Quantum versus Classical Online Algorithms with Advice and Logarithmic Space

by   Kamil Khadiev, et al.
University of Latvia

In this paper, we consider online algorithms. Typically the model is investigated with respect to competitive ratio. We consider algorithms with restricted memory (space) and explore their power. We focus on quantum and classical online algorithms. We show that there are problems that can be better solved by quantum algorithms than classical ones in a case of logarithmic memory. Additionally, we show that quantum algorithm has an advantage, even if deterministic algorithm gets advice bits. We propose "Black Hats Method". This method allows us to construct problems that can be effectively solved by quantum algorithms. At the same time, these problems are hard for classical algorithms. The separation between probabilistic and deterministic algorithms can be shown with a similar method.


page 1

page 2

page 3

page 4


Quantum Online Algorithms with Respect to Space Complexity

Online algorithm is a well-known computational model. We introduce quant...

Quantum Online Streaming Algorithms with Constant Number of Advice Bits

Online algorithms are known model that is investigated with respect to a...

Quantum Logarithmic Space and Post-selection

Post-selection, the power of discarding all runs of a computation in whi...

Towards quantum advantage for topological data analysis

A particularly promising line of quantum machine leaning (QML) algorithm...

Improved Low-qubit Hidden Shift Algorithms

Hidden shift problems are relevant to assess the quantum security of var...

Quantum Logspace Algorithm for Powering Matrices with Bounded Norm

We give a quantum logspace algorithm for powering contraction matrices, ...

Exponential separations between learning with and without quantum memory

We study the power of quantum memory for learning properties of quantum ...

Please sign up or login with your details

Forgot password? Click here to reset