How can quantum computing potentially change the paradigm of classical algorithm design?

With the advent of quantum computing, many fundamental aspects of algorithm design and computational theory are being re-evaluated. Classical algorithms, which operate under the constraints and capabilities of traditional computing architecture, may not be directly applicable or optimal in the quantum realm. Understanding how quantum algorithms can leverage the principles of superposition and entanglement presents a radical shift in how problems might be approached and solved. Given these potential advantages, what are some of the most compelling ways in which quantum computing could redefine the methodologies used in classical algorithm design?