Open Problems Related to Quantum Query Complexity

Author:

Aaronson Scott1

Affiliation:

1. University of Texas, Austin TX

Abstract

I offer a case that quantum query complexity still has loads of enticing and fundamental open problems—from relativized QMA versus QCMA and BQP versus IP , to time/space tradeoffs for collision and element distinctness, to polynomial degree versus quantum query complexity for partial functions, to the Unitary Synthesis Problem and more.

Funder

Vannevar Bush Fellowship

US Department of Defense

Simons Investigator Award

Simons “It from Qubit” collaboration

Publisher

Association for Computing Machinery (ACM)

Reference49 articles.

1. S. Aaronson. 2009. Quantum copy-protection and quantum money. In Proceedings of IEEE Conference on Computational Complexity (CCC’09) . 229–242.

2. S. Aaronson. 2016. The complexity of quantum states and transformations: From quantum money to black holes. Lecture Notes for the 28th McGill Invitational Workshop on Computational Complexity with guest lectures by A. Bouland and L. Schaeffer. www.scottaaronson.com/barbados-2016.pdf.

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