# What's the default value for a quantum register?

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.

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.

• Thanks for your answer. Do we decide which initial value will have the quantum register or this register will have the same initial value regardless of what we do? I think that "set up" means intentionality: we do something to set this value to the register. Feb 8 at 7:53
• Every qubit will start in the initial state $|0\rangle$. You do not need to specify anything. The moment you create a circuit, the initial state of each qubit is in the state $|0\rangle$. Feb 8 at 8:06

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 ├───────
└───┘

• Wow! There are a lot of things to learn! Thanks a lot! Feb 8 at 8:36