Challenges and opportunities in the supervised learning of quantum circuit expectation values

Area of Science:

• Quantum computing
• Machine learning
• Computational physics

Background:

• Deep neural networks (DNNs) show promise in predicting quantum circuit outputs.
• Supervised learning (SL) is a key technique for training DNNs.
• Variational quantum algorithms (VQAs) utilize specific circuit architectures.

Purpose of the Study:

• Investigate the potential of DNNs for quantum circuit emulation.
• Determine the limitations and successful applications of this approach.
• Compare DNN emulation with conventional direct simulation methods.

Main Methods:

• Trained DNNs using supervised learning on random quantum circuits.
• Tested circuits common in variational quantum algorithms (VQAs).
• Analyzed computational cost scaling with circuit parameters (interlayer variance, angle variations).

Main Results:

• SL cost scales exponentially with interlayer angle variance, indicating a potential quantum advantage.
• Circuits with only interqubit angle variations are efficiently emulated.
• Trained DNNs accurately predict expectation values for larger, deeper circuits intractable for classical simulators.

Conclusions:

• DNN-based emulation offers a pathway to quantum advantage for specific circuit types.
• This approach can outperform classical simulation for large-scale quantum circuits.
• Standard circuit metrics (entanglement, expressibility, cost) do not predict emulation difficulty.