1.5 Working with multiple qubits and universality
Now that we have mastered working with two-qubit systems, it will be fairly straightforward to generalize all the notions that we have been studying to the case in which the number of qubits in our circuits is arbitrarily big. You know the drill: we will start by defining, mathematically, what a multi-qubit system is, we will then learn how to measure it and, finally, we will introduce quantum gates that act on many qubits at the same time.
1.5.1 Multi-qubit systems
With all that we have learned so far, it will now be very easy to understand how to work with multi-qubit systems.
As you may have already deduced, if we have qubits, the states that constitute the computational basis are
We usually omit the symbol to write
or
or simply
Important note
When using the notation for basis states, the total number of qubits must be clear from context. Otherwise, a state like, for example,
might mean either
,
,
, or any string with...