2 Preparing quantum states

This chapter covers

Using quantum gates to change quantum states
Using Q# and Qiskit to write quantum programs
Running and testing quantum programs using simulators
Watching the state of a quantum program during its execution

Quantum algorithms revolve around manipulating the states of quantum systems. Figure 2.1 shows the flow typical for many quantum algorithms. The algorithm starts with preparing the quantum system in a certain superposition state and then applies a sequence of transformations to it before performing a measurement to extract the results. The goal of the algorithm is to lead the system to a superposition state in which the basis states that are answers to the problem being solved have large amplitudes, and all the other basis states have much smaller amplitudes. This allows the final measurement to yield the answer to the problem with high probability.

Note Not all quantum algorithms follow this approach. Some algorithms focus on estimating the probabilities of measurement outcomes instead; you’ll see an example in chapter 5 when we discuss different phase estimation algorithms. However, preparing the quantum system in a certain initial state is an important step for these algorithms as well.

2.1 Preparing a single-qubit state

2.1.1 Math

2.1.2 Qiskit

2.1.3 Q#

2.2 What does your solution do?

2.2.1 Qiskit

2.2.2 Q#

2.3 Preparing a two-qubit state

2.3.1 Refresher: Controlled gates in Dirac notation

2.3.2 Math

2.3.3 Qiskit

2.3.4 Q#

2.4 Testing your solution

2.4.1 Qiskit

2.4.2 Q#

2.5 Preparing a multiqubit state