Programming Quantum Computers

Chapter 3. Multiple Qubits

As useful as single qubits can be, they’re much more powerful (and intriguing) in groups. We’ve already seen in Chapter 2 how the distinctly quantum phenomenon of superposition introduces the new parameters of magnitude and relative phase for computation. When our QPU has access to more than one qubit, we can make use of a second powerful quantum phenomenon known as entanglement. Quantum entanglement is a very particular kind of interaction between qubits, and we’ll see it in action within this chapter, utilizing it in complex and sophisticated ways.

But to explore the abilities of multiple qubits, we first need a way to visualize them.

Circle Notation for Multi-Qubit Registers

Can we extend our circle notation to multiple qubits? If our qubits didn’t interact with one another, we could simply employ multiple versions of the representation we used for a single qubit. In other words, we could use a pair of circles for the ∣0⟩ and ∣1⟩ states of each qubit. Although this naive representation allows us to describe a superposition of any one individual qubit, there are superpositions of groups of qubits that it cannot represent.

How else might circle notation represent the state of a register of multiple qubits? Just as is the case with conventional bits, a register of N qubits can be used to represent one of 2^N different values. For example, a register of three qubits in the states ∣0⟩∣1⟩∣1⟩ can represent a decimal value of 3. When talking about multi-qubit ...