Optimized quantum singular value thresholding algorithm based on a hybrid quantum computer

Quantum singular value thresholding (QSVT) algorithm, as a core module of many mathematical models, seeks the singular values of a sparse and low rank matrix exceeding a threshold and their associated singular vectors. The existing all-qubit QSVT algorithm demands lots of ancillary qubits, remaining a huge challenge for realization on nearterm intermediate-scale quantum computers. In this paper, we propose a hybrid QSVT (HQSVT) algorithm utilizing both discrete variables (DVs) and continuous variables (CVs). In our algorithm, raw data vectors are encoded into a qubit system and the following data processing is fulfilled by hybrid quantum operations. Our algorithm requires O[log(MN)] qubits with O(1) qumodes and totally performs O(1) operations, which significantly reduces the space and runtime consumption.     

Au-Bi2Sr1.94La0.06CuO6+δ点接触中的Andreev反射：能隙函数及其温度关系

我们用Ａｕ 针尖对过掺杂的Ｂｉ２Ｓｒ１ ．９４Ｌａ０ ．０６ＣｕＯ６ ＋ δ（Ｂｉ２２０１） 单晶进行点接触隧道谱测量．在Ｔｃ 以下观测到典型的Ａｎｄｒｅｅｖ 反射．用扩展的ＢＴＫ 理论拟合实验数据，发现除了ｄ 波外还必须考虑ｓ 波成份才能较好的拟合，并且ｓ 波含量随不同的实验而不同．这种含量变化可能和针尖与单晶表面的接触程度有关．实验观测到的总能隙随温度的关系偏离ＢＣＳ的能隙温度关系