I think it’s reasonable to be more optimistic than you put it. Qubit counts and qubit fidelity have been increasing at a remarkable rate. Just five years ago we could barely eek out a handful of qubits, and when we did, they’d be bad. Google’s quantum supremacy result is a testament to that. (At this stage, whether they actually demonstrated the “supreme” part of supremacy is, imho, irrelevant. They’ve demonstrated a much larger, controllable, programmable quantum computer and measured its quality characteristics accurately.)

Of course, I’m saying it’s reasonable to be more optimistic, not that we have a proof we will certainly be able to scale to enormous machine sizes. But it’s definitely more than “speculative physics”: real machines have been built and demonstrated to exhibit truly measurable quantum effects that allow for programmable computation.

(To be sure, there is hype, there is a lot of cash sloshing around, and there are totally bogus claims some companies are publicly making.)

Admittedly, it's not a gate-model system, but at D-Wave we've been able to scale up to 5,000+ qubits now, and the future is promising for further advancements in qubit count, noise, and other advanced features.

The gate-model systems have shown that they are pursuing a much more difficult path, one that may indeed be fruitless for years or decades before they can approach our raw qubit count. We also have examples of nontrivial, paying-customer use cases that become more compelling with each new announcement. Factoring integers is indeed an interesting hard problem which would have a massive (negative?) impact on the world if realized, but besides Shor's and Grover's algorithms, it's not like gate-model QPUs have a ton of use cases significantly better than what a quantum annealer can accomplish.

I like to think of it this way: we're basically at the point of an ENIAC scale machine, if you liken quantum computing progress to classical computing. Fills up a room, very specific environmental and power requirements, little or no "memory" to speak of, esoteric and hard for anyone without years of training to master. Only a few decades later, the state of the art machine was thousands of times more capable, far cheaper and smaller, more reliable, more accessible in every way. Imagine describing the Internet as we use it today to an ENIAC operator, or a speculative investor considering IBM, Honeywell, etc. - it would sound like an impossible, Asimovesque dream, not something that children would literally be playing with sixty years later.

The only difference is that so far, we don't really seem to have a real exponential Moore's Law effect in quantum computing. Google et al. still have very low numbers of qubits without any real promise that they'll be able to deliver more of them in any consistent timeframe. At D-Wave we've done better on the scaling front, and we've been trying to keep up to our former founder's "Rose's Law" of qubit scale growth, but fabrication is an incredibly expensive, complicated, competitive endeavour that necessitates incredible quality control in order to produce processors that are up to spec. There are also other factors beyond the raw qubit count; the bigger advantage in our latest Advantage chip may actually be the higher connectivity between qubits on the graph, rather than their raw number.

Of course, we expect that we'll continue to push the envelope in this regard, and given enough time and investment, some of the early applications we're seeing now may well eventually be integrated into large scale products people use every day.

I thought the Quantum threshold theorem said that it was possible to scale up quantum computers as much as you like? Or am I misinterpreting it?

https://en.wikipedia.org/wiki/Quantum_threshold_theorem

The hope is that quantum computers will give us an exponential speed up on some problems, which could (again, hopefully) allow us to solve some NP hard problems. This can be extremely useful for scientific computing (e.g. protein folding) and engineering, where computers have to solve complex NP-hard optimisation problems.

It could also be possible to use the technology developed for the precise control and measurement of qubits to "rebuild" natural phenomena like the interaction of chemical molecules, something which is currently extremely hard to simulate.

In a classical computer, every bit of information in the system is in a definite state- 1 or 0. In a quantum system with such definite possible states, what you actually have most of the time of the system in some interpolation of the possible states- so in the quantum computer case each bit is usually in a state a1 + b0, where a and b are complex numbers such that |a^2|+|b^2| = 1.

Most of the time, the 'weight' flows back and forth between a and b according to certain equations over time. When you measure the system- that is, when the bit interacts with the outside world, hopefully your measuring apparatus- you see a 1 or a 0, with probabilities |a^2| and |b^2| respectively.

So what you can do is get a whole bunch of these quantum bits- qubits together, and set things up so that the time-evolution of their quantum state is correlated and probabilistically moves towards something you're interested in. Say you can set things up so the bit array- which, at first, will give you a mere perfectly random bit string on measurement- becomes more and more likely to give you, say, a prime factor, or the answer to some other question.

So yes, the quantum phenomenon is that the bits of the computer are quantum objects as opposed to classical.

They're built off fundamentally different basic units. Contemporary computers use transistors, which occupy traditional physics and do logic with voltage thresholds. Quantum computers use a quantum phenomenon -- one easy-to-understand (and fairly easy to construct) quantum computer substrate uses the spin of electrons in superconducting loops. Electron spin is a quantum phenomenon, in that the spin isn't deterministically positive or negative, it's a probability distribution -- initially, equally likely to be positive or negative, but you can't tell what it is until you actually read it. It's not 0.0, it's either -0.5 or 0.5, both with a 50% chance. Equally importantly, you can perform (physical) operations on electrons singly or in pairs in order to manipulate these probabilities. Quantum computing is turning these probability fields and operations into useful computational results.

Here is a long-ish video that explains quantum computers without using pop-science hand-wavy terminology

https://www.youtube.com/watch?v=F_Riqjdh2oM

A quantum computer is defined as a machine that can implement an arbitrary "unitary evolution" (up to arbitrary precision). If you don't know enough math to understand what a unitary evolution is, think of it as a quantum computer doing basically any possible thing that you can do with a given number of qubits. As another comment said, the idea is to (ab)use this to do some operations on qubits such that they end up in a state where measuring it will give you an answer to something you're interested in. It has very little to do with classical programming.

The math on quantum computers checks out, it's "just" an engineering challenge at this point, and many are doubtful whether these challenges will ever be overcome to build a quantum computer of sufficient complexity.

Essentially, some "unitary evolutions" are complex to implement, as in requiring a lot of quantum "gates". This causes an accumulation of error and a whole lot of other problems, which limits the complexity of the calculations that can currently be performed.

"Processing power" is colloquially the term most people I know use to describe computers of varying capabilities.