Paper Info
Title
Quantum Query Complexity of State Conversion
Abstract
State conversion generalizes query complexity to the problem of converting between two input-dependent quantum states by making queries to the input. We characterize the complexity of this problem by introducing a natural information-theoretic norm that extends the Schur product operator norm. The complexity of converting between two systems of states is given by the distance between them, as measured by this norm. In the special case of function evaluation, the norm is closely related to the general adversary bound, a semi-definite program that lower-bounds the number of input queries needed by a quantum algorithm to evaluate a function. We thus obtain that the general adversary bound characterizes the quantum query complexity of any function whatsoever. This generalizes and simplifies the proof of the same result in the case of boolean input and output. Also in the case of function evaluation, we show that our norm satisfies a remarkable composition property, implying that the quantum query complexity of the composition of two functions is at most the product of the query complexities of the functions, up to a constant. Finally, our result implies that discrete and continuous-time query models are equivalent in the bounded-error setting, even for the general state-conversion problem.
Year
DOI
Venue
2011
10.1109/FOCS.2011.75
FOCS
Keywords
Field
DocType
quantum query complexity,schur product operator norm,query complexity,input-dependent quantum state,function evaluation,general adversary,boolean input,continuous-time query model,state conversion,natural information-theoretic norm,quantum algorithm,computational complexity,quantum physics,algorithm design and analysis,boolean function,quantum mechanics,quantum computing,quantum walk,vectors,algorithm design,lower bound,boolean functions,satisfiability,operator norm
Query optimization,Quantum complexity theory,Boolean function,Discrete mathematics,Combinatorics,Computer science,Quantum computer,Quantum state,Quantum algorithm,Operator norm,Computational complexity theory
Conference
ISSN
Citations 
PageRank 
Proc. 52nd IEEE Symp. on Foundations of Computer Science (FOCS), 2011, pages 344-353
54
2.06
References 
Authors
18
5
Name
Order
Citations
PageRank
Troy Lee127628.96
Rajat Mittal217017.59
Ben Reichardt329517.45
Robert Spalek423412.63
Mario Szegedy53358325.80