Open Problems Related to Quantum Query Complexity
Scott Aaronson
TL;DR
This paper highlights numerous open problems in quantum query complexity, emphasizing unresolved questions across complexity class separations, tradeoffs, and foundational issues in quantum computation.
Contribution
It systematically identifies and discusses key open problems in quantum query complexity, guiding future research directions.
Findings
No definitive solutions to major open problems yet
Highlights the complexity class separation challenges
Points out the need for further research in quantum algorithms
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.
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