As a Millennial, I've been spoiled by the rapid pace of technological advancement that defined the late 90's and early 2000's. I remember when having internet access was a luxury, because many of my friends had to visit the library to play Runescape. I remember when my grandparents had a corded phone installed in their Buick, and it blew my mind. And by the time I was in high school, I had my own Nokia flip phone. And it wasn't long before I was cruising the internet over broadband wifi on a Macbook Pro with a 17" monitor.

Transistors proved to be ubiquitously disruptive. Moore's Law had its impacts on everything - it changed how we communicate, how we work, how we learn, how we think... And it made us have a certain kind of opinion about technology.

I think my generation is making the mistake of assuming Moore's Law applies to everything, and you can't blame us: that's been the experience our entire lives. But there's an important factor to consider: Lithography.

Lithography is the process they use for printing PCBs (printed circuit boards). In the early days of PCB manufacture, the primary limitation in transistor density was optics - essentially the precision of photo development. The science was well-known, it had a clear path forward, and the manufacturers who succeeded were always looking far enough ahead to anticipate the next set of lithographic limitations.

In other words, the writing was on the wall. Clearly, it was only a matter of iterative improvements using evermore sophisticated lithographic techniques, and the rate of progress would continue. That is, until the next physical limitation presented itself, which it inevitably did.

I remember hearing about quantum computers when I was young, I remember learning about the double slit experiment and the "spooky action at a distance" and quantum entanglement from videos on YouTube. I was definitely left with the impression that quantum phenomena were quite remarkable, almost magical in some sense. It seemed to challenge every intuition I had about reality. Surely some smart person would figure out how to exploit this bizarre behavior and build some kind of machine that could predict the future, or something equally impressive.

Ok, maybe predicting the future was a stretch. But invalidating practically every form of cryptography currently in use today? That could cause a radical paradigm shift; all forms of internet-based business would suddenly be entirely reliant on "quantum safe" cryptography, which have comparatively weaker hardness assumptions (although this is my own speculation) than their prime-number-factorization counterparts.

But is it even feasible? Could such a quantum computer actually exist sometime soon, or ever?

You've probably been told that the "computational power" of a quantum computer is directly proportional to its qubit count. More qubits means faster qu-computer. But that's actually not true. It's like saying a 64-bit processor is faster than a 32-bit processor: it's categorically wrong. The number of bits doesn't tell you anything. The clock speed might mean something, but even that can be misleading. The most reliable metric we use for classic computer is: the number of transistors. Bits are not transistors, and qubits are not quantum gates.

If a quantum computer matches the specifications described by Shor's algorithm, we'll call it "Shor Complete," a nod to the Turing completeness of classic computers.

For a quantum computer to be considered "Shor Complete," it must be fully connected. Fully connected means that every qubit is directly connected to every other qubit via quantum gates. Technically this requires 3 gates between each pair of qubits to be Shor complete.

In order to reduce the security effectiveness of the globally-standard RSA encrpytion scheme, you'd need a quantum computer with thousands of fully connected qubits. Now, imagine we were talking about classic computers for a moment: how difficult would it be to directly connect a single transistor to thousands of little copper traces?

Modern lithography techniques can have roughly 50 layers on a PCB before you start reaching physical limitations. And even so, where would all those traces go? The further the distance between qubits, the higher the likelihood of decoherence. It's simply not practical to build.

So a perfect quantum computer is impossible to build, sure, but a perfect Turing machine is impossible to build also. That doesn't mean quantum computers couldn't be a disruptive technology, right?

Modern techniques exist to alleviate many of the shortcoming of quantum computation. Error correction and SWAP are the primary features of a quantum computer that allow it to be productive despite the other physical limitations. But these features also impose limitations on the reliability and accuracy of quantum algorithms.

But, error correction and SWAP don't matter. They are completely unnecessary.

In fact, a quantum computer is 100% realizable, just not as an analog device.

Modern GPU technology has blossomed with the advent of machine learning. Companies like nVidia manufacture extreme computation environments with unfathomable shared memory caches available to enormous networks of tensor processing units (TPUs), designed for AI but also perfect for, you guessed it, quantum simulations.

The best thing about a quantum simulation is: there's no uncertainty principle. Coherence is always guaranteed, and the runtime can be debugged like any other program. Unlike the analog quantum computer, the simulation can be paused at any time, and resumed with perfect coherence.

The common objection to quantum simulations is the Hilbert representation of the quantum state. It's believed that due to the sheer size of the Hilbert, n^q where n is the number of bits of precision, and q is the number of qubits being simulated. Obviously, a memory of that size, even 2^1000 is beyond anything a classic computer could possibly handle. It's unfathomably big, MUCH bigger than the observable universe.

The Hilbert, at least on paper, appears devastating for classic quantum simulations - it looks like an insurmountable problem. But it's not.

Saying quantum simulations are impossible at scale is like saying fluid simulations are impossible because you'd never be able to account for each and every atom in the volume.

It's silly, frankly, to suggest the Hilbert representation imposes any limitations whatsoever on quantum simulations. Sure, maybe it's not the kind of problem a college graduate could solve during a hackathon. But SHA-256 wasn't designed that way either, nor was the Google Search algorithm. Overcoming the size of the Hilbert in simulations is just another difficult technical problem that will be overcome, and it likely already is.

Even current implementations of the "sparse Hilbert" - a technique used to reduce the memory footprint to a tiny fraction of its full theoretic size, running on a state-of-the-art nVidia TPU datacenter, can already break low-security RSA tokens.

And companies operating in this space have a tendency to publish results combining an analog quantum computer with a simulation - the simulation likely contributing the lion's share of actual computation. I can't help but notice that these Fortune-100 companies fundraising for quantum side-hustles are spending their own money on GPUs. It's as if they're not stupid.