MINIMIZING POLYNOMIAL FUNCTIONS ON QUANTUM COMPUTERS

RAOUF DRIDI; HEDAYAT ALGHASSI; SRIDHAR TAYUR

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MINIMIZING POLYNOMIAL FUNCTIONS ON QUANTUM COMPUTERS

机译：最小化量子计算机上的多项式函数

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This expository paper reviews some of the recent uses of computational algebraic geometry in classical and quantum optimization. The paper assumes an elementary background in algebraic geometry and adiabatic quantum computing (AQC), and concentrates on presenting concrete examples (with Python codes tested on a quantum computer) of applying algebraic geometry constructs: solving binary optimization, factoring, and compiling. Reversing the direction, we also briefly describe a novel use of quantum computers to compute Groebner bases for toric ideals. We also show how Groebner bases play a role in studying AQC at a fundamental level within a Morse theory framework. We close by placing our work in perspective, by situating this leg of the journey, as part of a marvelous intellectual expedition that began with our ancients over 4000 years ago.

机译：本展品纸质审查了近期在经典和量子优化中计算代数几何的一些用途。本文假设代数几何和绝热量子计算（AQC）中的基本背景，并专注于呈现具体示例（在量子计算机上测试的Python代码）应用代数几何构建体：解决二进制优化，分解和编译。逆转方向，我们还简要描述了一种新颖的量子使用量子计算机来计算Toric理想的Groebner基础。我们还展示了格罗布纳基地如何在莫尔斯理论框架内以基本级别研究AQC发挥作用。我们通过在这个旅程中将我们的工作置于透视之地，作为一个奇妙的智力探险的一部分，从我们的古人开始超过4000年前开始。

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《Science and Culture》 |2019年第6期|152-162|共11页
作者
RAOUF DRIDI; HEDAYAT ALGHASSI; SRIDHAR TAYUR;
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Quantum Computing Group Tepper School of Business Carnegie Mellon University Pittsburgh PA 15213;

Quantum Computing Group Tepper School of Business Carnegie Mellon University Pittsburgh PA 15213;

Quantum Computing Group Tepper School of Business Carnegie Mellon University Pittsburgh PA 15213;

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1. MINIMIZING POLYNOMIAL FUNCTIONS ON QUANTUM COMPUTERS [J] . RAOUF DRIDI, HEDAYAT ALGHASSI, SRIDHAR TAYUR Science and Culture . 2019,第5a6期

机译：最小化量子计算机上的多项式函数
2. Quantum Chemistry on Quantum Computers: A Polynomial-Time Quantum Algorithm for Constructing the Wave Functions of Open Shell Molecules [J] . Sugisaki Kenji, Yamamoto Satoru, Nakazawa Shigeaki, The journal of physical chemistry, A. Molecules, spectroscopy, kinetics, environment, & general theory . 2016,第32期

机译：量子计算机上的量子化学：构造开壳分子波函数的多项式时间量子算法
3. A New Method of Minimization of Logical Functions in the Polynomial Set-Theoretical Format 2. Minimization of Complete and Incomplete Functions [J] . Rytsar B. Ye. Управляющие системы и машины . 2015,第4a258期

机译：多项式集理论格式的逻辑函数最小化的新方法2.完全函数和不完全函数的最小化
4. A polynomial expansion line search for large-scale unconstrained minimization of smooth L_2-regularized loss functions, with implementation in Apache Spark [C] . Michael B. Hynes, Hans De Sterck SIAM International Conference on Data Mining . 2016

机译：多项式扩展线搜索平滑L_2-正规损耗函数的大规模无约束最小化，实现Apache Spark
5. A Polynomial-Time Approach to Schatten Quasi p Norm Minimization and Its Application to Sensor Network Localization. [D] . Ji, Senshan. 2015

机译：Schatten准规范最小化的多项式时间方法及其在传感器网络定位中的应用。
6. Quantum Chemistry on Quantum Computers: A Method forPreparation of Multiconfigurational Wave Functions on Quantum Computerswithout Performing Post-Hartree–Fock Calculations [O] . Kenji Sugisaki, *, Shigeaki Nakazawa, 2019

机译：量子计算机上的量子化学：一种方法在量子计算机上准备多配置波函数不执行后Hartree-Fock计算
7. A New Method of Minimization of Logical Functions in the Polynomial Set-theoretical Format. 2. Minimization of Complete and Incomplete Functions [O] . Rytsar B.Ye. 2015

机译：多项式集合理论格式的逻辑函数最小化的新方法。 2.最小化完整功能和不完整功能
8. Askey-Wilson Polynomials as Zonal Spherical Functions on the SU(2) Quantum Group [R] . Koornwinder, T. H. 1990

机译：askey-Wilson多项式作为sU（2）量子群上的带状球面函数

MINIMIZING POLYNOMIAL FUNCTIONS ON QUANTUM COMPUTERS

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