Quantum Computation
Barry C Sanders
TL;DR
Addresses foundational aspects of quantum computation, connecting classical complexity with quantum processing and surveying major algorithms and paradigms. The approach surveys Boolean/reversible computation, the quantum formalism, and a wide range of algorithms and heuristics, including Shor's factoring, Grover's search, and Hamiltonian simulation, as well as quantum linear systems (HHL) and the Abelian Hidden Subgroup Problem. It also discusses alternative models (adiabatic, measurement-based) and the role of dequantisation results for some quantum speedups. The significance lies in clarifying potential quantum advantages, while acknowledging current hardware limits and the Noisy Intermediate-Scale Quantum (NISQ) era.
Abstract
This chapter summarizes quantum computation, including the motivation for introducing quantum resources into computation and how quantum computation is done. Finally, this chapter articulates advantages and limitations of quantum computation, both fundamental and practical.