Читать книгу Principles of Superconducting Quantum Computers - Daniel D. Stancil - Страница 23

When we consider a system with two qubits, we don’t just consider each qubit independently of the other. Instead, this forms a two-qubit system with its own set of basis states. If we know the state of each qubit, then the combined two-qubit state is described using the tensor product of the two state vectors, defined as follows:

(1.32)

Using the standard basis, the basis states for a two-qubit system are defined by combinations of the |0⟩ and |1⟩ states:

(1.33)

(1.34)

(1.35)

(1.36)

Any two-qubit state can be written as a linear combination of the basis states:

(1.37)

Two-qubit state vectors are also normalized:

(1.38)

As we will see later, while every two-qubit state can be written in the form of Eq. (1.37), not every two-qubit state can be written as the tensor product of single-qubit states.

This can be generalized into a system with n qubits, requiring state vectors with 2ⁿ components with 2ⁿ complex coefficients.