Representational separation between unitary and channel quantum generative models via shared classical randomness at shallow depth
2026-08-05 • Artificial Intelligence
Artificial IntelligenceMachine Learning
AI summaryⓘ
The authors study quantum generative models, which are quantum circuits used to create complex random patterns. They show that adding a simple kind of randomness shared across the system lets these shallow quantum circuits generate patterns that purely unitary (deterministic) shallow circuits cannot, especially as the system size grows. This means sharing classical randomness enhances what these small-depth quantum circuits can do without needing deeper or more connected circuits. They also demonstrate how a specific quantum computation method (MBQC) naturally implements this shared randomness and confirm their findings with computer simulations.
quantum generative modelsunitary Born modelclassical randomnessshallow quantum circuitsbounded-connectivitychannel modelmeasurement-based quantum computation (MBQC)long-range correlationsquantum circuit depth
Authors
Arunava Majumder, Marius Krumm, Hendrik Poulsen Nautrup, Hans J. Briegel
Abstract
Near-term quantum hardware limits circuit depth and often imposes geometrically local connectivity for quantum generative models, restricting the output distributions accessible to shallow unitary Born models. Introducing stochasticity into a unitary quantum Born model can improve the empirical generative performance of the resulting channel model and, for a restricted small-scale architecture, has been proven to represent a strictly larger family of distributions than its unitary counterpart. However, whether such randomness provides a provable separation at fixed shallow depth for arbitrarily large systems has remained open. Here, we show that shared classical randomness, a comparatively weak resource from entanglement theory, is sufficient to establish such a strict scalable representational separation over the corresponding shallow unitary Born model. More specifically, we augment bounded-connectivity shallow unitary circuits, followed by computational-basis measurements, with spatially separated local Pauli operations, whose joint application is controlled by a single classically sampled random bit. The resulting shallow-depth channel model generates long-range correlations in the classical output distribution that no purely unitary shallow-depth model with bounded connectivity can reproduce. For one-dimensional nearest-neighbour architectures, reproducing such distributions with a purely unitary model can require depth $Ω(N)$ in the worst case. We further show that measurement-based quantum computation (MBQC) provides a natural implementation of the required shared classical randomness through suitable adaptation of the random measurement outcomes. Numerical experiments on MBQC-based generative models support the analytical results.