Xiaodi Wu

Parallel Approximation of Min-Max Problems

AbstractThis paper presents an efficient parallel approximation scheme for a new class of min-max problems. The algorithm is derived from the matrix multiplicative weights update method and can be used to find near-optimal strategies for competitive two-party classical or quantum interactions in which a referee exchanges any number of messages with one party followed by any number of additional messages with the other. It considerably extends the class of interactions which admit parallel solutions, demonstrating for the first time the existence of a parallel algorithm for an interaction in which one party reacts adaptively to the other. As a consequence, we prove that several competing-provers complexity classes collapse to PSPACE, such as QRG(2), SQG and two new classes called DIP and DQIP. A special case of our result is a parallel approximation scheme for a specific class of semidefinite programs whose feasible region consists of lists of semidefinite matrices that satisfy a transcript-like consistency condition. Applied to this special case, our algorithm yields a direct polynomial-space simulation of multi-message quantum interactive proofs resulting in a first-principles proof of QIP =PSPACE.

Exact quantum search by parallel unitary discrimination schemes

We study the unsorted database search problem with items

Parallel repetition for entangled k -player games via fast quantum search

N

VERIFIER-BASED ALGORITHM FOR UNSORTED DATABASE SEARCH PROBLEM

from the viewpoint of unitary discrimination. Instead of considering the famous

An Improved Semidefinite Programming Hierarchy for Testing Entanglement

O(\sqrt{N})

Epsilon-net method for optimizations over separable states

Grovers the bounded-error algorithm for the original problem, we seek for the results about the exact algorithms, i.e. the ones succeed with certainty. Under the standard oracle model

Tight SoS-degree bounds for approximate nash equilibria

\sum_j (-1)^{\delta_{\tau j}}|j>< j|

Physical Randomness Extractors: Generating Random Numbers with Minimal Assumptions

, we demonstrate a tight lower bound

Sample-optimal tomography of quantum states

{2/3}N+o(N)

Parallel Approximation of Min-max Problems with Applications to Classical and Quantum Zero-Sum Games

of the number of queries for any parallel scheme with unentangled input states. With the assistance of entanglement, we obtain a general lower bound