Parallelized Solution to Semidefinite Programmings in Quantum Complexity Theory

In this paper we present an equilibrium value based framework for solving SDPs via the multiplicative weight update method which is different from the one in Kale's thesis [Kal07]. One of the main advantages of the new framework is that we can guarantee the convertibility from approximate to exact feasibility in a much more general class of SDPs than previous result. Another advantage is the design of the oracle which is necessary for applying the multiplicative weight update method is much simplified in general cases. This leads to an alternative and easier solutions to the SDPs used in the previous results QIP(2)PSPACE [JUW09] and QMAM=PSPACE [JJUW09]. Furthermore, we provide a generic form of SDPs which can be solved in the similar way. By parallelizing every step in our solution, we are able to solve a class of SDPs in NC. Although our motivation is from quantum computing, our result will also apply directly to any SDP which satisfies our conditions. In addition to the new fr...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Xiaodi Wu
• Keywords: CORR 2010, Education, Equilibrium Value, Multiplicative Weight, SDPs