Quantum–inspired Methods for Training Machine Learning Models

Machine learning model training, which ultimately optimizes a model’s cost function is usually a time- consuming and computationally intensive process on classical computers. This has been more intense due to the in- creased demand for large-scale data analysis, requiring unconventional computing paradigms like quantum computing to enhance training efficiency. Adiabatic quantum computers have excelled at solving optimization problems, which require the quadratic unconstrained binary optimization (QUBO) format of the problem of interest. In this study, the squared error minimization in the multiple linear regression model is reformulated as a QUBO problem enabling it to be solved using D-wave adiabatic quantum computers. Same formulation was used to obtain a solution using gate-based algorithms such as quantum approximate optimization algorithm (QAOA) and sampling variational quantum eigensolver (VQE) im- plemented via IBM Qiskit. The results obtained through these approaches in the context of runtime and mean squared error(MSE) were analyzed and compared to the classical approaches. Our experimental results indicate a runtime ad- vantage in the D-wave annealing approach over the classical Scikit learn regression approach. The time advantage can be observed when N>524288 compared to Sklearn Linear Regression and when N>65536 compared to Sklearn SGDRegressor. Support vector machine induced neural networks, where the margin-based entropy loss is converted into a QUBO with Lagrangian approach is also focused in this study concerning the applicability for nonlinear models.