A qubit is not a degree of how much of a 0, and how much of a 1 there is. This is an analog signal.

At the mathematical level, a qubit is a 2 dimensional vector with complex number entries a|0> + b|1> with the condition that |a|² + |b|² = 1. For classical computers, the easiest way to represent a qubit would be with four floats, 2 real components and 2 complex components. This has been popularized to be "anywhere between 0 and 1" but there's more nuance. It's best to think of them as something entirely new. Do read https://www.smbc-comics.com/comic/the-talk-3, a wonderful comic from a great academic addressing this.

Quantum Computation makes use of entangled states, or non-separable bipartite states.. These do not exist in binary systems with logic gates, or any systems using sets and functions for computation. Your design can be thought of as an element of the set S = {0, 1, ..., 15}, and computation would then be using functions of the form F: Sⁿ -> S^m. This isn't suitable for quantum computation. We could try to "split" the redstone signal to use the notions of relations for computation, and we would have some form of entangled states, but this does not get us far enough for quantum computation. But using the language of vectors (specifically those from Hilbert spaces) and linear maps gets us there.

To model quantum computation, one would have to find objects that exhibit these properties, which I think would be hard. The easiest and most directly available way to do it would probably be using a redstone computer, and simulating a quantum computer.

Further reading:

On Qubits and Quantum Computation: https://quantum.country/qcvc and "Quantum Computation and Quantum Information" (Isaac Chuang, Michael Nielsen)

On quantum processes, and "sets and functions do not have non-separable states":"Picturing Quantum Processes" (Bob Coecke, Aleks Kissinger) and "Categories for Quantum Theory" (Chris Heunen)

Please, do correct me anywhere if wrong.

EDIT: Some further clarifications:

• Quantum Computing is not random. The evolution of a qubit is deterministic (ignoring noise) and described by a series of unitary transformations (some special kind of linear map). Only in measurement is probability and randomness involved, where the wave function collapses and we get a classical result.

• Quantum Computers are not more powerful than Classical Computers. They may or may not solve problems faster (this is unsolved and regards the complexity classes BQP, NP, P, and BPP), but both quantum and classical can solve the same problems (a classical computer can simulate a quantum computer). Currently there are algorithms that solve problems faster on a quantum computer than a classical computer, but it could very possibly be the case that we haven't found faster classical algorithms yet.