TL;DR
The paper introduces a new quantum complexity class, MQ^2, which includes important algorithms like Deutsch-Jozsa and Shor, and explores its relation to BQP within the hierarchy of quantum complexity classes.
Contribution
It defines MQ^2 with a simple mathematical framework and situates it within the complexity hierarchy, showing it contains key quantum algorithms.
Findings
MQ^2 is contained in AWPP.
MQ^2 includes Deutsch-Jozsa and Shor's algorithms.
The relation between MQ^2 and BQP remains unknown.
Abstract
We present a new quantum complexity class, called MQ^2, which is contained in AWPP. This class has a compact and simple mathematical definition, involving only polynomial-time computable functions and a unitarity condition. It contains both Deutsch-Jozsa's and Shor's algorithm, while its relation to BQP is unknown. This shows that in the complexity class hierarchy, BQP is not an extraordinary isolated island, but has ''siblings'' which as well can solve prime-factorization.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Computability, Logic, AI Algorithms · Quantum Information and Cryptography