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The flat band system is an ideal quantum platform to investigate the kaleidoscope created by the electron-electron correlation effects. The central ingredient of realizing a flat band is to find its compact localized states. In this work, we develop a systematic way to generate the compact localized states by designing destructive interference pattern from 1-dimensional chains. A variety of 2-dimensional new flat band systems are constructed with this method. Furthermore, we show that the method can be extended to generate the compact localized states in multi-orbital systems by carefully designing the block hopping scheme, as well as in quasicrystal and disorder systems.

Coarse-Grained Reconfigurable Arrays (CGRAs) are promising to have low power consumption and high energy-efficiency characteristics as accelerators. Recent years, many research works focus on improving the programmability of the CGRAs by enabling the fast reconfiguration during execution. The performance of these CGRAs critically hinges upon the scheduling power of the compiler. One of the critical challenges is to reduce memory access conflicts using static compilation techniques. Memory accessing conflict brings the synchronization overhead which causes the pipelining stall and reduces CGRA performance. Existing compilers usually tackle this challenge by orchestrating the data placement of the on-chip global memory (OGM) in CGRA to let the parallel memory accesses avoid the bank conflict. However, we find bank conflict is not the only reason that causes the memory access conflicts. In some CGRAs, the bandwidth of the data network between OGM and processing element array (PEA) is also limited due to the low power design principle. The unbalanced network bandwidth loads is another reason that causes memory access conflicts. Furthermore, the redundant data access across iterations is one of the primary causes of memory access conflicts. Based on these observations, we provide a comprehensive and generalized compilation flow to reduce the memory conflicts. Firstly, we develop a loop transformation model to maximize the inter-iteration data reuse of the loops to reduce the memory accessing operations under the software pipelining scheme. Secondly, we enhance the bandwidth utilization of the network between OGM and PEA and avoid the bank conflict by providing a conflict-aware spatial mapping algorithm which can be easily integrated into existing CGRA modulo scheduling compilation flow. Experimental results show our method is capable of improving performance by an average of 44% comparing with state-of-the-art CGRA compiling flow.