Quantum Time-Space Tradeoffs for Exponential Dynamic Programming

TL;DR

This paper explores quantum algorithms for dynamic programming, focusing on improving space complexity through time-space tradeoffs while maintaining quantum speedups over classical methods.

Contribution

It introduces novel quantum time-space tradeoffs by adjusting algorithm parameters and integrating classical strategies, reducing QRAM requirements.

Findings

Achieved quantum speedups over classical algorithms

Developed methods to trade space for time in quantum dynamic programming

Reduced QRAM requirements in quantum algorithms for NP-hard problems

Abstract

We investigate the quantum algorithms for dynamic programming by Ambainis et al. (SODA'19). While giving provable complexity speedups and applicable to a variety of NP-hard problems, these algorithms have a notable drawback: they require a large amount of Quantum Random Access Memory (QRAM), which potentially could be very challenging to implement in a physical quantum computer. In this work, we study how we can improve the space complexity by trading it for time, while still retaining a speedup over the classical algorithms. We show novel quantum time-space tradeoffs, which we obtain by adjusting the parameters of these algorithms and combining them with "quantized" classical strategies.