mxx1's avatar

Quantum Computing

From a pattern recognition POV, quantum computing looks to be a boondoggle writ large. I have seen one or two in my time, and this looks bigger and hairier than most.

Practically speaking one wonders how the entrepreneurs and their minions get away with fooling so many investors.
Well, the same way they always do.
Spruiking through third party observers, creating the Fear Of Missing Out, hiding behind the technical mumbo jumbo, and genuinely believing their own bullshit.
And in this case the mumbo jumbo is hiding in plain sight – it is so opaque as to be impenetrable to most.

And that is the key for my research – is it possible or likely that quantum computers will ever work and do anything worthwhile?

About the only algorithm that has any value on a QC is Shor’s algorithm.
All it does is find the prime factors of an integer.
Practically speaking the best QC to date has run this algo for the integer 21.
No shit, 21.
My 6 year old can do that maths using brute force or intuition. 3 x 7 = 21, where 3 and 7 are prime numbers.
IBM tried to do the integer 35 and failed due to noise.

If Shor’s algorithm could work on a real QC it is in theory exponentially quicker than a digital computer.
Or super-polynomial faster, or whatever. Just much better, on paper.
You wouldn’t notice any improvement however until the integers got really big.

One might ask how a QC solves Shor’s algorithm…but that is the wrong question altogether.
In fact you would disappear into a bottomless pit of mumbo jumbo of integrals, Bra-kets, qubits and gates.
Its far more instructive to consider what limits quantum computers from solving the prime factors of large integers…

Qubits work by mysteriously solving vector and matrix problems through qubit entanglement.
The right answer just pops out of qubit entanglement like magic, so long as you setup and run the gates properly.
I don’t think the details matter much unless you are doing the programming.
Let’s call it “rabbit in the hat” computing. Ta-da.

I did some research with Simon Devitt and we concluded (i.e. I did such shit calcs that Simon was compelled to do it well) that by making reasonable assumptions, namely with the theoretical maximum of 4.2PB of RAM, using the entire MIPS computing capacity of the whole world in 2024 (ca. 2.8×10^16 MIPS) , we could emulate a 48-qubit quantum computer, error free and approximation free at an effective clock rate of approximately 21KHz.

However, Simon has a plan to create a 90 qubit emulator for Quokka v2.
So that got me wondering, does he have access to the RAM and CPUs of an entire other planet or two quadrillion, that I don’t know about?

No, Simon is going to use “non-exact” emulation.
The key to this sleight of hand is the amount of entanglement that is generated in a particular quantum circuit.
If your quantum circuit is not generating a lot of entanglement globally over the entire computer but instead works by generating limited “pockets” across smaller qubit subsets, it runs fast and more accurately.

As the circuit starts generating more and more entanglement across the whole computer, the tensors that you use to model the QC either begin to grow in size (exponentially) and you run out of memory or you start truncating them.

The truncation now introduces an error in the emulation (i.e. the output of your emulator becomes less and less accurate compared to what would be expected in a real machine). Sometimes you can theoretically bound the error in your final output, sometimes it is chaotic and your output from the emulated QC is completely unreliable. Which circuits you can bound, the approximation error, and which you can’t, changes depending on what you’re running.

Note that these approximation techniques always crap out too and often are not useful in quantum algorithms that provide exponential advantage over classical versions (such as factoring). If these emulation techniques worked well for general purpose QC then we wouldn’t really need to build actual QCs – we could run these algos using emulation on digital computers.

What this tells us is that to get rid of noise and errors you need to stabilise or isolate the qubits.
However to make a QC device useful you need to get entanglement over all the qubits.

Qubits that are controllable means they couple when you want them to couple, which also means they couple to shit when you don’t want them to, creating noise.
You’re playing a balancing act to have qubits that interact with you sufficiently to do stuff vs interact with everything else weakly enough to reduce noise.

This is fundamental and will likely result in the fact that QC will forever need high levels of redundancy through error correction. Unlike classical semiconductors, it is unlikely that errors in qubits will ever be low enough to remove the need for error correction.

But luckily, error correction is effective once error rates hit 0.1% or lower (that is, the additional qubit overhead used to correct errors doesn’t ruin the so-called supremacy of QCs over digital computers for certain problems) which is an error rate achievable with quantum technology while balancing on that knifes edge.
No one knows today if this needle can be threaded successfully. Of course they are all saying , yes we can. No self-interest there.

In my working experience developing all sorts of technology products, you need a (meta) steady state zone to make a product. If you are on a knife’s edge you can never make your product reliably enough for it to be sold.

So my money is on not, today. But we will see. Also I can sniff self-serving BS a mile away.

I would be happy to be wrong of course. So much money and so many brains – they might get lucky.
But you actually can’t beat entropy not matter how far into quantum theory you go.
I get this feeling that quantum people don’t actually understand entropy and how it applies to practical systems, i.e. the interface to these QCs is up here in the real world.

However even if they make the devices work, their application will be very limited to certain sorts of algorithms/problems which are enabled by rabbit-in-the-hat computing.
Actually they will be at least 10-100x times more limited than super-computers (by problem), which have never achieved, at any single moment, more than 0.5% of worlds MIPS processing capacity.
So let’s say $140m-$1.4b per annum based on the current supercomputer industry market size ($14b)
They will stay as supercomputers because of the cryogenic requirements, the size and cost, and the limited market need.

Even if it all works out, we have already over-invested into this market opportunity.