Ansatz-Independent Variational Quantum Classifiers and the Price of Ansatz

Area of Science:

• Quantum Machine Learning
• Computational Quantum Physics
• Classical Machine Learning

Background:

• Variational Quantum Classifiers (VQCs) encode classical data into quantum states for quantum processing and measurement-based prediction.
• VQCs offer potential for noisy intermediate-scale quantum (NISQ) devices, using fewer qubits for high-dimensional datasets via amplitude encoding.
• A general framework for VQC design and training is lacking, with Quantum Circuit Learning (QCL) being a specific embodiment using parameterized ansatz circuits.

Purpose of the Study:

• To develop a computational framework for designing and training VQCs, addressing the lack of general design principles.
• To estimate the 'price of ansatz'—the performance gap between QCL and ansatz-independent VQCs.
• To quantify the 'price of quantum circuits'—the performance gap between VQCs and equivalent classical classifiers.

Main Methods:

• Established that VQCs, including QCL, can be integrated within the established kernel method framework.
• Introduced the Unitary Kernel Method (UKM) for designing ansatz-independent VQCs.
• Proposed Variational Circuit Realization (VCR) to decompose target unitary operators into quantum circuits, optimizing parameters and layers.

Main Results:

• Developed computationally-determined bounds for the price of ansatz and potential VQC speedup advantages.
• Numerical results across datasets (dimensions 4 to 256) show ansatz-induced gaps of 10–20% and VQC-induced gaps (vs. kernel methods) of 10–16%.
• The representational power of QCL is limited by ansatz choice, potentially leading to challenging optimization landscapes like barren plateaus.

Conclusions:

• The developed framework provides a method to estimate performance limitations and potential advantages of VQCs.
• UKM enables ansatz-independent VQC design, mitigating performance issues related to ansatz selection.
• VCR offers a way to understand and approximate unitary operators using parameterized quantum circuits.