Universal and optimal coin sequences for high entanglement generation in 1D discrete time quantum walks

Abstract

Entanglement is a key resource in many quantum information applications and achieving high values independently of the initial conditions is an important task. Here we address the problem of generating highly entangled states in a discrete time quantum walk irrespective of the initial state using two different approaches. First, we present and analyze a deterministic sequence of coin operators which produces high values of entanglement in a universal manner for a class of localized initial states. In a second approach, we directly optimize the sequence of coin operators using a reinforcement learning algorithm. While the amount of entanglement produced by the deterministic sequence is fully independent of the initial states considered, the optimized sequences achieve in general higher average values of entanglement that do however depend on the initial state parameters. Our proposed sequence and optimization algorithm are especially useful in cases where the initial state is not fully known or entanglement has to be generated in a universal manner for a range of initial states.

Generating highly entangled states via discrete-time quantum walks with Parrondo sequences

“…It was also seen that the strategies displayed Parrondo's paradox even when large number of steps are considered. Finally, we compare our results with the previous works [24,[29][30][31]. Fig.…”

“…Fig. 5 (a) suggests that, for any small time step we could find coin sequences that yield high average values of entanglement over a large number of initial states, which is particularly useful in cases where the initial state is not fully known, very noisy, or simply whenever it is required to generate highly entangled states independent of the initial state [31]. In Fig.…”

“…The comparison also suggested that, for any number of time steps t, one could find coin sequences that yield high average values of entanglement for a large number of initial states. This is advantageous in cases where the initial state is not fully known, very noisy, or simply whenever it is required to generate highly entangled states independent of the initial state [31]. It was also seen that the strategies displayed Parrondo's paradox even when large number of steps are considered.…”

“…Fig. 6 shows a comparison plot between Parrondo strategies and optimal entanglers [31]. Schmidt norm S was plotted for 3, 5, 7, 15 step DTQW's.…”

“…However, the experi-mental implementation requires potentially the full set of possible coin operators. Recently, two new approaches were proposed in [31]. The first approach presented an entangling sequence (Universal entangler) consisting of a deterministic sequence of Hadamard and Fourier coin operators that created a universal amount of entanglement for a class of localized initial states with vanishing relative phase.…”