Abstract
This article proposes the first discrete-time implementation of Rydberg quantum walk in multi-dimensional spatial space that could ideally simulate different classes of topological insulators. Using distance-selective exchange-interaction between Rydberg excited atoms in an atomic-array with dual lattice-constants, the new setup operates both coined and coin-less models of discrete-time quantum walk (DTQW). Here, complicated coupling tessellations are performed by global laser that exclusively excite the site at the anti-blockade region. The long-range interaction provides a new feature of designing different topologically ordered periodic boundary conditions. Limiting the Rydberg population to two excitations, coherent QW over hundreds of lattice sites and steps are achievable with the current technology. These features would improve the performance of this quantum machine in running the quantum search algorithm over topologically ordered databases as well as diversifying the range of topological insulators that could be simulated.
Highlights
There is a significant effort in making quantum hardwares that outperform classical counterparts in performing certain algorithms and simulating other complicated quantum systems
This paper proposes a new approach that improves the level of control over the interaction connectivities in the lattice, leading to Rydberg discrete-time quantum walk (DTQW) in multi-dimensions
The proposed model could be used for making an enriched form of Floquet topological insulators, as formulated and discussed in the appendix A2
Summary
There is a significant effort in making quantum hardwares that outperform classical counterparts in performing certain algorithms and simulating other complicated quantum systems. Particles that perform a quantum walk can take superposition of all possible paths through their environment simultaneously, leading to faster propagation and enhanced sensitivity to initial conditions [4, 5, 6] These properties provide an appealing basis for implementation of quantum algorithms like searching [7, 8, 9, 10, 11], quantum processing [12, 13, 14, 15, 16] and simulating the topological insulators [17]. This paper proposes a new approach that improves the level of control over the interaction connectivities in the lattice, leading to Rydberg DTQW in multi-dimensions. Benefitting from the long-range Rydberg interaction, the scheme features QW implementation on topologically ordered periodic boundary conditions. This article is supplemented by the application of the scheme in simulating multi-dimensional topological insulators
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