Qbits CA

[simsim314]

I don't a design for this yet just an idea.

Think of grid of Qbits just like regular CA. Each Qbit might be |0> and |1> state as well as superposition with its neighbors. We can start from simple case - each iteration the Qbits are in superposition with their neighbours make some quantum calculation and then return to 0 or 1.

The question is can we make CA based on Qbits that will be more efficient or interesting than the classical CA?

[calcyman]

I don't a design for this yet just an idea.

Think of grid of Qbits just like regular CA. Each Qbit might be |0> and |1> state as well as superposition with its neighbors. We can start from simple case - each iteration the Qbits are in superposition with their neighbours make some quantum calculation and then return to 0 or 1.

The question is can we make CA based on Qbits that will be more efficient or interesting than the classical CA?

Well, yes. You'll probably want to use the Margolus neighbourhood, in which case the space of rules is the group U(16) of 16x16 unitary matrices. (The subgroup of permutation matrices correspond to classical reversible rules, such as Billiard-Ball Machines and the Single Rotation Rule.)

[simsim314]

in which case the space of rules is the group U(16) of 16x16 unitary matrices

Wouldn't it be just a permutation in 16 possible states of 2x2, if I want that every iteration will end up in state |1> or |0>? What kind of limitation the unitarity adds? Also what is the Qbit operation which is simplest to implement, I mean what is the equivalent of B/S notation in such a space?

[calcyman]

in which case the space of rules is the group U(16) of 16x16 unitary matrices

Wouldn't it be just a permutation in 16 possible states of 2x2, if I want that every iteration will end up in state |1> or |0>?

Then you'd just have classical reversible Margolus rules. Isn't the point of using qubits so that you can have a cellular automaton in which a quantum speedup is possible? (For example, so you can build a pattern which implements Shor's algorithm?)

What kind of limitation the unitarity adds?

Those are the only gates allowable in quantum computation, due to physical laws.

Also what is the Qbit operation which is simplest to implement, I mean what is the equivalent of B/S notation in such a space?

Irreversible computations aren't allowed, so there's no quantum analogue of B/S rules. The most popular two-dimensional reversible rules are the bijective Margolus rules (which you can view as 16x16 permutation matrices), and the quantum analogue is the space of 16x16 unitary matrices.