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Fundamentals

01 /Quantum computers with magical advantage? 02 /Bra-ket notation 03 /Born rule 04 /Bloch sphere 05 /Measurement operators 06 /Experimental and theoretical measurements 07 /How to measure in any basis 08 /State decomposition 09 /Why every maximally entangled state is secretly a Bell state 10 /Coherence 11 /Relaxation 12 /Quantum materials: the environment of a qubit 13 /Introduction to quantum error correction (QEC) 14 /Multiqubit systems 15 /Multiqubit gates 16 /Entanglement 17 /Measuring multiqubit systems 18 /Superdense coding 19 /Teleportation 20 /Entanglement swapping

Multiqubit gates

Now that we have already seen the states of the multi-qubit systems, we want to apply gates to them. But how do we do this? David Elkouss (QuTech) will guide us through the steps and the possible kinds of gates. We will see the CNOT gate, a two-qubit gate that can generate entanglement!

Prerequisite knowledge

So far you learned how to express a single qubit state in the braket notation and its representation on the Bloch sphere. In this video, David Elkouss (QuTech) will explain more in detail how these concepts extend to two and multiple qubit systems.

Further thinking

Which of the following properties for the matrix M defines unitarity?

When we write CNOT|ij>, we mean flip j if i=1.  We could also redefine the gate to mean flip i if j=1.  What is the matrix of this new CNOT?

Solutions

Further reading

For a more detailed explanation on controlled gates see section 4.3 in M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information, 10th anniversary ed. Cambridge ; New York: Cambridge University Press, 2010.