Qusim.py – A toy multi-qubit quantum computer simulator written in Python

by adamisntdead • 8 years ago

242 44 8 years ago

ahelwer5• 8 years ago

For the uninitiated - to simulate a basic quantum computer, all you need is the following:

* A product state vector, which is a vector of size 2^n filled with complex numbers where n is the number of qbits you're using. You derive the product state from a series of individual qbits by taking their tensor product; this exponential term is why simulating quantum computers takes exponential space.

* A set of common quantum logic gates, which are (2^n)x(2^n) matrices you multiply against the product state vector to derive the new product state vector; these matrices must be unitary (their conjugate-transpose is their inverse) (edited, see [0]) and therefore reversible (quantum computers are reversible computers). The full (2^n)x(2^n) matrices are derived by taking the tensor products of several 2x2 and 4x4 matrices.

* The measurement logic, where you calculate how the product state collapses by taking the square of the absolute value of each entry in the product state (these entries are called amplitudes).

This project is an implementation of those three things in Python. There is nothing special about the above mathematical constructs save that they match the observed semantics of a quantum system. This is good! Quantum computing is accessible to anyone who has taken a basic undergraduate course in linear algebra.

[0] I previously believed all quantum operators were their own inverses (Unitary and Hermitian) but apparently that is not the case; see comments below.

adamisntdead6• 8 years ago

That's pretty much it! There obviously is loads of optimizations that can be done, but it obscures the pretty standard linear algebra that is used to represent and calculate the states of the quantum computer!

A well-written version using OpenCL and written in rust is also available: http://github.com/qcgpu/qcgpu-rust if you are interested! Always looking for feedback

ahelwer5• 8 years ago

I've wondered - is it a common memory optimization tactic to store the individual qbit values until they become entangled and the product state cannot be factored? Or is entanglement common enough that it wouldn't be worth the overhead?

sytelus• 8 years ago

This is awesome. Over time I have came across too many posts claiming to explain QCs to hackers and they go on pages and pages without distilling this simple little thing. It would be great if you can also implement something like Shore's algo with your simulator.

adamisntdead6• 8 years ago

You can, but it would be very slow! This implementation gets really really slow around 15/16 qubits.

I am currently working on implementing shors algorithm into my main, simulation library. I already have grovers algorithm! https://qcgpu.github.io/qcgpu-rust/book/algorithms/grover.ht...

thethirdone• 8 years ago

these matrices must be their own inverse (in mathematical terms, Unitary and Hermitian). The full (2^n)x(2^n) matrices are derived by taking the tensor products of several 2x2 and 4x4 matrices.

Gates don't have to be Hermitian right? Like NOT^(1/2) is not Hermitian.

adamisntdead6• 8 years ago

Yep, observables in quantum mechanics are represented by hermitian matrices

ahelwer5• 8 years ago

Oh wow, am I wrong? I thought all quantum operators were their own inverses, which since they're all unitary means they must be hermitian.

andrepd2• 8 years ago

these matrices must be their own inverse (in mathematical terms, Unitary and Hermitian)

Not necessarily. The only requirement on quantum operators is that they must be unitary. Only observables have to be Hermitian (so they have real eigenvalues).

ahelwer5• 8 years ago

Thanks for the correction! I thought all quantum operators were their own inverse, but I guess I was wrong.

comnetxr• 8 years ago

Neither unitary or hermitian means that operators are there own inverse. Unitary here means that the inverse is the same as the complex transpose - which means that there is an inverse and it is easy to find. This is important as quantum circuits must be composed of unitaries, i.e. the circuit is reversable. Hermitian operators have no particular special property with respect to inverses.

keyle• 8 years ago

Thanks for the description but that made very little sense to a 'regular' developer like me. Any chance you could break it down and bring it down to my level?

ahelwer5• 8 years ago

I recommend the textbook Quantum Computing for Computer Scientists.

adamisntdead6• 8 years ago

You should check out these videos, one of them might give you an understanding!

- https://www.youtube.com/watch?v=JhHMJCUmq28 | Quantum Computers Explained - https://www.youtube.com/watch?v=IrbJYsep45E | The Mathematics of Quantum Computers - https://www.youtube.com/watch?v=wUwZZaI5u0c | Hacking at Quantum Speed with Shor's Algorithm - https://www.youtube.com/playlist?list=PL1826E60FD05B44E4 | A series by the author of the standard textbook

These are videos I particularly like!

bcwu• 8 years ago

Quantum Computation and Quantum Information, a.k.a "Mike and Ike" is the authoritative textbook in the field. It also happens to be very readable and beginner friendly. It's well worth reading the introduction to QC in the first twelve pages and skimming the first sixty. And the rest, as time/interest permits.

Deestan• 8 years ago

This sounds snide, but please believe me my intention is to be helpful.

Have you considered instead raising your level? The relevant topic, as stated in the comment, is linear algebra.

Moodles• 8 years ago

I'm no expert, but SMBC covers quantum computers quite well too :-)

https://www.smbc-comics.com/comic/the-talk-3

alemhnan• 8 years ago

The red button was a nice touch. I genuinely laughed.

lorenzorhoades• 8 years ago

After reading that article, you pretty much become an expert. I'm going to go apply to dwave now.

rorykoehler• 8 years ago

This is a great succinct explanation. I definitely understand QC's better after reading it. Thanks.

mentos• 8 years ago

Is it possible that a massive array of GPUs might be more economical than a few real quantum chips that need to be cooled to absolute zero?

sgillen• 8 years ago

That absolutely is the case right now, it may not be in a few decades.

ejdanderson2• 8 years ago

In the short term, yes, while the number of qubits is small and even smaller when you consider logical qubits require multiple real qubits to account for error.

In simplified terms though, for every logical qubit you add to the system, you effectively double the power of the machine. To double the power of your GPU stack, you'd need 2x more GPUSs each time. There is also the additional caveat of the type of problem - not every problem currently suited for a gpu is going to be better run on a qpu.

adrianN2• 8 years ago

That depends on the number of qbits you want to simulate. Doing the calculations on classical computers has an exponential slowdown as you need 2^n classical bits to store n qbits. It's pretty unlikely that you will ever be able to simulate a quantum computer with more than a few dozen qbits.

AstralStorm2• 8 years ago

Indeed. I'd expect this to top of at about 64 qbits with smart maths. (Mostly due to pointer limitations.) You could try to extend addressing but it'll be even slower...

da-bacon2• 8 years ago

Cool! My April fools day joke this year was a quantum programming language made up entirely of "entanglement" and "superposition": https://github.com/dabacon/qsel The simulator takes about 150 lines of python as well.

vtomole• 8 years ago

Hey Dave, your lecture notes [0] helped us a lot when we were building our simulator [1]. Thank you!

[0] https://courses.cs.washington.edu/courses/cse599d/06wi/

[1] https://github.com/QCHackers/qchackers/tree/master/software/...

da-bacon2• 8 years ago

That class was so many careers ago. Glad you enjoyed the notes. I wonder if I taught it today: maybe I'd start by having students use a simulator, or maybe trying to write a simple simulator themselves!

ejdanderson2• 8 years ago

Hey that code looks familiar :)

laughingman2• 8 years ago

There is this quote by Jürgen Schmidhuber, director at the Swiss AI Lab IDSIA , creator of LSTM Neural Nets that power many of our current machine learning applications.

" General purpose quantum computation won’t work (my prediction of 15 years ago is still standing). Related: The universe is deterministic, and the most efficient program that computes its entire history is short and fast, which means there is little room for true randomness, which is very expensive to compute. What looks random must be pseudorandom, like the decimal expansion of Pi, which is computable by a short program. Many physicists disagree, but Einstein was right: no dice. There is no physical evidence to the contrary randomness.html[http://people.idsia.ch/~juergen/randomness.html].

For example, Bell’s theorem does not contradict this. And any efficient search in program space for the solution to a sufficiently complex problem will create many deterministic universes like ours as a by-product. Think about this. More here computeruniverse.html [http://people.idsia.ch/~juergen/computeruniverse.html] and here.

I am out of depth with regards to quantum theory and quantum computation. If anyone with better knowledge with regards to quantum computation can clarify it would be great.

Is there any rationale to support Schmidhuber's argument, and has any advance in making actual quantum computers disprove his theory?

jrochkind12• 8 years ago

Hint: "There is no physical evidence to the contrary" isn't really a proof.

rejschaap• 8 years ago

You are getting down-voted because you are shifting the burden of proof.

comicjk• 8 years ago

Whether or not the universe is deterministic, quantum computers will work as long as nature works by wavefunctions and unitary matrices. There are many good reasons for believing this to be true, including experiments. Real randomness is not a requirement.

akvadrako• 8 years ago

I have looked into this somewhat deeply and he might have a point, but it's a bit subtle. First, current computers are not powerful enough to show him wrong. Second, the Many Worlds interpretation of QM is both deterministic and quantum, and since Jurgen is assuming his super-program creates a multiverse anyway, it's a logical next step.

The meat of Jurgen's proposal is that "fast" programs are more likely (which makes sense, IMHO) and quantum universes are too wasteful computationally (which seems less obvious).

If you want to read more along these lines, I can recommend something quite interesting from last year. It references Jurgen but argues that computational speed doesn't matter, only the length of the algorithm needed to produce our subjective experiences:

Could the physical world be emergent instead of fundamental, and why should we ask? (short version) by Markus P. Mueller https://arxiv.org/abs/1712.01816

adrianN2• 8 years ago

Schmidhuber doesn't seem to be a physicist, so I'll go with the majority of physicists on this one. Currently there is no reason to assume that quantum computers are impossible. There might be engineering challenges that we can't overcome, but quantum mechanics is a decently well established field and unless its assumptions are fundamentally wrong, quantum computers should work.

Panoramix• 8 years ago

Sounds like a crackpot to be honest. QC doesn't work yet because of practical limitations, but individual blocks have been shown to work separately and even small computers [1]. In looking at his wording he may be addressing a straw man, because QC has never aimed to be a general purpose general computer.

The universe is usually thought of as not deterministic. The deterministic interpretations out there come with huge problems: non-locality. Basically, that all particles in the universe are connected with a wave of sorts that acts instantaneously no matter the distance. But this is a philosophical distinction at best. Quantum computers work just fine.

[1]https://www.technologyreview.com/s/609451/ibm-raises-the-bar...

nathanshammah• 8 years ago

If you’re interested in quantum tech, here is my newsletter https://medium.com/quantum-tech

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Qusim.py – A toy multi-qubit quantum computer simulator written in Python

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