Can a quantum circuit learn how quarks become hadrons?

Motivation

Hadronization, the step where quarks and gluons bind into the hadrons a detector actually sees, has no first-principles calculation. Event generators like Pythia fit a phenomenological Lund string model instead. A generative model that learns these distributions directly is a natural test case for quantum generative modeling, and a demanding one, because the answer has to hold up on noisy hardware.

Approach

A quantum circuit Born machine is a parameterized circuit whose measurement statistics are the model:

$$q_\theta(x) = \bigl\lvert \langle x \rvert\, U(\theta)\, \lvert 0 \rangle^{\otimes n} \bigr\rvert^2 .$$

I train it so that $q_\theta$ matches momentum distributions $p$ from Pythia 8 simulations, scoring the fit with the Kullback-Leibler divergence

$$D_{\mathrm{KL}}(p \,\Vert\, q_\theta) = \sum_x p(x) \log \frac{p(x)}{q_\theta(x)}$$

and the Kolmogorov-Smirnov statistic. I wrote a 6-qubit model in JAX with just-in-time compiled variational optimization, and a hardware-efficient ansatz in Qiskit that stays within IBM Brisbane’s deployment constraints. Both are tested under the FakeBrisbane noise model, with zero-noise extrapolation and dynamical decoupling to mitigate the damage. I also ran circuit-depth and entanglement ablations comparing trainable RXX gates with fixed CX gates.

Results

• KL divergence below 0.14 for the 6-qubit JAX model under FakeBrisbane noise, with zero-noise extrapolation and dynamical decoupling.
• Transverse-momentum KS score of about 0.075 with only 32 native two-qubit (ECR) gates in the best Qiskit circuit under FakeBrisbane noise.
• The ablations found configurations where trainable RXX gates scaled better than fixed CX gates.

The lesson so far is that on noisy hardware the budget is two-qubit gates, not depth.

figure in preparation

Links

The code lives in a private group repository while the write-up is in progress.