7.8 Summary

The quantum states of a qubit are the unit vectors in C², where we identify two states as being equivalent if they differ only by a multiple of a complex unit. To better visualize actions on a qubit, we introduced the Bloch sphere in R³ and showed where special orthonormal bases map onto the sphere.

Any new idea seems to deserve its own notation and we did not disappoint when we introduced Dirac’s bra-ket representation of vectors. This significantly simplifies calculation when working with multiple qubits.

Given the ket form of qubit states, we introduced the standard 1-qubit gate operations. In the classical case in section 2.4 not. In the quantum case, there are many, in fact an infinite number, of single qubit operations.

We next look at how to work with two or more qubits and the quantum gates that operate on them. We also introduce entanglement, an essential notion from quantum mechanics.

References

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