Quantum Computing for Beginners

[Bob Walance]

TL;DR

A document, for beginners, describing how quantum computers work with comparisons to conventional computers.

This article provides an accessible introduction to quantum computing, a cutting-edge technology that processes certain types of information much faster than conventional computers. Major companies like Google, Microsoft, IBM, and Intel are heavily investing in its development due to its potential to solve complex problems that are currently infeasible for classical computers, such as creating efficient carbon capture methods to combat climate change.
Quantum computing holds the promise of revolutionizing how we solve complex problems by leveraging the principles of quantum mechanics. Its ability to process and manipulate enormous amounts of information rapidly could lead to breakthroughs in various fields, including cryptography, optimization, and environmental science. While practical, large-scale quantum computers are still in development, ongoing research continues to push the boundaries of what’s possible, paving the way for a new era of computing technology.

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[atyy]

There are some tutorials on https://quantum-computing.ibm.com/docs/ which may be useful.

This might also be useful: https://dl.acm.org/doi/10.1145/3517340
Quantum Algorithm Implementations for Beginners
"We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM’s quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs."

Code is available at : https://github.com/lanl/quantum_algorithms

 

[malawi_glenn]

Free kindle book

Quantum Computing for the Quantum Curious​

https://www.amazon.com/dp/B08ZSFRP2K/?tag=pfamazon01-20

 

[anorlunda]

Great idea for a new thread. I had a question that never got answered. It has to do with programming quantum computers.

If I have an algorithm S (Shor's Algorithm), how do I interconnect the qubits to implement it?

 

[gentzen]

If I have an algorithm S (Shor's Algorithm), how do I interconnect the qubits to implement it?

You implement a classical control to orchestrate to required direct interactions between your qubits. The physical layout of your qubits determines which qubits can directly interact with each other, given the right classical control signal.

Such control signals could be microwave pulses of the right frequency and duration, or electrical wires put on the right potential, or a combination of both. Or it could be laser pulses, or modulations of a magnetic field, or other classically controllable phenomena.

 

[Bob Walance]

If I have an algorithm S (Shor's Algorithm), how do I interconnect the qubits to implement it?

Shor's algorithm is fairly complex. In the quantum realm you need to do modular exponentiation and also the Fourier transform. In this thread (post #2), atyy shared a link to some code on github that will factor '15' but with a fixed initial guess. It's tough to factor bigger numbers and be more flexible on the initial guess because it takes 3x qubits to do the job and simulators are very limited due to current memory size.
I gave up implementing Shor's on the simulator that I wrote because with my 13 qubits max I could only hope to factor the number '15', too. It didn't seem worth the effort. We need faster processors and exabytes of ram to make it interesting (imo), or we can just wait for real quantum computers with a couple hundred error-corrected qubits .

 

[Tom.G]

Excellent!

 

[Greg Bernhardt]

Would this be useful to add to PF Insights? @Bob Walance?

 

[Bob Walance]

Would this be useful to add to PF Insights? @Bob Walance?

Greg - That's certainly okay with me. If you do that then, if you can, please use the attached updated pdf. There were a couple of spelling errors in the first draft (thanks to Tom.G for helping me out on this). There is now a 'r2' in the footnotes.

 

[Greg Bernhardt]

The Insight is live at https://www.physicsforums.com/insights/quantum-computing-for-beginners/

 

[vanhees71]

Here's the direct publisher's link to the book mentioned in #1. It's open access!

https://rd.springer.com/book/10.1007/978-3-030-61601-4

 

[antonantal]

These video lectures by Vazirani (as in Bernstein–Vazirani algorithm) are very good:

https://www.youtube.com/channel/UCq9B8tT3oXl8BSyaoBPQXQw/playlists

 

[anorlunda]

I love the challenge to learn offered by this thread. Thank you @Bob Walance .I'm working my way carefully through Quantum Algorithm Implementations for Beginners linked in #2. I

I'm stuck on the notation in equation 11, page 18:5. I presume that the summation is for all possible values of X2 and X3, but I don't see how the notation says that.

 

[antonantal]

$\left(x_2x_3\right)\in\{0,1\}^2$ just means that the string $x_2x_3$ is from the set of all 2-tuples of numbers belonging to $\{0,1\}$. The notation is similar to how you would use $R^n$ for a coordinate space, just replace $R$ with $\{0,1\}$ and n with 2.
Then, as you presumed, the "bra" vectors in the sum will be $\langle0\mathbf{00}|, \langle0\mathbf{01}|, \langle0\mathbf{10}|, \langle0\mathbf{11}|$.

 

[Rich Thomasy]

Summary: A document, for beginners, describing how quantum computers work with comparisons to conventional computers.

revisions for the attached PDF:
r3 - Changed all occurrences of the word 'conventional' to 'classical'. Headings are no longer all capital letters.
r2 - Fixed a couple of spelling and grammar errors.

Fun article. Thanks. How do I get access to a computer which will answer the question "what is the best possible method for getting humans to conceive only one child or less?" Thanks.

 

[Tom.G]

How do I get access to a computer which will answer the question "what is the best possible method for getting humans to conceive only one child or less?"

No computer needed; it's called a chastity belt (or sterilization if you are a 'belt & suspenders' type of guy).

 

[Rich Thomasy]

No computer needed; it's called a chastity belt (or sterilization if you are a 'belt & suspenders' type of guy).

Fun reply. However, I was being serious.

 

[Ssnow]

"Quantum computation and quantum Information" by Nielsen e Chuang.
Ssnow

 

[Bob Walance]

I have updated the PDF (now rev 4) with a few clarifications and corrections. Also, a table of contents has been added.

 

[Bob Walance]

The PDF is now rev 6.
An appendix has been added that gives some details on a classical computer's simulation of a quantum computer.