? isn't a qbit already a qtrit anyway?

QBIT

1 = 0

2 = 1

3 = both

Eh, that's an ugly and inaccurate way to think about qubits because at all times there exists a probability for each of the qubit's states 0 or 1, so at all times there is already the following expression for the overall ("system") state that already takes any possible mixture into consideration:

alpha * |0> +

beta * |1>

alpha = the probability of that qubit being in state 0

beta = the probability of that qubit being in state 1

Both alpha and beta are numbers anywhere between or including 0 and 1, though I believe constrained in certain mathematical ways. I don't believe alpha and beta can both equal 1 at the same time, for example, but I don't understand the details thoroughly enough to know for sure. (See the topic of Bloch spheres, for example, then please explain it to us all in a simple way!)

At any rate, what you were calling state 3 is what's called a "mixed state" or "superposition" and was already described by the math expression I showed above, so there is no need to list such a state 3.

So a qtrit is like *6* states->

No, just 3 states, due to what I explained above, although with an infinite number of possible mixed states due to all the choices for alpha and beta.

1 qubit has 2^1 = 2 possible states: 0, 1

1 qutrit has 3^1 = 3 possible states: 0, 1, 2

In general, with N digits you get:

N qubits have 2^N possible states

N qutrits have 3^N possible states

It's with multiple digits that quantum computers really start to excel over classical computers, since then the representational power goes up exponentially. One digit is fairly useless, even if it's a qubit or qutrit, but even with two qubits you can start to do some things you couldn't do before on a classical computer that had two classical bits (

https://physics.stackexchange.com/questions/63412/how-are-qubits-better-than-classical-bit-if-they-collapse-to-a-classical-state-a). Since we're dealing with exponential increase in the above expressions, a small change in base (like from 2^N to 3^N) can quickly make a huge difference. You can plot several points on a graph of each of those two functions to prove that to yourself.

()

https://cosmosmagazine.com/physics/quantum-computing-for-the-qubit-curious()

How Does a Quantum Computer Work?

Veritasium

Published on Jun 17, 2013

https://www.youtube.com/watch?v=g_IaVepNDT4There exist advantages of using higher bases even in classical computers. For example, a ternary computer (base 3) is easier to build and needs fewer digits to represent numbers than does a binary computer (base 2):

https://hackaday.com/2016/12/16/building-the-first-ternary-microprocessor/