Efficient learning for linear properties of bounded-gate quantum circuits.

Area of Science:

• Quantum Computing
• Quantum Information Theory
• Machine Learning

Background:

• The complexity of many-qubit systems hinders classical simulation and quantum tomography.
• Quantum learning theory investigates efficient learning of quantum properties.

Purpose of the Study:

• To determine if linear properties of quantum circuits can be learned efficiently from measurement data.
• To develop a method for learning these properties despite computational challenges.

Main Methods:

• Proving sample complexity requirements for learning linear properties.
• Developing a kernel-based method using classical shadows and truncated trigonometric expansions.
• Conducting numerical simulations for validation.

Main Results:

• Sample complexity scales linearly with d (number of gates) for small prediction error.
• Computational complexity can scale exponentially with d.
• The proposed kernel method offers a controllable trade-off between prediction accuracy and computational cost.

Conclusions:

• Efficient learning of linear quantum circuit properties is possible with appropriate methods.
• The proposed method advances practical quantum algorithms and quantum system certification.
• Validated across diverse quantum computation scenarios up to 60 qubits.