Topological data analysis on noisy quantum computers
This addresses the bottleneck of high computational demands in TDA for data scientists, offering a near-term quantum solution, though it is incremental as it builds on prior quantum TDA proposals.
The authors tackled the computational impracticality of classical topological data analysis (TDA) for high-dimensional data by developing NISQ-TDA, a quantum machine learning algorithm with short circuit-depth that achieved successful execution on quantum devices and simulators, showing preliminary robustness to noise.
Topological data analysis (TDA) is a powerful technique for extracting complex and valuable shape-related summaries of high-dimensional data. However, the computational demands of classical algorithms for computing TDA are exorbitant, and quickly become impractical for high-order characteristics. Quantum computers offer the potential of achieving significant speedup for certain computational problems. Indeed, TDA has been purported to be one such problem, yet, quantum computing algorithms proposed for the problem, such as the original Quantum TDA (QTDA) formulation by Lloyd, Garnerone and Zanardi, require fault-tolerance qualifications that are currently unavailable. In this study, we present NISQ-TDA, a fully implemented end-to-end quantum machine learning algorithm needing only a short circuit-depth, that is applicable to high-dimensional classical data, and with provable asymptotic speedup for certain classes of problems. The algorithm neither suffers from the data-loading problem nor does it need to store the input data on the quantum computer explicitly. The algorithm was successfully executed on quantum computing devices, as well as on noisy quantum simulators, applied to small datasets. Preliminary empirical results suggest that the algorithm is robust to noise.