The Born Ultimatum: Conditions for Classical Surrogation of Quantum Generative Models with Correlators

Understand

Quantum Circuit Born Machines (QCBMs) are powerful quantum generative models that sample according to the Born rule, with complexity-theoretic evidence suggesting potential quantum advantages for generative tasks.

• Here, we identify QCBMs as a quantum Fourier model independently of the loss function.
• This allows us to apply known dequantization conditions when the optimal quantum distribution is available.
• However, realizing this distribution is hindered by trainability issues such as vanishing gradients on quantum hardware.