Qubit Complexity of Continuous Problems

TL;DR

This paper explores the relationship between classical query complexity and qubit complexity in quantum algorithms for continuous problems, providing a formula to estimate the minimum number of qubits needed.

Contribution

It introduces a method to derive lower bounds on qubit complexity based on classical query complexity for continuous problems.

Findings

Derived a formula linking classical query complexity to qubit complexity

Established lower bounds on qubit requirements for quantum algorithms

Highlighted the importance of qubit resource estimation in quantum computing

Abstract

The number of qubits used by a quantum algorithm will be a crucial computational resource for the foreseeable future. We show how to obtain the classical query complexity for continuous problems. We then establish a simple formula for a lower bound on the qubit complexity in terms of the classical query complexity