Likewise, we must impose additional constraints for the other quantum gates we have in mind. As de Vivie-Riedle and coworkers pointed out 17 , the phase correction of quantum gates is one of the key issues for the implementation of quantum algorithms. Therefore, for two-qubit systems, z has to be more than 4.…”

“…Recently, de Vivie-Riedle and coworkers 17 proposed a method for phase-correct and basis-set-independent quantum gates in order to perform the correct universal quantum computing. As far as we know, their work is the first one where the phase correction was taken into account adequately.…”

Simulation of the elementary evolution operator with the motional states of an ion in an anharmonic trap

“…4(c) and 4(d) show the gate optimum field E F (t) [Eq. (24)] and its spectrum. The background at high frequencies has been filtered.…”