Before we dive deeper into the different layers of a quantum computer, we first want to introduce you to ket notation. Ket notation is a specific quantum method used to perform operations and measurements. Ben Criger will introduce you to the basics of ket notation.

Note that this is a densely packed video, and that you are not expected to understand everything after the first viewing. You will likely need more time to grasp the basics of Ket notation, and we advice you to re-watch the video and pause certain passages. Please do not let this subject deter you from following this course. It is important that you understand the basics, because that will be used in the continuation of the course. We realize this is a difficult topic. Based on the feedback in previous runs of this course, we have made additional videos with examples of Ket notation, which will be available via the tabs above.

Main takeaways

• In ket notation, a quantum state is expressed using a column vector with complex coefficients. The squared magnitudes of these coefficients are the probabilities of measuring that particular outcome.
• Devices used for storing and manipulating qubit states are described by a Hamiltonian, which is a matrix that assigns energies to each of its eigenstates or preferred basis states.
• Quantum logic gates are described by unitary matrices. Probabilistic measurements are described by Hermitian matrices.
• An entangled state is a multi-qubit state that cannot be written as a tensor product of one-qubit states.
• Qubit states are geometrically represented using the Bloch sphere.
• Multi-qubit states and operations can be described using the tensor product. Note, an actual two-qubit gate cannot be described with a tensor product.