That’s a personal opinion.

Personally, yes, I think quantum computers are basically just a kind of non-classical probabilistic computer, with the non-classicality being the fact the stochastic rules are non-Markovian. Non-Markovianity just means there is a history-dependence to it.

Typically, we think of stochastic laws in this form:

p(t+1)=f(O(t),p(t))

Basically, the probability distribution of the system at the next time interval is just a function of some matrix describing the logic gate, O, and the probability distribution at the current time interval.

You can represent a quantum computer using a stochastic law of the following form:

p(t+1)=f(O(t),p(t),O(t-1),p(t-1),O(t-2),p(t-2),…)

That is to say, it is not just a function of the current operator and current probability distribution, but all past ones as well, extending to the beginning of the circuit. The same logic gate can have different behavior, in terms of the actual stochastic perturbation it applies to the bits, if the history of the quantum circuit prior to that gate is different. For example, if you apply H gate once, the first time, it behaves like a fair coin flip. The second time it forces the bit back to its original value deterministically. The difference in the second behavior is caused by the fact that the history of to the second H is different than the history prior to the first H.

This representation does not require additional assumptions. You can get to it purely from a mathematical transformation that is mathematically equivalent to the traditional wavefunction formulation and therefore is just a different way of representing the same thing. But the difference in representation implies something different about how you should think about what the mathematics means.

You get there by first decomposing the wavefunction ψ(t) into the probability distribution p(t) and a phase vector we can call θ(t): p(t)=|ψ(t)|²; θ(t)=arg(ψ(t))

Then, you write update rules for both of them in this form, so you can evolve them in this form without having to convert back to the wavefunction formalism. When you write out both of their update rules, they both depend upon the previous value of p and θ. Since we only care about p, we can take θ’s update rule and just substitute it in for θ in p’s update rule. But because θ’s update rule also takes θ’s previous value as an input, this definition becomes recursive, and it expands backwards into the past up until it reaches a basis case, which it’s trivial to prove that a degenerate distribution (which is usually the beginning of any quantum circuit) is always a base case. This then allows us to interpret θ as a sufficient statistic over the system’s history and not as a physical object.

This is just a mathematically equivalent way of representing the same formalism. You don’t have to take ψ to be a physical entity at all. The mathematical object carries two degrees of freedom, p, which is just a probability distribution at the current time, and θ, which is just a sufficient statistic over the system’s history which is just mathematically convenient to carry along rather than recomputing its whole history at every logic gate. And these two degrees of freedom are just represented together as a single complex number.

But like I said, this is a personal opinion. Most people don’t agree with interpreting the quantum state statistically, and insist ψ is a physical wave-like object. So, this is just my opinion and not some sort of consensus or anything.

I also find that treating ψ as a physical object is not even entirely coherent, because even if ψ exists, it is invisible to us, so it then creates a disconnect between the state of the system before we look, and what we actually look when we observe it. We don’t see ψ when we look at the memory of a quantum computer, but we see bits with definite values. This disconnect is known as the measurement problem. It is a problem unique to non-statistical interpretations of ψ.

The typical explanation is that ψ “collapses” to those definite values when you look at it. But what defines “when you look at it”? Is it a subjective collapse, meaning, literal conscious awareness of it leads to collapse? Then this leads directly to solipsism, as shown by the Wigner’s friend paradox. Is it an objective collapse, meaning by some physical process “at measurement” it collapses? Then you would be arguing that quantum mechanics switches to classical mechanics after some certain threshold, and so this would be empirically detectable in principle. It is trivial to prove that a physical collapse model simply cannot reproduce the mathematical predictions of quantum mechanics in all regimes.

Then, you have Many Worlds, which claims that ψ never collapses at all. But then the universe just consists of a giant invisible ψ, and so then you cannot explain anything we can observe at all, or make any empirical predictions at all. Tim Maudlin has a good lecture on this problem in particular: https://www.youtube.com/watch?v=us7gbWWPUsA

In my view, the statistical approach is really the only logically consistent one that also is mathematically consistent with quantum mechanics (objective collapse is logically consistent but ultimately constitutes a different theory). There are no good rebuttals to it other than complaining over it being too “overly metaphysical” because it posits that there are indeed underlying states, but because they evolve randomly we can never know them or track them, we can only track a statistical distribution of their possible values, and therefore they complain that we’re positing something “hidden.”

I mean, sure, it is something “hidden,” but physics is filled with non-empirical assumptions. Special relativity relies on the assumption that the one-way speed of light is half of its roundtrip. That is empirically impossible to prove, yet everyone believes it. I cannot prove that the moon exists when you’re not looking at it, to hearken back to something Einstein said. By definition, we cannot observe what we are not observing, so we can never prove anything exists independently of observation. They are indeed always “hidden” to us. But I don’t think it is particularly that fair to claim that we’re being “overly metaphysical” for believing in object permanence, because it seems to be a necessary prerequisite to any coherent physical theory of nature.

But, alas, this is all my opinion, and a tiny minority view.