The wiki article says twice that a the motivation for studying continuous variable quantum computing is to understand "the ways in which quantum computers can be more capable or powerful than classical ones". But it never explains why you want to use continuous variable quantum computing over qubits. What are your arguments for why the correct path forward is not qubits?
Why do the real numbers solve more rational equations than the integers? They’re both infinite (though not equinumerous), but the integers can only come close to the reals.
And this line of reasoning completely fails when you start considering error correction. This is why we need bits and qubits. Aaronson's lecture notes go into the mathematical details if you are interested.
But now you have to demonstrate that your analogy holds.
This is pretty common misconception (that qubits are a bad idea). Qubits or qudits are necessary to achieve scalable error correction. I work at one of the research institutes that pushes the use of continuous variable systems (they are great). But we implement qubits on top of them (that is the whole point).
What makes qubits a bad idea? What problems of qubits does continuous variable quantum computing solve?
I’m not being Socratic, I just don’t know.
My guess is the quantum computer that Feynman theorized about was continuous. I’d bet it needs to be continuous to solve all the NP problems and so on.
No variant of quantum computing is expected to solve NP problems in polynomial time. That's just a common misconception.
In principle. Not in the actual universe we inhabit, with its Beckenstein Bound.
Arbitrary precision (not infinite) is good enough for me.
Sort of like coming arbitrarily close to the speed of light, in that it will require energy on the same asymptotic scale you’re hoping to achieve precision in. Degenerate matter computers?
"Real computation," which allows you to solve NP and #P problems in polynomial time, require infinite precision. With just arbitrary precision it isn't any more powerful than classical computation.
"Real computation" is a flawed model because it does not permit scalable error correction mechcanisms. Check out Aaronson's lecture notes if you are interested in the rigorous argument.
I disagree with Aaronson but am not quite there to have a serious discussion about it.
If you think real computation is in any way feasible why don't you build one and make a silly amount of money?
Those seem more similar to old school analog computers, in a sense.
The interesting thing is that a perfect analog classical computer is more powerful than the qubit quantum computer model (which is what people mean by quantum computing). But analog computers (whether classical or quantum) do not permit error correction, and as such are useless for anything but the smallest problem. You need bits and qubits in the real world.
They very much are.
They’re equivalent. A continuum can be encoded into qubits and vis versa.
They definitely aren’t.
Consider an array of qubits forming a register. Now, a cavity resonator’s state can be expanded in a photon number basis. If you truncate the cavity resonator to 2^n photons, then map the 0 photon ket to the 0 state of the register, the 1 photon key to the 1 state of the register, all the way up to the 2^n photon state of the register to the 2^n photon state of the register. Now you’ve mapped the cavity state onto the register and they’re informationally equivalent
sure, however analog computing has the advantage that you can solve optimization problems natively, in hardware. with qubits, you get a speedup but not O(1) solutions.
Absolutely not. The time complexity is exactly the same. A quantum computer can simulate quantum annealing with exactly the same asymptotic complexity as an “analog” physical system that takes advantage of quantum mechanics would.