A Low-Complexity Quantum Principal Component Analysis Algorithm

In this article, we propose a low-complexity quantum principal component analysis (qPCA) algorithm. Similar to the state-of-the-art qPCA, it achieves dimension reduction by extracting components of data matrix, rather than all registers, so that samples measurement required can be reduced considerably. Both our qPCA and Lin’s are based on singular-value thresholding (QSVT). The key is combine QSVT, modified QSVT obtain superposition components. algorithm, however, modify replacing rotation-controlled operation with controlled-not As result, small trick makes circuit much simpler. Particularly, proposed requires three phase estimations, while five estimations. Since runtime mainly comes from roughly 3/5 state art. We simulate IBM computing platform, simulation result verifies yields expected state.