# A question about Qubit (number of states)

samaaa
Hi

"N Qubits are equivalent 2^N classical bits (2^N states)"

But I couldn't understand that, because I know that each single Qubit could be one and zero at the same time, so each single Qubit is equivalent two classical bits (two states)
That mean:
If we have 3 Qubits it will be equivalent 6 classical bits(from 3×2)
If we have N Qubits it will be equivalent N×2 classical bits (not 2^N)

So can anyone tell me what is my misconception ?

Mentor
A qubit is not "zero or one", it can be both at the same time, with an unknown phase between the states. You cannot read out all those 2 bits, but you need two for a full description.

With more qubits, you can have entanglement between the bits - they can depend on each other, something you cannot get with 2*N bits.
You basically get 1 bit for each possible set of binary bit values in a measurement, and there are 2^n of them.

samaaa
With more qubits, you can have entanglement between the bits - they can depend on each other, something you cannot get with 2*N bits.
You basically get 1 bit for each possible set of binary bit values in a measurement, and there are 2^n of them.

i don't understand
should i study quantum theory carefully to understand the qubit ? or i just need the basic concept of this theory ?

samaaa
i will give example:
if we use the direction of Electron spin to represent the Qubit,spin up= 1 spin down=0
each electron could be spin up and down simultaneously (two states at the same time)

but if we have 3 Qubits, we will get a 8 states simultaneously ,
that mean each Qubit has a 8 states not two states
if the Qubit has a 8 states that mean Qubit is not binary

thegarbageman

the qubits exist in 8 states simultaneously, but don't forget that when we measure them they will no longer exist as a superposition of states and will collapse to a set of their probabilistic values, which are binary because they can only be 0 or 1 as spin will be either up or down. Qubits are not manipulated in a binary matter but will always read out binary results, which is where the power of quantum computing lies.

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samaaa
Qubits are not manipulated in a binary matter but will always read out binary results, which is where the power of quantum computing lies.

thank you for this information
now i understand how the Qubit works

thegarbageman
also to answer your original question, yes a qubit in a sense is like 2 classical bits because it can be one of 2 values but a system of qubits interacts differently than a system of bits.

if you have 2 bits, 00 and you want to add a third bit of information to the end, you will either have 000 or 001

whereas if you have 2 qubits which could be 00, 10, 01, or 11 and you want to add another qubit to the end,
now you will either have 000, 001, 100, 101, 010, 011, 110, or 111.

the probabilistic nature of qubits means with each one you add to a system, you are doubling the possibilities of what the group of qubits can be read as which is why N qubits have the computing power of 2^N classical bits.
with classical bits, with each bit you add to the system you are only adding 2 possibilities