epistemic status: Stating impressions, but I don't know much about quantum physics (or computing!). Someone more qualified please write the accurate version of this post.
I think people have been hyping quantum computing backwards. The specific algorithms that are always brought up as providing a relevant speedup over their classical counterparts are Shor's algorithm and Grover's algorithm, but not much relevant economic activity is tied up with finding the prime factors of numbers, and while getting a radical speedup in unsorted search, the setup costs may only be worth it for extremely large searches:
Even when considering only problem instances that can be solved within one day, we find that there are potentially large quantum speedups available. ... However, the number of physical qubits used is extremely large, ... . In particular, the quantum advantage disappears if one includes the cost of the classical processing power required to perform decoding of the surface code using current techniques.” The most recent of the references listed above [11] estimates that achieving a quantum advantage via a quadratic speedup requires at least a month-long computation already if each iteration contains at least one floating-point operation.
—Dalzell et al., “Quantum algorithms: A survey of applications and end-to-end complexities” p. 76, 2023
Relevantly, with cheaper quantum error correction this may drop, and I vaguely remember Aaronson claiming that performing unsorted search with tens of terabytes is a low estimate for when Grover speedups will be useful.
For cracking 2048-bit RSA and 256-bit ECC:
The physical resources required to implement these logical circuits fault tolerantly depends on many details of the hardware, including the error rate, the physical gate speed, and the available connectivity. In both cases (2048-bit RSA [10, 29] and 256-bit ECC [25, 26, 27]), given current hardware schemes restricted to nearest-neighbor 2D connectivity with logical qubits encoded into surface codes, the number of physical qubits is estimated to be on the order of 10 million and the computation runs for at least 3–10 hours (significantly longer than this for platforms with relatively slower physical gate speeds).
—Dalzell et al., “Quantum algorithms: A survey of applications and end-to-end complexities” p. 114, 2023
which is certainly much faster, but also much less economically useful, and in some sense economically disvaluable because now we have to find post-quantum cryptography.
I don't have a full picture of the possible applications for quantum algorithms but my impression is that for purely bit-focused areas such as e.g. logistics or supply chain optimization or even machine learning (1) are fairly narrow, (2) usually don't offer an exponential speedup or only offer it if we postulate specific setups (e.g. the HHL algorithm for estimating quadratic functions of the solution of a system of linear equations depends on "the solution vector, , […] be efficiently prepared", (3) often the best classical algorithms exploit some structure that makes them comparable in performance to quantum algorithms (such as sorting an index once and searching in logarithmic time repeatedly) and (4) that finding exact solutions to computational problems efficiently is not a large bottleneck on bit-focused parts of the economy, except in training LLMs. I feel skeptical about quantum machine learning, and my guess is that if we read the fine print on quantum machine learning speedups we'll often not find them useful in practice:
So in summary, how excited should we be about the new quantum machine learning algorithms? To whatever extent we care about quantum computing at all, I’d say we should be excited indeed: HHL and its offshoots represent real advances in the theory of quantum algorithms, and in a world with quantum computers, they’d probably find practical uses. But along with the excitement, we ought to maintain a sober understanding of what these algorithms would and wouldn’t do: an understanding that the original papers typically convey, but that often gets lost in secondhand accounts. The new algorithms provide a general template, showing how quantum computers might be used to provide exponential speedups for central problems like clustering, pattern-matching, and principal component analysis. But for each intended application of the template, one still needs to invest a lot of work to see whether (a) the application satisfies all of the algorithm’s “fine print,” and (b) once we include the fine print, there’s also a fast classical algorithm that provides the same information.
—Scott Aaronson, “Quantum Machine Learning Algorithms: Read the Fine Print”, 2015
Hence: Quantum computing looks quite underwhelming on the side of bits.
My best guess is still that quantum computing is still extremely promising, because quantum algorithms are really good at simulating quantum systems, and the world is quantum.
Despite the apparent exponential cost of exact classical methods for this task, scientists have made incredible progress over the last century via increasingly sophisticated approximate methods. As a result, quantum chemistry is now a core part of several applications, including the analyses of chemistry experiments, the pharmaceutical drug discovery pipeline, and the optimization of materials for catalysts and batteries.
—Dalzell et al., “Quantum algorithms: A survey of applications and end-to-end complexities” p. 36, 2023
There's been some speculation that accurate quantum computers can even help with the construction of next-generation quantum computers
I wish we had a quantum computer because by the way, the first thing the quantum computer will allow us to do is build quantum computers, because it's going to be so much easier to simulate atom-by-atom construction of these new quantum gates.
—Dwarkesh Patel & Satya Nadella, “Satya Nadella — Microsoft’s AGI plan & quantum breakthrough”, 2025
but my impression is that these kinds of flywheel-arguments are usually not applicable and usually some different bottleneck kicks in.
But otherwise, quantum algorithms seem really useful for simulating the interactions of small molecules and their formation, figuring out the dynamics of chemical interactions, maybe even making progress on atomically precise manufacturing and resolving the Drexler-Smalley debate???
There is also some hope that quantum computing will allow us to make progress in nuclear and particle physics, but I can't think of any immediate industrial applications of such progress.
If my understanding here is correct, then that's way more interesting than progress in bits! Humanity hasn't made much progress in atoms recently, while making tons of progress in bits, so that might be why people are hyping quantum computing as a bit-focussed technology—they can't conceive of anything else? And communicating the advantages of quantum computing has been extremely backwards, which is usually lead with "quantum computing will break this strange cryptography thing", not "quantum computing will let us make batteries that are substantially more efficient", guess which of those is more easily understandeable to laypeople‽
So, yeah, I think quantum computing is hype-worthy, but the current hype is mis-directed, and can be redirected in the correct direction with a simple message: Quantum Computing is About Atoms, Not Bits.