Evolution of quantum correlations in quantum algorithms

Abstract

Quantum systems are often correlated in classically inaccessible ways. Hence non-classical correlations in a system are signatures of genuinely quantum systems. Hence quantum correlations are precious resources for quantum information processing and need to be preserved. It’s useful to study their dynamics, evolution and employ methods to protect them from decoherence during computational processes. Dynamical Decoupling (DD) is a decoherence suppression scheme that decouples system & environment interactions by performing a sequence of rapid flips on the system. The evolution of quantum discord for the two-qubit case of Grover's algorithm is used as a testbed to understand the effectiveness of DD. The evolution of quantum discord in Grover’s algorithm for a two-qubit system has been studied. Then, a dephasing noise is introduced into the system to realistically observe the evolution of discord during various stages of the algorithm. DD is integrated into the gate operations of Grover’s algorithm, and the evolution of discord for different DD schemes based on π and non-π pulses are simulated. Realistic pulses are seldom perfect, so this is taken into account by simulating the evolution of discord with DD in the presence of radio-frequency field inhomogeneities (RFI). It was experimentally found that some DD sequences based on π/2 pulses performed as well as, if not, better than DD based on π pulses. DD sequences based on different non-π pulse angles were tested for their performance in decoherence suppression in Grover’s algorithm through simulations. Unlike the conventional notion that dynamical decoupling is achieved only by π pulses, we show by numerical analysis that if properly incorporated into control sequences, even non-π pulses can bring about efficient dynamical decoupling, for low noise amplitudes.