报告人： 高攀博士（清华大学）
报告题目： Iterative quantum optimization algorithms for polynomials
报告时间：7月4日（周一）下午4:00-6:00pm
腾讯会议ID：299-389-445 （密码：无）
邀请人：白敏茹
摘要：Optimization of problems with high-dimensional variables is common in both scientific research and industrial activities, whose computational complexity usually grows linearly with variable dimensions, and thus it will be intractable for some of nowadays complex systems with billions of parameters. Since polynomials are the most simple function basis and their optimization will be a representative of more general problems, theoretical research of its quantum speedup will show much significance.
In the work of Patrick Rebentrost et.al[1], they proposed a quantum optimization algorithm for constrained polynomials with only even order and homogeneous terms, it is neither friendly to nowadays experimental realization nor suitable for more general polynomials. Here, I will talk about some of our works developed from Ref[1]. Firstly, we use Linear Combination of Unitaries(LCU) method to construct the effective Gradient operators, thus simplified the circuits, and demonstrate it in NMR system[2]. Secondly, we introduce an extra dimension to the usual quantum amplitude encoding, propose a quantum gradient descent algorithm for general polynomials, without constraint and requirement for even order and homogeneous[3]. Lastly, we consider the second order derivative in, and give a quantum Newton algorithms for general polynomials, which can highly reduces the iteration steps and therefore the overall complexity.
References
[1]New Journal of Physics, 2019, 21(7): 073023
[2]npj Quantum Information, 2021, 7(1): 1-7.
[3]Physical Review A, 2021, 103(4): 042403.
[4]Science China Physics, Mechanics & Astronomy, 2021, 64(10): 1-10.
报告人简介：高攀，北京量子信息科学研究院博士后。2015年本科毕业于哈尔滨工业大学物理系，2021年博士毕业于清华大学物理系。研究兴趣包括基于容错量子计算和有噪中等规模量子(NISQ)器件的量子算法设计、量子模拟等。
