You're not wrong. The scope for quantum computers remains small Back when I was field CTO for VMware in Asia-Pacific and Japan, many of my colleagues expected me to know something about everything in tech, and it was sometimes hard to bring myself to say "I don’t know." And so in 2018 when someone asked me to explain quantum computing I gave it a shot and made a complete mess of the …
I'm old enough to remember a time when we were informed that no one would ever have a computer in their home because computers were the size of an office building and required enough power to run a small city. I expect that once quantum computers are of a sufficient size and stability, uses (meaning algorithms and/or new programming techniques) will be found for them that we aren't thinking about today.
It's true we haven't found all the algorithms in complexity class BQP. (You can derive that conclusion from algorithmic information theory, for one.)
It's unlikely we've found all the interesting algorithms in BQP, though that looks like an untestable assumption (at least without a formal definition of "interesting", and even then it seems pretty problematic).
So, yes, we can assume some "new uses" of GQC will be found, modulo civilization-destroying events. However, it's an open question whether any interesting new classes of uses for GQC will be found, if we define the existing known classes suitably broadly.
Solving certain weird-structure discrete-mathematical problems faster1 than conventional TMs can, such as factoring and discrete log and search, is one class. Simulating quantum systems is another class, and in fact it's the class that's being used in some of the current tussles over quantum supremacy/advantage experiments. Evaluating quantum circuits is another, if you consider that distinct from one of the other two. (Similarly, you might make QC algorithms for solving various graph problems distinct from the first class, if you think the first class was defined too broadly.)
Are there other distinct, interesting classes?
We know a great deal more about the theoretical possibilities of GQC than we did for, say, nonlinear electronic devices in their early days. People love these sorts of historical comparisons but they really don't stand up, because technology is developed differently these days.
1Remember that "faster" here means "in a complexity sense", i.e. in how fast the number of basic operations required grows in relation to problem size. (We'll just look sideways at the space question for a moment and then pretend it doesn't exist.) Whether it's faster in wall-clock time then becomes a question of whether the particular instance you're trying to solve is big enough that faster-by-complexity gives you enough of a benefit to overcome the necessarily slower operation of qubit gates versus classical ones, and other real-world hardware constraints.
1) If its not scaling by virtue of the parallelism of superposition, then its an analogue computer not a quantum computer.
2) Shors algorithm scales by the parallel circuits in the inverse fourier transform, its an analogue computer.
*However*
ANALOGUE COMPUTERS ARE USEFUL!
If they can scale those circuits then Shore's can factor with logarithm scaling, potentially beating Quadratic and GNF Sieves. It doesn't need the quantum marketing to do that.
Instead of narrowly defining the research budget into kickstarting "quantum computing", (something that will never happen because superposition does not work the way it is claimed*). Widen it to the specific factorizing problem, solved *any way possible*. Then the limitation of needing to pretend its based on superposition goes away and massive parallel co-processors, new factoring algorithms etc. all become possible to fund research into. No more good algorithms and good hardware pretending to be quantum crap, simply to get research funding. Imagine a coprocessor even.
* Look, you already accept that the frequency of light is red/blue shifted. i.e. what you measure depends on a motion of the observer. You are not setting that property in the photon by measuring it, because the property you are measuring is a net property of the photon and detector. A different detector moving differently would measure a different value for that property. It's a *net* property.
Two such net oscillations make a net spin (which for a photon is its circular polarization), and such a spin would *also* be a net motion, because its made of two net motions. You're not setting that property solely in the photon either, it is not a property purely of the photon and does not travel with that photon.
Three such oscillations and you can make a waddle, a curved translation across an oscillating field. Hence 3+ dimensions needed for space. Again, you're not setting that motion either, its a motion relative to the detector too.
You can get more complex oscillating there too, some real nice tank slappers, spirals, all manner of *net* motions, even from just 3 components you get that.
So the idea that measuring the property of a photon (or electron or other) sets that property and the universe adjusts to be consistent with your measurement, is not correct, because the property is a net property between detector and photon, it's not solely a property of the photon, not solely carried by the photon. Superposition is not correct.
Likewise entanglement, your photon P1 measured by detector D1 has all these shared property with P2 measured by D2.... yet D1 and D2 were never entangled, even if P1 and P2 were, that experiment could not work., All properties are net properties. You would have to filter to make D1=D2, something you do in every entanglement experiment.
Quantum computing is the cold fusion of, um, computing. In each case there is the theory, the hope, the dream, that just because it would be so darn useful if it only worked, then the whole universe is willing to violate every known law of entropy, combinatorics, conservation, all for you.
One of the main barriers to parallelism today is power consumption (and the related need for cooling), so in terms of solving otherwise intractable problems, I see more future in extreme parallelism using extremely low-power processing elements. Sure, it won't reduce asymptotic complexity of hard problems, but it will allow larger problems to be solved. My laptop can, using its graphics processor, in seconds solve problems that required hours of supercomputer time twenty years ago. Sure, graphics processors use a lot of power, but per compute element it is much less than a CPU. Reducing the power use even further will allow more parallelism.
Radical reduction in power usage will probably require something other than shrinking or otherwise improving CMOS technology. Exactly which technology will replace CMOS is not clear. Nanomagnets or superconducting materials have potential for extreme low power, but require complex setups (such as extreme cooling), but this is not so different from the requirements of quantum computers. Carbon nanotubes is a another possibility. Landauer's principle (https://en.wikipedia.org/wiki/Landauer%27s_principle), extreme low power computation may require restriction to reversible operations, but this is true also of quantum computation (unitary operations are reversible).
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