Book a Demo!
CoCalc Logo Icon
StoreFeaturesDocsShareSupportNewsAboutPoliciesSign UpSign In
quantum-kittens
GitHub Repository: quantum-kittens/platypus
 Path: blob/main/notebooks/summer-school/2021/lec1.1.ipynb
3855 views
Kernel: Python 3

Vector Spaces, Tensor Products, and Qubits

In this lecture, Elisa introduces some mathematical tools used to describe quantum systems and their interactions such as Dirac notation, density matrices, inner product, outer product, Born rule, and the geometrical representation of qubits; the Bloch sphere. She also introduces the basic building block in quantum computing: The qubit, which is analogous to the classical bit. She also briefly introduces quantum measurements.

FAQ

What does it mean that a state is maximally entangled? A maximally entangled state is a quantum state (e.g. the Bell state) that has maximum von Neumann entropy; which is analogous to the, classical, Shannon entropy for a fair-coin flip.
For quantum teleportation, we need to send classical bits too and cannot just use entanglement to send information. Is this the reason we cannot send information faster than the speed of light? Yes. In fact, since the entangled state itself does not represent a probability distribution, but its inner product, one always has to measure the state to extract information from it.
Why did you use the outer product representation when applying a gate instead of using the spectral decomposition? The outer product representation in terms of 0 and 1 states (the so-called computational basis) is useful for a gate, because then you can easily how the gate acts on the 0 and 1 states.
How's teleportation useful in quantum computation compared to classical? It is useful when you want to encrypt the data (information) you are transferring (i.e., instead of cloning it, you are actually transferring it to the target party, which will include destroying the original information (data) from the source).

Other resources