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Representational separation between unitary and channel quantum generative models via shared classical randomness at shallow depth

Arunava Majumder, Marius Krumm, Hendrik Poulsen Nautrup, Hans J. Briegel

Featured August 8, 2026

Original Paper

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Simply

By using a single shared random coin flip to decide if certain simple operations happen on distant parts of a quantum computer, the authors show these simple machines can create much more complex patterns than if they just ran fixed programs, without needing deeper or more connected hardware.

In depth
The paper demonstrates that augmenting shallow-depth quantum generative models with shared classical randomness significantly enhances their representational power. This allows them to generate complex, long-range correlations in output distributions that purely unitary shallow circuits cannot, without increasing quantum circuit depth or using long-range quantum gates. The key is coordinating local Pauli operations across distant qubits with a single random bit.

Key Takeaways

  • 1
    Shared classical randomness enables shallow quantum circuits to generate output distributions with long-range correlations that are otherwise inaccessible.
  • 2
    This representational advantage is achieved without increasing quantum circuit depth or requiring long-range entangling gates.
  • 3
    The mechanism involves a single classically sampled random bit controlling spatially separated local Pauli operations, effectively creating a stochastic channel model.

Conceptual Flow

HIGH LEVEL
1
Methodology (The "Logic")

Instead of a fixed quantum program, a shared random choice decides if simple operations happen on distant parts of the machine, making it more powerful.

Fixed Quantum Program
Add Shared Random Choice
More Powerful Program
2
Results (The "Impact")

This new way lets shallow quantum machines create complex patterns across distant parts that old shallow machines couldn't, proving a clear advantage.

Shallow Fixed Program
Shallow Program with Randomness
Compare Output Patterns
Randomness Creates Complex Patterns