If quantum computers are not deterministic, how are we solving problems? - by Mark John Fernee - Quora Question Review

This document contains a review of the answer by by Mark John Fernee on the question in Quora: "If quantum computers are not deterministic, how are we solving problems?*"
To order to read all the answers select: https://www.quora.com/If-quantum-computers-are-not-deterministic-how-are-we-solving-problems

Contents

Reflection

1. Answer Review

They can be deterministic!

If a quantum state is an eigenstate of the measurement apparatus, the measurement result is deterministic. That means, if you want deterministic answers, you need to design an algorithm where the desired answer is an eigenstate of the measurement apparatus. In effect, quantum interference is used to ensure that all other possibilities destructively interfere, leaving the desired output.

Think of each bit as being an arrow in three dimensional space. The quantum computer rotates those arrows around according to the algorithm. The aim is that in the final state, the arrows point either up or down. These are the two deterministic qubit directions. That means, to get a deterministic answer, you need to find an algorithm that ensures that all the rotations are precisely aligned at the output.

This requirement severely limits the design of quantum algorithms, and that is why there are still relatively few. The notable examples being Shor’s factoring algorithm, Grover's search algorithm, and a few others.

It would be futile if Shor's algorithm only found prime factors probabilistically. How would you sort the correct answer from all the incorrect answers? In practice, with error-prone operation, you could find that nine times out of ten, you get the correct answer. Then that's just a signal-to-noise problem. The algorithm is designed to give the correct factors in the absence of noise. In fact, if you are interested in learning about quantum computing, I suggest looking at the details of Shor's algorithm.

There clearly are some amazing intricacies in this algorithm.
For an introduction select this document: shor.htm
For example, the input number to be factored must have a larger bit size than the factors, however, the unitary transformation of the quantum processor means the output must contain the same number of bits as the input. That means there will be some superfluous bits, and how they are treated is beyond the scope of this answer.

The most natural problems to run on a quantum computer are actually quantum simulations. There have been quite a number of those that have been successfully run to date. Furthermore, these applications are in an area where classical computers struggle. These are applications applicable to materials, chemical, and pharmacological research. In other words, these are big money applications if they can be realised on a large scale quantum computer. That's why people are pouring money into this area.

3.

Reflection 1 - Question Review

The question: "If quantum computers are not deterministic, how are we solving problems?" is tricky.
Suppose that a quantum computer is deterministic, does that mean that this QC can solve any or all problems we have?
or if a quantum computer is not deterministic, does that mean that this QC can not solve any problem?
The question is more: which type of problem can a quantum computer solve
For a digital computer the issue more or less that you have to describe your problem in the form of an algorithm and this description (of the algorithm) has to be written in a programming language for a DC. If you have accomplished that you problem can be solved on a DC.
My understanding for a quantum computer this is the same, but this exercise is much more complex.

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Created: 1 June 2023

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