What's the default value for a quantum register?

Question

I've just started to learn Quantum computing with Qiskit: I'm reading the Qiskit documentation and the book "Quantum Computing in Practice with Qiskit® and IBM Quantum Experience®".

In this book, on page 79 we can read: "..., as we set up our qubit to start as 0, ..."

Can we set up the start value for a quantum register?

Because I think I have read that they have its default value to 0, and we only can set it to one using the NOT gate.

I have tried to set it to 0 in Quantum Experience and I haven't found how to do it, and also with Python and I haven't found it.

Answer 1

One of the seven DiVincenzo's criteria is the ability to initialize the state of the qubits to a simple fiducial state. In most quantum hardware, this is taken to be the state $|0\rangle^{\otimes n} = \overbrace{|0\rangle \otimes |0\rangle \otimes \cdots \otimes |0\rangle}^{n \ times} = |0 0 \cdots 0\rangle$.

If you create a quantum circuit on IBM hardware and pretty much all other hardware platforms, then the initial state is taken exactly to be this $|0\rangle^{\otimes n} $ state. For example, a 3 qubit circuit will starts out like this:

Then you can operate on this initial state by applying different quantum gates. For example:

---

Note that the basis in quantum computing is taken to be $|0\rangle = \begin{pmatrix} 1 \\ 0 \end{pmatrix}$ and $|1\rangle = \begin{pmatrix} 0 \\ 1 \end{pmatrix} $. This is known as the computational basis.

Answer 2

The default value for a quantum register depends on the hardware. In the case of most of the IBM hardware, that's $|0\rangle$.

However, Qiskit is hardware agnostic and do not assume an initial state. In order to initialize your circuit, you need to use the instruction Initialize. You can initialize with the values $|0\rangle$ (0), $|1\rangle$ (1), $|+\rangle$ ( +), $|-\rangle$ (-), $|i\rangle$ (r), and $|\mbox{-}i\rangle$ (l).

from qiskit import QuantumCircuit
from qiskit.extensions.quantum_initializer.initializer import Initialize

circuit = QuantumCircuit(6)
circuit.append(Initialize("10+-lr"), range(6))
circuit.draw()

     ┌──────────────────────────┐
q_0: ┤0                         ├
     │                          │
q_1: ┤1                         ├
     │                          │
q_2: ┤2                         ├
     │  initialize(1,0,+,-,l,r) │
q_3: ┤3                         ├
     │                          │
q_4: ┤4                         ├
     │                          │
q_5: ┤5                         ├
     └──────────────────────────┘

Notice that the instruction Initialize, when decomposed, starts with a Reset instruction (|0>):

circuit.decompose().draw()

          ┌───┐ ┌───┐ 
q_0: ─|0>─┤ H ├─┤ S ├─
          ├───┤┌┴───┴┐
q_1: ─|0>─┤ H ├┤ SDG ├
          ├───┤└┬───┬┘
q_2: ─|0>─┤ X ├─┤ H ├─
          ├───┤ └───┘ 
q_3: ─|0>─┤ H ├───────
          └───┘       
q_4: ─|0>─────────────
          ┌───┐       
q_5: ─|0>─┤ X ├───────
          └───┘