1999/04/26 by H. Buhrman, Harry Buhrman, Richard Cleve +8 · 4 citations
Computer Science · Physics and Astronomy · #Computational Complexity (cs.CC) #F.1.1 #F.2.0 #FOS: Computer and information sciences #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata #cs.CC #quant-ph
paper · pdf · doi:10.48550/arxiv.cs/9904019
11 pages, LaTeX. New title and some sections are rewritten. This version to appear in IEEE FOCS'99
openalex publication_date 1999/04/26 · arxiv created 1999/08/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search algorithms, their error probability, the size of the search space, and the number of solutions in this space. Using this, we deduce new lower and upper bounds for quantum versions of amplification problems. Next, we establish nearly optimal quantum-classical separations for the query complexity of monotone functions in the zero-error model (where our quantum zero-error model is defined so as to be robust when the quantum gates are noisy). Also, we present a communication complexity problem related to a total function for which there is a quantum-classical communication complexity gap in the zero-error model. Finally, we prove separations for monotone graph properties in the zero-error and other error models which imply that the evasiveness conjecture for such properties does not hold for quantum computers.