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Comment by tcgv | Hacker News Reader

Here are my two cents on the subject:

-- The need for complex numbers (...)?

Complex numbers are just a mathematical tool. They are used to deal with calculations that involve magnitudes and phases, such as modeling qubit’s internal state.

-- The fact that an n-qubit quantum computing system is significantly powerful than classical system (...)?

Due to the physical phenomenon of entanglement quantum computers allow a coherent superposition of multiple states. Quantum algorithms sort of operate on all superposed states at the same time. Classical computing can only handle one state at a time.

A while ago I wrote a blog post explaining how quantum computing works, from a programming perspective, in case you're interested:

- https://thomasvilhena.com/2019/11/quantum-computing-for-prog...

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Quantum algorithms sort of operate on all superposed states at the same time.

This is not entirely correct.

Also, from your linked article:

I will now introduce the Deutsch Oracle algorithm, one of the first examples of a quantum algorithm that is exponentially faster than its classical counterpart on the size of the input.

This is not entirely correct either.

See [1] for an authoritative source.

[1] https://www.nytimes.com/2011/12/06/science/scott-aaronson-qu...

Hi, thanks for going through my blog post!

Could you elaborate on why you believe my writings are imprecise? I read the link you provided, but couldn't find any divergence with its text though.

Here's the line of thought behind my statements if it's not clear to you:

1) Until a measure is made leading to the collapse of the quantum state qubits remain (possibly) in a superposed state. When a quantum gate is applied to these qubits it affects all superposed states (from a linear algebra point of view).

2) I took this statement from Wikipedia [1], forgot to link the source in the article: Simon, Daniel (November 1994). "On the Power of Quantum Computation". 94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science: 116–123.

[1] https://en.wikipedia.org/wiki/Deutsch%E2%80%93Jozsa_algorith...

It's not entanglement that allows for coherent superpositions of states but, well, superposition. (Note, however, that entanglement is responsible for decoherence.)

You are correct in that superposition phenomenon is independent from entanglement!

Nevertheless, In addition to supporting coherent superpositions, what makes qubits powerful for information processing is the ability of coupling multiple qubits for creating entangled i.e., non-separable states. This property confers exponential complexity to a N-qubit system which can then encode and ultimately process 2^N bits of information simultaneously.

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