I work in this field.

Although the prospects for using quantum computers to solve classical problems are pretty bleak, the primary motivator for the invention of quantum computers was not to solve classical problems, but to solve quantum ones: https://tinyurl.com/3ndp36y7.

With regards to using quantum computers as they were originally intended, things are looking pretty good! To cherry pick two examples, quantum computers have been used to create a time crystal https://www.quantamagazine.org/first-time-crystal-built-usin... and observe other exotic phases of matter https://arxiv.org/abs/2305.03766.

Think of early quantum computers as tools for scientific discovery, not for addressing industrial problems. Their abilities to solve commercial problems comes later, that is, decades from now.

Is there a place for quantum computers if classical algorithms become more capable at simulating quantum mechanics in ways we find useful?

Breaking crypto, unless that falls too. Not all crypto, I'm skeptical on Grover's. Mostly elliptic curve and integer factorization stuff.

> Is there a place for quantum computers if classical algorithms become more capable at simulating quantum mechanics in ways we find useful?

There is not. Our existence as a field pretty much hinges on classical computers not being able to simulate all quantum mechanical problems efficiently. We imagine that designing quantum matter: https://cognitivemedium.com/qc-a-science, https://arxiv.org/abs/1508.02595 will be very useful in the scientific and technological sense and we don't think classical computers will ever fully stand up to that task.

> Breaking crypto, unless that falls too

If classical computers can simulate quantum efficiently then using quantum computers to break crypto also falls. Simulating quantum physics and factoring are in the same complexity class: https://en.wikipedia.org/wiki/BQP

> Our existence as a field pretty much hinges on classical computers not being able to simulate all quantum mechanical problems efficiently.

I don't think this is quite accurate. It could be that many of the kinds of quantum simulations we care about can be done efficiently classically, even if the worst-case quantum simulations are classically intractable. Certainly, classical simulation algorithms are steadily improving.

Right. We are now arguing over the nuances of what would make quantum computers useful, which I address in a comment where I say "Everything matters" later in this thread.

Most people who work in this field doubt that every quantum simulation problem we care about will be classical tractable in practice, that is, non worst-case. If we believed that, we might as well give up and continue to use the robust, mature classical computers we have and will continue to have better instances of for the foreseeable future.

I don't put too much stock into complexity classes. They're a real thing for sure, but implementation difficulties and constant factors are too.

I agree. "Everything" matters when it comes to these applications: complexity theory, heuristics, constant factors, quantum error correction overhead, qubit quality, improvements in classical algorithms, CPU and GPU improvements e.t.c. Doesn't make sense to put too much stock in just one of these components at the cost of others.

You are kind of asking if quantum computers would still be useful if quantum computers are not useful. By definition the answer is no.

Computational physicists have been thinking about algorithms for simulating quantum systems essentially since computers were invented. We have decent algorithms for approximating ground states, or for systems in equilibrium (contingent on it being spin-balanced, or at half-filling, or at 0 density, ... depending on the model), or in other limited circumstances.

But lift any of those special restrictions, and simulation methods hit a sign problem [sign]. In particular, real-time evolution of quantum systems, which is what a quantum computer does by its very nature, poses in some sense the most difficult sign problem for approaches leveraging classical computing.

That's not a proof that classical algorithms can't become more capable, but it's almost certainly a question that must be answered system-by-system. The generic sign problem is NP-hard, so special-case reasoning is required.

[sign]: https://en.wikipedia.org/wiki/Numerical_sign_problem

That's for the strong force. The challenge with quantum chemistry is the 2^N state space for N particles.

The reason those lattice field theory computations are done that way is that they provide stochastic but polynomial-time algorithms for exactly the same kind of exponentially-large state space that appears in quantum chemistry.

> Think of early quantum computers as tools for scientific discovery, not for addressing industrial problems. Their abilities to solve commercial problems comes later, that is, decades from now.

Well, they might become very useful for simulations in material science, even if they 'only' thing they can do better than normal computers is simulate quantum physics.

Yes. It's a spectrum. In the worst case, quantum computers only help us gain a deep understanding of quantum physics. In the best case, they beat classical computers on optimizations problems as well. Materials science falls somewhere along this spectrum.

Yes. Though it's more than a one dimensional spectrum:

There's also the orthogonal possibility that quantum computers don't work, or don't work well, and eventually we'll learn some new physics that tells us why. (Given that orthodox quantum mechanics says that quantum computers work, but so far they've been hard to do. It's most likely 'just' engineering issues, but there's still the possibility of something deeper.)

Every communication or marketing I have ever seen done by quantum computing actors has been about very "classical" problems: finance, clean energy, AI...

It's all snake oil, obviously. Those are keywords thrown out for VC money. IMO, there would be no way for this many companies to raise this much money if the investors knew what kind of problems quantum computing is really addressing.

The people who claim that current quantum computers are useful for classical problems contribute to "Quantum hype" which is frowned upon by most members of the community.

I mean, I wish. I have met these so-called giants of the field when I was at conference (they had a yearly big-brains meeting the same time, same place). I bet they talk about classic stuff because otherwise they wouldn't get funding. Quantum mechanics and using quantum computers for quantum problems actually would have convinced me. But who cares about me. What they need this is this thing called MONEY and that doesn't come with intellectually interesting problems -- it comes with overinflated claims over things that the committee understands. So classical problems it is. Can't blame them playing the game, but at the same time, I wonder how they look into the mirror at night.

To be fair, this is what academics in basically every field do.

If you prove a useless result about an exotic construction in your niche topology, you mention that recently topology has been successfully applied i.e. in data science. If you study some pathological convergencs properties if unheard of stochastic processes, you cite Black-Scholes equation and remind the reader of its importance in finance.

Indeed, this is how the game is played.