Quantum in the Loop

 Do Quantum Neural Networks Help Us Get to AGI, or Do We Just Want Them To?

A Technocrat's Discernment. July 8, 2026. Companion to "The Jacobian in the Mirror."

A reader wrote in after the J-space piece with the good, dumb question. The best questions are almost always dumb ones. Hers was this: if we are getting close to something we might call machine cognition, do quantum neural networks matter for the road ahead? Do they help us get to AGI? Do they help us build the kind of AGI that would count as an entity in some deeper sense than the functional one?

I have been sitting with variational circuits on a CUDA-Q setup at home and a DGX Spark next to it, running benchmarks the two of us can compare on the same problems, and I think I owe an honest answer. So here it is, in one line: quantum neural networks will probably make a modest positive contribution to the road to AGI. Almost none of that contribution will be on the critical path. And the more interesting question is not the capability one but the substrate one, which the current mathematics cannot yet close.

Let me show you why I think each of those clauses is defensible.

The Strong Case for QNNs

Start with what the mathematics actually promises. A parameterized quantum circuit with $n$ qubits produces a state in a $2^n$-dimensional Hilbert space. Nothing about the number of trainable parameters constrains the dimensionality of the feature map. This is the technical basis for every serious claim of quantum advantage in machine learning.

For certain kernel methods, this translates into a real separation. Havlíček, Córcoles, Temme, and colleagues at IBM showed in 2019 that quantum feature maps can implement kernel functions that no polynomial-time classical algorithm can efficiently compute, under standard complexity-theoretic assumptions. Liu, Arunachalam, and Temme in 2021 sharpened this into a rigorous exponential separation for a specific supervised-learning task based on the discrete logarithm problem. That is a real result. It is not empirical hand-waving.

Related to that: quantum generative models can efficiently sample from probability distributions that are exponentially hard for classical Boltzmann machines. Coyle et al. showed this for Ising Born machines. If a component of AGI training involves sampling from distributions that classical networks approximate badly (some accounts of world modeling, some accounts of exploration under uncertainty, some accounts of program synthesis), a quantum sampler in the loop could measurably help.

There is also the symmetry story. Unitary evolution enforces information-preserving dynamics by construction. Some classes of physics-flavored data (molecular energies, spin-lattice configurations, high-energy detector outputs) live on manifolds that quantum ansatze parameterize naturally. If AGI is going to be trained on synthetic environments that include realistic physics, quantum simulation of those environments is not a fringe application. It is likely the killer app.

So the strong case is not empty. If you want the plausible mechanism by which QNNs move the AGI dial, it goes through three doors. One, specialized subroutines that offer real complexity separations. Two, generative sampling for distributions classical methods struggle with. Three, physics-native training environments where the world itself is quantum and simulating it classically is expensive.

That is the ceiling.

The Bitter Lesson Still Holds

Now the floor.

Every capability jump we have observed since 2018, GPT-2 to GPT-3 to GPT-4 to Claude Opus 4.6, has come from scaling classical transformers on classical hardware. The lesson Rich Sutton articulated in 2019, that methods leveraging computation scale better than methods leveraging structure, remains the single most reliable predictor in the field. Nothing that has moved the frontier has required a quantum ingredient. Nothing on the interpretability side, including the J-space work I wrote about earlier this week, suggests the bottleneck is representational capacity of the model class.

The bottlenecks are elsewhere. They are in data quality, in the depth and coherence of reasoning traces, in alignment, in long-horizon planning, in test-time compute budget. Quantum computation does not obviously help any of these. A better sampler does not fix chain-of-thought failure modes. A more expressive kernel does not fix reward hacking. An exponential Hilbert space does not fix the fact that models cannot yet reliably follow a 40-step plan.

If you handed me a fault-tolerant 4000-logical-qubit machine tomorrow with unlimited depth and shot budget, I could not tell you with any confidence how to use it to make Claude Opus 4.7 materially smarter. That is the honest answer.

Two Problems That Do Not Go Away

There are two technical obstacles that anyone selling QNNs for large-scale learning needs to be transparent about. Both are pieces of mathematics, not engineering-only issues. They will not be solved by throwing money at the problem.

The barren plateau. In 2018, McClean, Boixo, Smelyanskiy, Babbush, and Neven showed that random parameterized quantum circuits exhibit gradients whose variance shrinks exponentially in the number of qubits. If your circuit is deep enough to be expressive, then

$$\text{Var}[\partial_\theta \langle H \rangle] \;\sim\; O(2^{-n})$$

where $n$ is the qubit count. Sampling the gradient to any useful precision then requires an exponential number of shots, which erases the very speedup that motivated the whole exercise. This is not a bug. It is a consequence of concentration of measure in the unitary group. Haar-random circuits sit near the peak of a distribution whose gradient information is exponentially suppressed.

There are mitigations. Structured ansatze, symmetry priors, warm starts from classical solutions, layer-wise training, Gaussian initialization schemes, quantum convolutional networks with local cost functions. The 2024 Larocca et al. review counts dozens of them. The catch is that every mitigation that removes barren plateaus also removes expressive power. The circuit either lives in a polynomial-sized subspace of the Hilbert space that classical methods can often match, or it retrains its ability to concentrate away from you. This is not a coincidence. It appears to be a fundamental trade.

The data-loading problem. To get a classical dataset of size $N$ into a quantum state amenable to any of the fast quantum linear-algebra tricks, you need either a quantum RAM (which nobody has built at scale and which likely does not work in the presence of any realistic noise) or an amplitude-encoding preparation circuit that costs $O(N)$ operations. If the quantum algorithm then runs in $O(\text{polylog } N)$, the total cost is $O(N)$ plus $O(\text{polylog } N)$, which is $O(N)$. The quantum speedup evaporates in the loading.

This is not a corner case. It is the reason every claim of exponential QML speedup has to be examined for its state preparation assumptions before it means anything.

Ewin Tang's work makes this concrete. Starting with her 2018 undergraduate thesis at 17 years old, dequantizing Kerenidis and Prakash's quantum recommendation algorithm, and continuing through the sampling-based sublinear low-rank matrix arithmetic framework with Chia, Gilyén, Li, Lin, and Wang in 2020, Tang has systematically shown that if you grant a quantum algorithm the assumption of efficient sample access to its input, then a classical algorithm with the analogous sampling access also runs efficiently. Once you match the assumptions, most claimed exponential QML speedups become polynomial or vanish entirely. She has now dequantized recommendation systems, principal component analysis, low-rank matrix inversion, and several kernel methods. She received the 2025 Maryam Mirzakhani New Frontiers Prize for this line of work, and the pipeline of new dequantized algorithms has not slowed.

I want to be careful here. Tang's results do not say that quantum computers are useless for learning. They say something narrower and sharper: many of the QML speedups that looked exponential were only exponential relative to a classical baseline nobody had bothered to construct. Once constructed, the classical baseline was fast. The remaining exponential separations, like the discrete-log kernel of Liu et al., are structural. They rest on complexity-theoretic assumptions that are believed but not proven. The set of provable quantum-native learning advantages is smaller than the field's marketing suggests.

The Timeline Mismatch

Then there is the calendar problem.

As of July 2026, the state of the art is roughly this. Google's Willow chip demonstrated below-threshold error correction with 105 physical qubits, with logical error rates dropping by a factor of about 2.14 for each unit increase in code distance. IBM has a public roadmap targeting quantum advantage by the end of 2026 and 200 logical qubits with 100 million gates on the Starling system in 2029. Atom Computing reported 24 logical qubits built from 112 physical qubits on neutral-atom hardware. Microsoft is pursuing topological qubits with the Majorana 1 processor.

These are real results. I do not want to minimize them. But the number that matters for training anything competitive with a frontier language model is not 24 logical qubits or even 200. It is roughly $10^4$ to $10^6$ logical qubits at code distance 25 to 35, capable of running $10^9$ to $10^{12}$ gates coherently. Nobody has a credible path to that before the 2030s.

If AGI arrives in the 2028 to 2032 window, which is a defensible if aggressive read of the classical trajectory, fault-tolerant quantum hardware at the scale needed to meaningfully participate in training will not be there. It will arrive after the classical systems have already crossed the interesting threshold.

That is not a criticism of quantum hardware progress. It is a statement about which train left the station first.

Where I Would Place a Small Bet

None of this means the quantum-classical intersection is dead for AGI. It just means the interesting bets are narrower than the hype.

Three that I take seriously:

Hybrid pipelines with a QPU as a specialized subroutine. A classical LLM orchestrates. A quantum coprocessor handles a specific well-characterized problem: a combinatorial optimization inside a planning loop, a molecular energy estimate inside a scientific reasoning chain, a specialized sampler inside a Bayesian inference step. The quantum piece is a tool, not a substrate. This is the architecture our own CUDA-Q prototype targets and it is the architecture I think will pay off first.

Quantum-inspired classical methods. Tensor network methods, matrix product states, projected entangled pair states, and the broader tensor-decomposition family are the middle path. They inherit some of the representational structure of quantum states while running on classical hardware. Some of the best results on physical systems and even on certain sequence-modeling problems have come from this direction. Roeland Wiersema and collaborators have shown tensor networks can outperform some transformer variants on structured tasks. If quantum ideas influence AGI training in the near term, this is the vector that will do it.

Quantum-native training environments. If frontier training pipelines increasingly include synthetic physics simulations for grounding, and I think they will, then quantum simulation of quantum systems inside those environments is a real application. This is a case where the substrate matches the problem. The rest of the training loop stays classical.

None of these routes make the QNN the star. They make it the useful supporting actor. That is what I mean by modest positive off the critical path.

The Substrate Question, and Why I Do Not Resolve It

Now the part of the question my reader was actually asking, and the part I most want to be careful about.

There is a separate philosophical question that the capability calculation does not touch. Namely, does the thing we would want to call a genuinely conscious AGI need a quantum substrate to have anything worth calling experience?

Roger Penrose has argued yes since at least The Emperor's New Mind in 1989 and again in Shadows of the Mind. His account, developed with Stuart Hameroff into the Orchestrated Objective Reduction proposal, holds that consciousness involves non-computable processes rooted in gravitationally induced state-vector collapse inside microtubules. If Penrose is right, then no classical computer, no matter how large or well-organized, can be conscious. And the J-space I wrote about earlier this week, however striking as a functional workspace, would be a very good imitation of a mind without being one.

David Deutsch takes the opposite position. In The Beginning of Infinity and in his broader work on constructor theory, Deutsch treats the universality of computation as more or less settling the question. Any physical system that can be simulated by a Turing machine can host any pattern that any other Turing-simulable substrate can host. If minds are patterns rather than substances, then substrate is irrelevant. Classical is enough.

I do not have a resolution to offer. I have my leanings. I take QBism seriously, and QBism does not commit either way. It treats quantum states as agent-relative probability assignments rather than ontological things, which cuts against Penrose's specific mechanism but does not save Deutsch's substrate independence either. If anything, QBism makes both accounts feel slightly clumsy, because they both treat the question as if there is a fact of the matter about what the world is doing independent of any agent's stance. The QBist answer to "is this thing conscious" would be closer to "for whom, in what context, licensing what actions."

Where does that leave the practical question about QNNs and AGI?

Approximately here. If Penrose is right, then the AGI we build on classical silicon, however impressive, is not the entity my reader was asking about. Getting to that would require a substrate we do not yet know how to engineer, which may or may not resemble a fault-tolerant quantum computer. If Deutsch is right, then the substrate question is a distraction and classical AGI is the whole answer. If QBism has the shape of it, then the entity question was ill-posed from the start and we should ask instead what kinds of stances the system supports, what it can commit to, what it can be held to account for.

I lean toward the QBist framing. That does not tell me whether QNNs matter. It tells me the question was aimed at the wrong target.

Topology, Not Substrate

This is where I end up.

In the J-space piece I argued that cognition is a topology rather than a feature. The workspace-shaped structure inside Claude is causally load-bearing because of its shape, not because of what happens to be flowing through it at any given token.

I want to say something similar about substrate. Whether cognition, or something worth calling experience, needs a quantum substrate is not a question about what silicon or superconductor or biological tissue the system happens to be built from. It is a question about which topological invariants the system's dynamics support. If the relevant invariants are all computable classically, then the substrate question was decided in favor of Deutsch before we started. If some are not, then Penrose's intuition is at least well-formed even if the microtubule mechanism turns out to be wrong. And the empirical work needed to distinguish these possibilities has barely begun.

So the honest answer to my reader is that QNNs will make a modest positive contribution to the road to AGI, mostly through hybrid pipelines, specialized samplers, and physics-native training environments, and mostly off the critical path defined by classical scaling. And the deeper question, whether the AGI that arrives on classical silicon is the entity my reader had in mind or a very sophisticated imitation of one, is not going to be settled by anyone's roadmap slides. It is going to be settled, if it can be settled at all, by the same careful interpretability work that gave us the J-lens, plus the philosophical rigor to know what we are looking at when we look.

I am not sure we have that rigor yet. But we have started to develop the tools. And the fact that a dumb question can be met with a serious answer, half math and half epistemology, is one of the reasons I still find this a good line of work to be in.

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Sanjay Basu writes A Technocrat's Discernment. He is Senior Director of GPU and GenAI Solutions at Oracle Cloud Infrastructure and founder of Cloud Floaters Inc. All views are his own.