On an ordinary computer, we load data, copy it and save the result. With quantum states, even those basic steps become scientific challenges.
Having a description of a molecule on your laptop does not mean you can simply upload it into a quantum computer. You have to work out how to create the corresponding quantum state in the machine: which operations to perform, in which order, and how to keep that sequence short enough to run well on real hardware. A description that looks manageable on paper can demand an enormous amount of work to prepare.
And once you have created it, a quantum computer cannot simply send back its entire internal state as a file. Measurements give you pieces of information and generally change the state. In our experiment, collecting enough information means running the preparation again and again, then working out what the measurements tell us. The recipe that creates the state matters every single time we use it.
That is the challenge we took on: turn molecular data into practical instructions, create the states on a real quantum processor, measure them, and reconstruct a description we can check. Each part has to work, and all of them have to work together.
We have now run that entire chain on IBM quantum hardware, across twelve molecular systems.
Every experiment completed the full journey. For several molecules, the state we reconstructed closely matched the one we set out to prepare. We also pushed the process to a seventy-two-qubit case, where the run completed but the final reconstruction failed. That gave us a demanding test of the whole system and a clear target for improvement.
For our team, this is a major milestone. We have brought state preparation, real hardware execution and reconstruction together into a working experiment. We can now test the complete path from a molecular calculation to a quantum processor and back to a result we can evaluate.
We built this process around QTucker (research paper (external site), published chapter (external site)), our software for using patterns in quantum states to build compact preparation circuits and reconstruction models. The work was funded by the German Federal Ministry of Research, Technology and Space (BMFTR) under grant 13N17157 (project QROM), and quantum credits from the IBM Quantum Startup Program made the hardware experiments possible.
Building a state the machine can actually prepare
We began on an ordinary computer, calculating a description of how the electrons in each molecule behave. This description is called a quantum state. It is a mathematical model of the molecule, and we kept it as our reference: the starting point against which we would judge the result.
Our software then turned that description into a sequence of instructions for the quantum computer. You can think of it as a recipe for setting up the machine to represent the molecular state.
This is where the preparation method earns its place. A full description of a large quantum state can be far too big to store, let alone turn into a practical sequence of operations. QTucker uses structure in the molecular data to build a shorter recipe, accepting some approximation along the way.
For our largest example, the stored reference contained 54,167 non-zero entries. Our software generated its preparation circuit on an ordinary computer in about 53 seconds. That was the time to create the instructions; executing them and collecting measurements on the quantum device took much longer. It is a concrete example of the first part of the achievement: turning a substantial molecular description into something we could actually submit to the hardware.
Running the recipe and rebuilding the state
Next, IBM’s machine followed the instructions and took the measurements we had selected. We repeated the measurements thousands of times to estimate their average values, then saved those values along with their reported statistical uncertainties.
Finally, our software used those measurements to build a new description on an ordinary computer. We could then compare it with the reference we had kept.
That was the complete journey: design the preparation, create the state on real hardware, measure it, and reconstruct it.
How close was the result?
To compare the starting model with the reconstructed one, we use a number called fidelity. It is a similarity score between zero and one. One means the two quantum states match exactly. The closer the score is to one, the closer the match.
Hydrogen scored 0.986. That is a close match on this scale. Oxygen scored 0.929, nitrogen 0.895, and carbon monoxide 0.823.
Oxygen and nitrogen are particularly encouraging: both used twenty-qubit circuits on the real device. We constructed the preparation instructions, executed them on physical qubits, and rebuilt close matches from the resulting measurements. Those scores are the outcome of all three stages working together.
These scores compare the reconstructed state with our starting model, which is itself an approximation of the molecule. They do not tell us that every chemical prediction will be equally accurate. To find out whether a result is good enough for a particular job, we would need to check the property that matters for that job, such as its energy.
At the other end of the experiment was dichromium, a pair of chromium atoms. Its final score was almost zero. The machine ran the instructions and returned measurements, but our reconstruction did not recover the starting state.
That distinction matters. The whole process ran successfully; the quality of the answers varied.
The whole journey, on real hardware
There is a lot of work between having a mathematical method and being able to test it on a quantum computer. The instructions must fit the device. The measurements must refer to the right parts of the model. The returned data must make sense to the software that reads it.
We tested that whole chain with twelve molecular systems. They used between four and seventy-two qubits, the basic units of information in a quantum computer. The IBM device had 120 qubits available. The campaign took about six and a half hours, and every submitted job returned data.
The largest case also shows why we need to examine the stages separately. Before hardware noise, our dichromium preparation circuit had a calculated fidelity of about 0.88 against the reference. The method had produced a useful approximation at the preparation stage. We then executed the seventy-two-qubit circuit and requested 14,351 measured properties. The final reconstruction scored almost zero. Following the whole journey lets us see that a promising preparation alone is not enough, and investigate where the remaining accuracy is lost.
And those measurements are ours to keep working with. We can try better ways of rebuilding the models without repeating the expensive hardware step every time. A completed run becomes the starting point for further experiments in software.
The run also gave us a clearer direction for improvement. Oxygen, nitrogen and carbon monoxide used the same number of qubits. Yet the examples requiring longer, more complicated instructions gave poorer results. More operations give errors more chances to creep in. This suggests that making the instructions shorter could help, although we need more experiments to establish how much.
For dichromium, we also found a limit in our reconstruction method. We had chosen a very compact model, and it was too simple to fully describe the state we wanted. Even perfect measurements could not remove that limit. A more flexible model is one of the changes we can now test.
What comes next
This was one campaign on one device. We need to repeat it to learn how consistent the results are. We also need to compare the hardware measurements with carefully controlled computer simulations, so we can separate errors introduced by our software from those introduced by the machine.
Showing an advantage over ordinary computers at chemistry will require further evidence. What this campaign establishes is a complete working route through real hardware, with close reconstructions in several cases and specific limits we can now work on.
For our team, this opens up the next phase of the work. Better preparation means shorter circuits and potentially less accumulated error. Better reconstruction means making more of the measurements we collect. We now have a complete experiment in which to test both, and judge the result at the end.
From a molecular description, to a state prepared on real quantum hardware, to a reconstructed result: we have made that whole chain run. Across twelve systems, it delivered encouraging matches and exposed difficult limits. That is a substantial step forward for our work, and we are excited to build on it.
The technical account of the experiment includes the full results for all twelve molecules and more detail on how the software works.
This work was funded by the German Federal Ministry of Research, Technology and Space (BMFTR) under grant 13N17157 (project QROM). Experiments conducted with quantum credits provided through the IBM Quantum Startup Program.
The cover image was generated with AI. It is a conceptual illustration, not a photograph of IBM hardware or a visualisation of experimental results.
ChatGPT (OpenAI) assisted with drafting and editing this article. The experimental results were supplied by the research team.