Abstract. We propose a scheme for perfect transfer of an unknown qubit state via the discrete-time quantum walk on a line or a circle. For this purpose, we introduce an additional coin operator which is applied at the end of the walk. This operator does not depend on the state to be transferred. We show that perfect state transfer over an arbitrary distance can be achieved only if the walk is driven by an identity or a flip coin operator. Other biased coin operators and Hadamard coin allow perfect state transfer over finite distances only. Furthermore, we show that quantum walks ending with a perfect state transfer are periodic.

We introduce the Peierls substitution to a two-dimensional discrete-time quantum walk on a square lattice to examine the spreading dynamics and the coin-position entanglement in the presence of an artificial gauge field. We use the ratio of the magnetic flux through the unit cell to the flux quantum as a control parameter. For a given flux ratio, we obtain faster spreading for a small number of steps and the walker tends to be highly localized around the origin. Moreover, the spreading of the walk can be suppressed and decreased within a limited time interval for specific rational values of flux ratio. When the flux ratio is an irrational number, even for a large number of steps, the spreading exhibit diffusive behavior rather than the well-known ballistic one as in the classical random walk and there is a significant probability of finding the walker at the origin. We also analyze the coin-position entanglement and show that the asymptotic behavior vanishes when the flux ratio is different from zero and the coin-position entanglement become nearly maximal in a periodic manner in a long time range.

We reveal the emergence of environment-induced spontaneous synchronization between two spin-1/2 quantum objects in a collision model setting. In particular, we determine the conditions for the dynamical establishment of synchronous evolution between local spin observables of a pair of spins undergoing open-system dynamics in the absence of an external drive. Exploiting the versatility of the collision model framework, we show that the formation of quantum or classical correlations between the principal spin pair are of no significant relevance to the manifestation of spontaneous quantum synchronization between them. Furthermore, we discuss the consequences of thermal effects on the environmental spins for the emergence of quantum synchronization.

The quantum permutation algorithm provides computational speed-up over classical algorithms for determining the parity of a given cyclic permutation. For its n-qubit implementations, the number of required quantum gates scales quadratically with n due to the quantum Fourier transforms included. We show here for the n-qubit case that the algorithm can be simplified so that it requires only O(n) quantum gates, which theoretically reduces the complexity of the implementation. To test our results experimentally, we utilize IBM's 5-qubit quantum processor to realize the algorithm by using the original and simplified recipes for the 2-qubit case. It turns out that the latter results in a significantly higher success probability which allows us to verify the algorithm more precisely than the previous experimental realizations. We also verify the algorithm for the first time for the 3-qubit case with a considerable success probability by taking the advantage of our simplified scheme.

We explore the environment-induced synchronization phenomenon in two-level systems in contact with a thermal dissipative environment. We first discuss the conditions under which synchronization emerges between a pair of two-level particles. That is, we analyze the impact of various model parameters on the emergence of (anti-)synchronization such as the environment temperature, the direct interaction between the particles, and the distance between them controlling the collectivity of the dissipation. We then enlarge the system to be composed of three two-level atoms to study the mutual synchronization between different particle pairs. Remarkably, we observe in this case a rich synchronization dynamics which stems from different possible spatial configurations of the atoms. Particularly, in sharp contrast with the two-atom case, we show that when the three atoms are in close proximity, appearance of anti-synchronization can be obstructed across all particle pairs due to frustration.