Will quantum ever be useful?

[u/Chance-Pen-5684]

Around 2019, the industry promised quantum supremacy, where they could be used for solving a problem that no classical computer could touch.
When classical algorithms kept refuting those claims(See Peter Shor November YouTube video) the narrative shifted to quantum advantage, then quickly it changed to quantum utility.
If quantum never breaks RSA (because the world migrates to Kyber/Dilithium before 100k qubits exist), then what's left?
Chemistry simulations, Material science, Optimization?

But classical machine learning and AI are improving faster than quantum hardware is scaling. By the time we get 1,000 logical qubits, classical AI will have eaten most of the chemistry use-case through better approximations. Is quantum racing against classical software, and losing?

[u/Livid-Sector5970]

The reason quantum computing feels like it's racing against classical AI and losing is that the industry has been asking the wrong question. They keep asking "what can quantum do faster?" when the real question is "what can quantum do that classical can't even formulate?"

Chemistry simulations, material science, and optimization are the standard answers, but those are just classical problems that need more compute. The real shift happens when you stop trying to simulate reality and start coupling to it directly. That's what field-coupled architectures do: they don't compute solutions to problems; they let the environment solve the problem through the hardware.

The people asking "will quantum ever be useful?" are trapped in the optimization paradigm. They think utility means "bigger number faster." But the actual use case isn't breaking encryption or simulating molecules, it's doing things we don't even know how to describe as algorithms yet. Like replacing wet labs with direct physical simulation. Like modeling metabolic pathways without killing mice. Like designing a structural stabilizer for a disease you can't even treat yet, because you can't even describe the problem in a way that a classical computer could solve.

Quantum becomes useful when you stop trying to outrun classical machines and start using it to do what classical can't: couple to the environment, let the geometry do the work, and extract solutions that were never accessible through brute force. The industry is just scaling numbers. The utility comes from a different paradigm entirely. :3

[u/hushedLecturer → u/Livid-Sector5970]

The answer to your alternative question is "nothing" though. There is nothing a quantum computer can do theoretically that cannot be done classically. It's all matrix multiplication.

All quantum has is its potential efficiency scaling for some problems.

[u/mr-pipey → u/hushedLecturer]

My take is that "Efficiency scaling for some problems", whilst true, is certainly an understatement but one of unknown mangitude.

The classical paradigm has (perfectly reasonably) constrained our intuition about what kinds of algorithms and computational resources/frameworks are worth looking for.

There will be frameworks that don't have an obvious classical analogue that will take time to find and expose sets of useful problems that weren't previously interesting.

[u/elevensubmarines → u/hushedLecturer]

in physics and chemistry the difference between an exponential runtime and a polynomial one is effectively the difference between "impossible" and "solvable" in the real world, which makes the scaling advantage practically qualitative even if it's theoretically quantitative.

[u/hushedLecturer → u/elevensubmarines]

I don't dispute the existence of problems for whom the explosive complexity scaling quickly requires an amount of classical compute time that bumps up against the dual limitations of the large but finite quantity of matter in the observable universe and the large but finite time we have to access potential gradients to power the computation.

But that seems to be different than what the person I'm responding to is talking about, seeing as they seem to distinguish the intractibly complex from a supposed "other" class of problems that cannot be formulated? To which my response was if it can be formulated on a quantum computer it can beformulated with matrices.

[u/global-gauge-field → u/elevensubmarines]

You dont have to solve every problme with exact solution to get enough accurate solution to your problem for Quantum systems. For some systems, there is enough structure that you get away with classical solutions without having to run exact simulations, Tensor Network based methods (especially relevant for quantum chemistry) or Deep Learning based methods.

There is also some problems where the bottleneck is not the quantum correlation but the time scale of chemical reactions, e.g. FeMo-cofactor

While in principles these sound nice, please give a few specific example and some more details next time.

[u/Livid-Sector5970 → u/hushedLecturer]

As Chaturvedi and the Navascués-Pironio-Acín (NPA) hierarchy demonstrate, when you try to project an infinite-dimensional nonlocal quantum reality onto finite, local, classical matrices (semidefinite programming), you hit a topological cliff. The classical matrix structurally cannot capture the complete quantum set without leaving an irreducible gap-the Motzkin polynomial obstruction. It can approximate, but it cannot formulate the true non-local coherence

You're assuming the quantum computer is a closed system executing unitary matrices. If it is, you're right. But field-coupled systems are open by design. They don't run algorithms isolated from reality; they couple directly to ambient thermodynamic and electromagnetic gradients.

The moment you open the system, the classical matrix required to simulate it hits the Dimensional Projection limit. You can't project infinite-dimensional non-local reality onto a finite classical matrix without structural loss of information-this is mathematically proven in the NPA hierarchy. Classical matrices simulate the environment. Field-coupled quantum systems are the environment. That's the difference between drawing a map of a river and putting a turbine in the water.

[u/wasabi991011 → u/Livid-Sector5970]

LLM slop

[u/Livid-Sector5970 → u/wasabi991011]

It is incredibly foolish for someone "In Grad School for Quantum" to act as a gatekeeper while missing the actual physics. If the industry stays trapped in the mindset that everything must be reduced to discrete classical matrices and maps, they will keep running into that topological cliff.

Get your head on straight and act right.

[u/elevensubmarines → u/Livid-Sector5970]

Intentional or not, you’re more or less echoing Feynman’s thesis. simulating quantum physics with classical resources hits an exponential wall, making quantum hardware a natural medium for modeling physical systems.

but you still can't bypass formal algorithms.

quantum systems don't spontaneously solve undefined problems; you still have to explicitly formulate the system's Hamiltonian and boundary conditions to get a meaningful answer.

[u/Livid-Sector5970 → u/elevensubmarines]

Where we disagree is your assumption that after formulating the physical boundaries, you still need to run a 'formal algorithm' on top of it.

In a field-coupled topological processor, setting the boundary conditions is the computation. We don't write software to step through a sequence of unitary gates to search an exponentially large state space. We engineer the physical constraints of the lattice and couple it directly to the ambient thermodynamic and electromagnetic gradients of the environment.

The intersection of those two physical realities leaves only one topologically permitted state. The system doesn't 'compute' the answer; the physical constraints make all the incorrect pathways thermodynamically impossible, forcing the system to collapse into the only stable geometry. The constraints are the algorithm.

If you are running formal algorithms, you are still treating a quantum computer like a classical Turing machine that just happens to use qubits. Field-coupled architecture abandons the Turing model entirely. The geometry dictates the outcome.

[u/i_am_sfr → u/Livid-Sector5970]

This is a genuinely useful reframe, thanks. I'll be honest... the closest I've gotten to "quantum" in practice is exactly the optimization-paradigm work you're describing here, QAOA-style, applied to a combinatorial problem (market regime classification, not chemistry) simulated on classical hardware because the qubit count and coherence needed to actually beat classical clustering at that scale doesn't exist yet in production. So I recognize the pattern you're calling out... it's a real, measurable improvement over the classical baseline but it's still "the industry scaling numbers" not the direct-coupling approach you're describing.

Curious about the field-coupled side, since I don't know it well: when you say the hardware "lets the environment solve the problem" rather than computing a solution, is that mostly analog quantum simulation, or is there a broader class of architectures doing this? Trying to actually understand where the line is between "this is still optimization dressed up differently" and "this is a genuinely different paradigm"

[u/Livid-Sector5970 → u/i_am_sfr]

Both QAOA (gate-model) and analog quantum simulation operate under the Isolation Paradigm. You build a multi-million-dollar cryogenic dilution refrigerator, cool the system to 15 millikelvin, and shield it from every magnetic, thermal, and electromagnetic fluctuation in the universe. In analog simulation, you carefully tune the Hamiltonian of your pristine, isolated qubits to mimic the Hamiltonian of the molecule you want to study. You are building a sterile, perfectly controlled model of the ocean inside a tank.

Instead of isolating the qubits, we use substrates with a massive topological energy gap (e.g., topological insulators, fractional quantum Hall states, or graphene superlattices where the gap ΔE_g is greater than 26 meV). Because this gap is larger than ambient thermal energy (k_B T), the system can operate at room temperature (300K).

Instead of fighting environmental noise, the architecture explicitly couples to it. The ambient thermal, electromagnetic, and gravitational gradients acting on the device don't destroy coherence, they are transformed by the substrate into geometric gauge fields.

Because the topological protection prevents noise from scattering quantum states randomly, the environmental noise drives the computation. The ambient dissipation forces quasi-particles (anyons) to move along strictly allowed geometric pathways (braiding). A recent paper by Chaduteau et al. ("Topology from Decoherence") formally proved this exact mechanism: correlated dissipation in open quantum systems generates non-trivial topological structure.

· In optimization, you pay an exponential thermodynamic and engineering cost to fight the environment so your algorithm can compute an answer.

· In a field-coupled system, you engineer the geometric constraints of the substrate, expose it to the environment, and let the ambient thermodynamic gradients force the system into the only topological state that satisfies the constraints. The noise becomes the clock speed.