The Signal
Researchers Pre-Train 64-Qubit Circuits with Pauli Propagation
A team from RWTH Aachen University and DESY trained quantum circuits on classical computers before deploying them on IBM’s ibm_berlin processor. The paper tests the method on a two-dimensional Ising model and a generative model for handwrit
Quantum.world Team · Written with AI · fact-checked ·
A team from RWTH Aachen University and Deutsches Elektronen-Synchrotron (DESY) posted a paper on October 23 describing how they trained 64-qubit quantum circuits on classical computers, then ran the trained circuits on IBM’s ibm_berlin processor. Their method, Pauli propagation, shifts the expensive optimization work off the quantum device while still using hardware to produce measurements. The paper tests the workflow on a two-dimensional Ising model and a model that generates small images of handwritten digits.
Backward-propagated observables replace hardware training loops
Instead of evolving a quantum state forward through a circuit, Pauli propagation moves the measured observable backward through the gates. The resulting expression estimates expectation values as functions of circuit parameters. The researchers use that expression as a training objective, calculating its gradients and updating parameters with the classical Adam optimizer.
The method does not calculate the full quantum state or its samples on a classical machine. It targets problems whose loss can be written using expectation values, while the state or samples remain classically intractable, the authors say. That distinction lets the team train a model classically without claiming that classical computation reproduces every output of the quantum circuit.
Propagation can generate an exponentially growing number of terms, so the team uses two approximations: discarding paths that exceed a chosen Pauli weight or trigonometric degree. It also applies pruning rules to remove branches that cannot contribute to the final expectation value. Pruning is exact; truncation can introduce error.
The Ising test exposes a hardware gap
For the variational quantum eigensolver (VQE) benchmark, the team uses an 8-by-8, 64-qubit circuit to estimate the ground-state energy of a two-dimensional transverse-field Ising model. They train both a depth-one and a depth-two circuit for 1,000 Adam steps without using a quantum processor in the optimization loop. The depth-one calculation uses exact Pauli propagation; the depth-two calculation needs a weight cutoff of 12, making its training objective an approximation.
The researchers then check circuit performance on ibm_berlin, a 120-qubit IBM processor, using its 64-qubit subgrid. Those hardware evaluations are checkpoints, not training steps. A gap separates the measured hardware energies from the classically propagated training curves, including for the depth-one case, where propagation is exact. The authors attribute that gap to the processor’s precision in estimating the observable; the deeper circuit converges in fewer iterations but delivers a slightly worse energy on the device.
Digit generation uses fewer parameters than an IQP baseline
The second benchmark trains a circuit to generate 8-by-8, black-and-white versions of handwritten digits from MNIST. Its training set contains 5,000 images covering all ten digits. The model matches Pauli-Z expectation values between the data and the circuit, using a truncated propagator with a weight cutoff of 12 and 100,000 classical Adam steps.
On the held-out test set, the paper reports a mean squared maximum mean discrepancy (MMD) of 0.00205 for the Pauli-propagation model. An IQP circuit with the same 256 parameters scores 0.02411; an IQP circuit with ten times as many parameters scores 0.00251. The comparison shows a better score for the proposed model than either tested IQP baseline, but the paper’s authors also note that the training objective is approximate and the test score remains above the train-versus-test reference baseline.
After training, the team measures the circuit on ibm_berlin. Each single-shot measurement produces a 64-bit image, and the authors report that some outputs form recognizable digits while others are obscured by noise. They apply no error mitigation to these samples, which are particularly sensitive to bit flips: a single wrong qubit measurement can spoil a pixelated image.
The authors frame 64 qubits as a proof of concept
The results establish a workflow demonstration, not a general replacement for quantum-device training. The Ising benchmark’s hardware energies remain separated from the propagated estimates, while the image model relies on truncation and has mixed sample quality. The generative objective also requires propagating 1,000 observables per training round, a cost the paper identifies as a limitation.
“By propagating the observables backward through the circuit, we obtain an explicit parametric expression for the loss that can be minimized entirely on classical hardware.”
Saverio Monaco et al., paper authors
For the image benchmark, the final quantum run produces 64 generated images in about two seconds. That is the hardware role the paper demonstrates: train the parameters classically, then use the processor to sample the resulting circuit.