19

Regarding your first question, you are essentially asking about the validity of a position taken by David Deutsch - a founder of quantum computing! For example, in his book 'The Fabric of Reality', Deutsch states: When Shor’s algorithm has factorized a number, using $10^{500}$ or so times the computational resources that can be seen to be present, where ...


12

Question 1 This description lies somewhere between the two extremes of a theory and mysticism, depending on how amiable one is to the concept. David Deutsch is vocal proponent of the former, Lee Smolin of the latter (he categorizes it as "Mystical Realism"). The general idea was initiated by one of John Wheeler's PhD students, Hugh Everett III, in his ...


6

In the many worlds interpretation (MWI) reality consists of a structure called the multiverse that looks like a collection of slightly interacting parallel universes in some circumstances: Deutsch, David. "The structure of the multiverse." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 458.2028 (2002):...


6

1 and 2 have elements of truth, but are only partially correct, with big caveats. 3 and 5 are complete nonsense. You can choose to read 4 the right way to make some sense out of it, but it doesn’t contribute to the computational speed of any algorithms.


5

tl;dr- Quantum computers can't really help us to simulate the whole universe as the universe is likely vastly more complex than even quantum mechanics can capture, plus we can't even begin to guess how big it is or many other basic fundamental features. In short, simulating the whole universe is beyond sci-fi. We can't really simulate the entire universe, ...


5

If you treat the gate sequence as fixed then by the same logic you can treat the actual gates as fixed. No parameters is better than polynomial number of them :) But the problem is not with this. Let's say we want to implement Shor's period finding routine. The output of the unitary gate sequence will be some state in $2^n$-dimensional Hilbert space. We do ...


4

I should probably start by describing my philosophical standpoint: I would never talk about "many worlds" or some such. However, I certainly believe that it is possible that everything, including measurement, is unitary. That apparently makes me a many-worldian. It's not necessary to buy wholesale into a picture of diverging worlds. And I think this question ...


3

There are a lot of comments and objections in the question, too many in fact to go through them all. I will try to address some of the points that I think hide misconceptions, to hopefully give a clearer idea of what's going on. About "interpretations of QM in which the measurement is non-unitary" The non-unitarity of the measuring process is not a matter ...


3

The $|x_i\rangle$ you mention here are qudits, they are the generalization of qubits to base $d$ with $|S| = d$. It is categorized by a superposition of $d$ states, same way a qubit is described by the superposition of 2 states. In base 3 it has a specific name as well, this is called qutrit.


2

Great question, and David Mermin dedicates an entire section of his great paper "From Cbits to Qbits" to it: Like my disapproving colleague, some physicists may be appalled to have finished what purports to be an exposition of quantum mechanics — indeed, of applied (well,gedankenapplied) quantum mechanics — without ever having run into Planck’s ...


2

I like this question although the question and answers may be a bit vague/a moving target. Initially I'll quote Gil Kalai who asked a very similar question on MathOverflow: the Planck constant plays almost no role (and, in fact, is hardly mentioned) in the literature on quantum computation and quantum information, and I am curious about it. We can take ...


2

I believe the issue you are missing is entanglement, which is an essential resource in quantum computing algorithms. Since we generate entanglement between these qubits, we can no longer think of independent subspaces of the Hilbert space where the final state can be represented as a tensor product of these subspaces. This is because an entangled state can't ...


2

The issue is that you are confusing the notions of Komogorov complexity and computational complexity. Kolmogorov complexity (roughly) means the smallest amount of data that you need to provide in order to completely specify an object. Computational complexity (roughly) refers to the minimum number of time steps that it takes any Turing machine to convert an ...


1

As Danylo Y have answered, the key is you don't need to read out the entire quantum state at the end of the quantum algorithm to get your answer. There is another algorithm, called HHL algorithm, which is design to solve linear system of equations $Ax = b$. It provides an exponential speed up, and uses $O(\log(N))$. If you think about it, it already takes $O(...


1

Time evolution of quantum systems is described by Schrodinger equation $$ i \frac{h}{2\pi}\frac{\partial}{\partial t}|\psi(t)\rangle = H |\psi(t)\rangle. $$ So any change on quantum computer can be described by the equation. Or in other words any quantum gate is described by its Hamiltonian and the equation describe how to the gate acts. When we discretize ...


1

The multiverse is not commonly accepted as the right description of reality and is just one of many interpretations of what exactly happens at the moment of the "wave function collapse". The multiverse is in its core just an idea to preserve determinism in nature by the argument: If you know in which exact universe you are, you can trace back every particle ...


1

You are 100% correct that this question has nothing to do with the Everett interpretation (also known as "many-worlds interpretation") of quantum mechanics, and in fact I would even agree with your professor's description of the many-worlds interpretation that "two branches interfere with each other if and only if they produce an outcome that'...


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