Introduction to Quantum Algorithms for Physics and Chemistry

This chapter introduces the basic concepts of digital quantum simulation. The study of the computational complexity of problems in quantum simulation helps us better understand how quantum computers can surpass classical computers. The chapter briefly summarizes a few important examples of complexity classes of decision problems. Quantum algorithms are procedures for applying elementary quantum logic gates to complete certain unitary transformations of the input state. The steps involved in carrying out a digital quantum simulation consist of three parts: state preparation, time evolution, and measurement of observables. The chapter provides an overview of state preparation and simulation of time evolution. The use of Suzuki–Trotter formulas in quantum simulation for time-independent sparse Hamiltonians is reviewed. The chapter reviews a method to effect nondestructive measurements of constants of the motion within the adiabatic model.