The Wall Is Real: What We Learned Putting Chemistry's Hardest Problems on a Quantum Computer

There is a sentence in our philosophy that the rest of this post is about:

Classical computers can only approximate quantum phenomena... but they hit a wall. Every electron added to a molecule doubles the work. The approximations grow heavier. The errors compound. Beyond a certain size, the answer stops being trustworthy, and beyond a certain complexity, classical methods simply cannot reach.

That is a strong claim. It is also a testable one. So we tested it.

Over the last two weeks we ran Kanad our quantum-chemistry framework against sixteen problems chosen specifically because they are where the standard tools of computational chemistry are known to fail. Not fail by a few percent. Fail qualitatively: predict a bond is unbound when it is bound, predict a molecule is a boring closed shell when it is a reactive diradical, miss an entire excited state. Six of those we also ran on real IBM quantum processors. Then we kept climbing through the iron-sulfur clusters at the heart of biology's hardest enzymes, all the way to FeMoco, the cofactor that fixes atmospheric nitrogen and the single most-cited target in the entire argument for why quantum computers matter to chemistry.

This is the honest report of what happened. It includes the wins, which are real. It also includes with equal weight, because this is the only way science is worth doing every place Kanad fell short, the two claims we had to retract after our own review caught them, and the exact boundary where the wall still stands today.

Why the wall exists

Chemistry is electrons arranging themselves around nuclei. The rule they follow is the Schrödinger equation, and the difficulty is that the honest description of N electrons lives in a space that grows like 2^N. Ten electrons is already a thousand-dimensional problem; thirty is a billion.

For most molecules, most of the time, you can cheat. The electrons stay politely paired, a single dominant configuration describes them well, and methods like Hartree–Fock, density functional theory (DFT), and coupled cluster (CCSD(T)) give excellent answers cheaply. These methods have carried chemistry for fifty years, and they deserve every bit of that success.

But there is a regime where the cheat fails completely. When bonds break, when electrons become unpaired, when a molecule has several nearly-equivalent ways to arrange its electrons at once the "single dominant configuration" assumption collapses. Chemists call this static, or multireference, correlation. It is exactly Feynman's point: past a certain complexity, a classical description isn't slow, it's wrong.

A quantum computer does not make that assumption. It represents the superposition of configurations directly, because it is made of the same stuff. That is the promise. Kanad's job is to turn the promise into an answer a chemist can use and our job here was to find out how far that actually works, today, on the hardware that actually exists.

How we did it

For every system we set up a small, physically-chosen active space the handful of orbitals where the interesting correlation lives and computed three things: the classical answer (HF, DFT, CCSD(T)), the place the wall shows up; the exact answer within that active space (full configuration interaction, FCI), the ground truth to check against; and Kanad's answer Sample-based Quantum Diagonalization (SQD).

The pipeline, briefly. We select the active space with AVAS, projecting the mean-field orbitals onto a target set of atomic valence functions carbon 2pz for a π system, the metal 3d shell plus bridging-ligand p orbitals for a cluster. To get the wavefunction on hardware we prepare a LUCJ (Local Unitary Cluster Jastrow) ansatz, chosen because it maps onto IBM's heavy-hex lattice with only nearest-neighbour two-qubit gates and shallow depth the difference between a circuit that survives the noise and one that doesn't. We sample it on the quantum processor, then because raw hardware samples are corrupted by bit-flips run iterative configuration recovery, which uses the average orbital occupations of the surviving shots to statistically repair the broken bitstrings back into the physical sector. The recovered configurations define a selected-CI subspace, a few hundred to a few million of the most important determinants out of the exponential total; we build the Hamiltonian in that subspace and diagonalize. For the large cases we run that diagonalization on an AMD MI300X GPU with a HIP selected-CI kernel our rocm-planck engine, bit-for-bit identical to the CPU result.

One number does most of the work below: C₀², the weight of the single most important electron configuration. When C₀² ≈ 1, one configuration dominates and classical methods are fine. When it collapses toward zero, no single configuration describes the molecule and the classical picture falls apart. Watch it fall.

We also never just report an energy. Every system is scored for how multireference it genuinely is C₀², the coupled-cluster T₁ diagnostic (above ~0.02, CCSD(T) is untrustworthy), and the effective number of unpaired electrons. And every claim was put through an adversarial verification pass: independent checks against the primary literature, instructed to find overstatement rather than confirm it. It reclassified fifteen claims as needing sharper caveats and overturned two outright. Those corrections are in this post.

What we found

A bond that classical theory cannot break

Nitrogen's triple bond is the strongest in common chemistry. Pull the two atoms apart and something revealing happens to Hartree–Fock: it can't let go. A single determinant cannot describe two neutral nitrogen atoms drifting free, so as the bond stretches the HF energy climbs to 665 milli-Hartree about 400 kcal/mol above the true answer. C₀² collapses from 0.95 to 0.12. CCSD(T), the gold standard near equilibrium, turns erratic in the stretched region.

Kanad's SQD tracks the exact curve to 0.037 mHa across the entire dissociation and on a real IBM quantum processor, at a stretched geometry where CCSD(T) is at its worst, it reproduced the exact answer to within rounding of zero.

A bond classical theory says shouldn't exist

Fluorine gas, F₂, is held together entirely by electron correlation. Give Hartree–Fock a fair, size-consistent comparison and it predicts F₂ is unbound that two fluorine atoms are lower in energy than the molecule. That is not a small error. It is the wrong sign. Add correlation and the bond reappears. On IBM hardware, Kanad recovered the bound answer exactly.

Molecules DFT sees as boring, and isn't

The acenes the long, flat carbon ribbons at the heart of organic electronics look to standard DFT like well-behaved closed-shell molecules. They are not. As they get longer their electrons increasingly unpair into a polyradical state that governs how they conduct, age, and split light. DFT reports essentially zero unpaired character. Kanad tracks it climbing steadily, up to a 52-qubit active space with 700,000 configurations, diagonalized in four seconds on a GPU a calculation impossible to hold in a classical statevector.

An excited state TDDFT is built to miss

Some molecular states are double excitations two electrons promoted at once. The standard tool for absorption spectra, TDDFT, is constructed from single excitations. It doesn't approximate these states poorly; it has no access to them at all. In the polyenes we measured the doubly-excited 2¹Aɡ state carrying 58–64% double-excitation character. Kanad captures it. TDDFT structurally cannot.

Chemical accuracy on a quantum computer

This is the result we care about most, stated with its limits intact. On IBM's Heron processors, Kanad's pipeline sample the noisy quantum circuit, then recover the physical configurations classically reached chemical accuracy against the exact active-space answer on a stretched nitrogen triple bond, the RHF-unbound fluorine bond, a relativistic uranium dioxide dication, and a 32-qubit [2Fe-2S] iron-sulfur cluster. On that cluster the raw hardware samples were 335 mHa off; configuration recovery pulled them to 5 mHa, a sixty-five-fold rescue, on a state with strong multireference character. Two smaller cases, C₂ and O₃, were only narrowed rather than closed the recovery quality, not the qubit count, is what decides.

A note on honesty, because it cut against us and then for us: our first analysis of that iron-sulfur run reported it as a 300 mHa failure. It wasn't. We had compared the quantum answer against the wrong classical reference the mean-field energy instead of the exact active-space energy. Against the correct reference it is a 5 mHa success. The same discipline that made us publish our failures made us catch this one.

Reaching for FeMoco

The iron-sulfur result above was genuine but it was the easy version, and honesty means saying so precisely. The cluster we ran was chloride-ligated, high-spin, all its iron spins aligned. The problem the field actually measures itself against is the opposite in every dimension: the antiferromagnetic singlet, where the two irons' spins oppose and no single configuration comes close. So we ran that. And then we kept going, all the way to FeMoco itself.

The monster, on its own terms

We took the [2Fe-2S] active-space model of Li and Chan (J. Chem. Theory Comput. 13, 2681, 2017) thirty electrons in twenty orbitals, forty qubits the identical Hamiltonian used in the IBM–RIKEN quantum-centric supercomputing study, in its S = 0 antiferromagnetic singlet ground state. It comes with a DMRG reference that is numerically exact for this space. There is nowhere to hide. We seeded SQD from a broken-symmetry guess one iron's d-electrons up, the other's down and grew the subspace iteratively. It climbed from eight thousand determinants to seven hundred thousand, and the energy fell cleanly with it: 245 mHa above exact, then 55, then 20, and finally 16.9 mHa above the DMRG-exact singlet. Not yet chemical accuracy, and we won't round it up but a real advance on the exact version of the problem, converging under its own iteration, every determinant of it on a single GPU.

Climbing the ladder

With the engine landing on the exact singlet, the honest thing was to keep climbing until it stopped.

• [4Fe-4S], the cubane cluster fifty-four electrons in thirty-six orbitals, seventy-two qubits. Against a DMRG reference (itself only approximate at this size) SQD reached 364 mHa with three hundred thousand determinants before we capped it. Undersampled, and we say so.
• FeMoco, the Reiher active space fifty-four electrons in fifty-four orbitals, one hundred and eight qubits the exact system IBM and RIKEN put on a quantum-centric supercomputer (arXiv:2405.05068). We grew the subspace to three million determinants and converged to 93.8 mHa against the CCSD(T) reference, in about ten minutes on the single GPU.
• FeMoco, the full valence one hundred and thirteen electrons in seventy-six orbitals, one hundred and fifty-two qubits the canonical "quantum advantage" target. We ran SQD on it. It executed. And it is nowhere near converged, because the subspace we could afford a few thousand determinants is a rounding error against a configuration space with more entries than there are atoms in the observable universe.

That last line is the whole story compressed. The gap did not shrink as we climbed. It grew seventeen milli-Hartree at forty qubits, to three hundred sixty at seventy-two, to ninety-four at a hundred and eight, to nearly three Hartree at a hundred and fifty-two. That is not a failure of the method; it is the method being honest about the size of the room. Selected configuration interaction captures a molecule by keeping the determinants that matter and discarding the rest. When "the rest" is 10^40 and you can hold three million, you are keeping the most important millionth of a millionth of a millionth of the wavefunction. For a well-posed forty-qubit space that is enough to land on the exact answer. For the full valence of FeMoco it is a toe in an ocean.

So here is the sentence we can stand behind, with all of it intact: we can now operate at FeMoco scale one hundred and fifty-two qubits, millions of determinants, on a single commodity accelerator and we have not converged it. A year ago the first half was a resource-estimate fantasy measured in millions of error-corrected qubits. It now runs on a GPU in a rack. The second half is where the real work now lives.

What the hardware said, at scale

We did not keep FeMoco on the GPU alone. We put the hundred-and-eight-qubit Reiher active space onto a real IBM Heron processor, ibm_fez. The circuit that prepares that state, transpiled to the heavy-hex lattice, is twenty-four thousand two-qubit gates deep. Of one hundred thousand shots, one thousand and ninety landed in the correct electron-number sector and here is the number that matters, the one it would be easy to hide: that is not signal. At a hundred and eight qubits, a random bitstring lands in the right sector about 1.17% of the time by chance. Our measured rate was 1.09%. The hardware samples were, to the precision we can measure, statistically indistinguishable from random noise.

We ran the recovery on them anyway, and it produced a hybrid estimate of 403 mHa worse than the 94 mHa the classical path reached, because feeding near-random samples into the subspace dilutes it. Every bit of that number came from the classical anchor, not the chip. At twelve to forty qubits the quantum device is a genuine sampler of a genuine correlated state; somewhere between forty and a hundred and eight qubits, at twenty-four-thousand-gate depth, that signal crosses below the noise floor and vanishes. That crossing point is the single most useful thing this run measured a coordinate, not a marketing number: this is where today's hardware stops contributing, and it is why the heavy lifting at FeMoco scale is, for now, the classical selected-CI engine's job. Shallower ansätze and better gates will move it.

Where it fails and we mean fails

A tool that only shows its wins is a marketing demo. Here is the boundary, stated plainly.

• These are active-space models, not experiments. Every number here reproduces the exact answer inside a chosen active space not the experimental bond energy. Getting from there to a number you could measure in a lab needs larger basis sets and dynamic correlation this study did not include. The qualitative walls fall. The last decimal of quantitative accuracy is future work.
• On the small problems there is no quantum advantage and we won't pretend otherwise. A 12-qubit active space is a few hundred configurations a laptop solves in milliseconds. On a simulator, Kanad's SQD is that classical calculation; the genuine quantum content lives only on the hardware runs, where we are demonstrating that the noise-recovery pipeline reproduces the known answer not that we have beaten a classical computer at something it cannot do.
• The 108-qubit hardware run produced no usable quantum signal, and we say so in those words. Its valid-sample rate was below the random-chance baseline; the recovered energy came entirely from the classical anchor and was beaten by the pure-classical path. We are not claiming quantum advantage on FeMoco the opposite. We ran it on the actual machine and measured, precisely, that at this depth the machine does not yet help.
• The 4Fe-4S and 152-qubit FeMoco numbers are not converged, and their references are not exact. Treat those two as scale demonstrations. The 40-qubit singlet (against a DMRG-exact reference) and the 108-qubit Reiher space (against CCSD(T)) are the numbers with a floor under them.
• Two claims did not survive our own review. We had described the uranyl dication as "multireference"; at equilibrium it is essentially single-reference, and the genuinely hard relativistic physics (spin-orbit coupling) was excluded from our model, not conquered by it. And a laser-photodynamics experiment had silently fallen back to a mean-field approximation because of a bug. We corrected the first and fixed the second. We report both because the alternative is not science.
• The high-spin metal cores are not there yet. For the manganese water-oxidation motif, including the bridging-oxygen orbitals that carry the magnetism made a naively-truncated valid active space balloon to sixty qubits; the honest fix is CASSCF orbital optimization into a compact space, which for these open-shell clusters is itself hard to converge. That one stays genuinely open for every method, classical and quantum. What we can offer is an honest map of exactly where the wall stands.

What we are and what we believe

Here is the part we most want to say directly, because it shapes everything else.

Our algorithm works genuinely impressively in places and we are the first to feel it could be better. We are not quantum information scientists. We did not invent Sample-based Quantum Diagonalization, and we would not claim to have wrung the last drop of performance out of it. We are programmers. What we are building is not a new theorem; it is the workflow the plumbing that takes a chemist's molecule, a biologist's cofactor, or a materials scientist's magnetic alloy, puts it on a quantum computer, and hands back an answer in the units of your own field, without you ever needing to write a quantum circuit.

That gap is the real reason quantum chemistry has stayed walled off. The physics has been within reach for a while; the access hasn't. Running your molecule currently means becoming a quantum programmer first. We think that's backwards.

And here is the part we actually believe, plainly: *our algorithm may only take this so far but we are convinced the work you build on top of it will go much further. The chemist who knows exactly which orbitals matter, the biologist who understands the enzyme's real environment, the materials scientist with the right intuition for a magnet the algorithms, active spaces, and ideas you bring will be the ones that cross the genuinely impressive benchmarks. We are not the story here. You are.* We built the instrument for you, and honestly, we are waiting for you to come and prove us right to run something on it that none of us could have done alone.

An open invitation

Everything above runs on kanad.xyz. Not a demo video the actual instrument.

If you are a chemist with a stubborn reaction, a biologist with a metalloenzyme, a materials scientist with a correlated magnet bring it. You can sign up and get verified directly on kanad.xyz, or contact us for access. We're opening a free three-month access window, and compute credits can be granted on an availability basis for serious work tell us what you're trying to simulate.

We are at the very beginning of this, and we mean the invitation literally: join us in the journey of hitting these simulation walls, one problem at a time. The near goal is honest answers to specific, stubborn molecules. The far goal is the one that got us into this in the first place to simulate matter as nature actually computes it, from a metalloenzyme's active site outward to the states of matter that have never existed on Earth and the first microseconds of the universe. There are millions of forms of matter we have never seen. With classical computers we've explored a corner of that space.

The wall is real. We reached it. We crossed it where the physics is static correlation and a well-posed active space, and we marked carefully where it still stands. Now come help us map the rest.

Full data, drivers, and the adversarial-review record are archived with this study. Kanad is a governance-driven quantum-chemistry framework built at DeepRealm Labs. The platform where you can run your own molecule on a quantum computer is at kanad.xyz.