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Quantum second-order optimization algorithm for general polynomials
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DOI：10.1007/s11433-021-1725-9.png)
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Abstract
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Quantum optimization algorithms can outperform their classical counterpart and are key in modern technology. The second-order optimization algorithm (the Newton algorithm) is a critical optimization method, speeding up the convergence by employing the second-order derivative of loss functions in addition to their first derivative. Here, we propose a new quantum second-order optimization algorithm for general polynomials with a computational complexity of O(poly(log d)). We use this algorithm to solve the nonlinear equation and learning parameter problems in factorization machines. Numerical simulations show that our new algorithm is faster than its classical counterpart and the first-order quantum gradient descent algorithm. While existing quantum Newton optimization algorithms apply only to homogeneous polynomials, our new algorithm can be used in the case of general polynomials, which are more widely present in real applications.
Keywords:
quantum computation
quantum algorithm
optimization
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