Ansatz-Independent Variational Quantum Classifier

Abstract: The paradigm of variational quantum classifiers (VQCs) encodes \textit{classical information} as quantum states, followed by quantum processing and then measurements to generate classical predictions. VQCs are promising candidates for efficient utilization of a near-term quantum device: classifiers involving $M$-dimensional datasets can be implemented with only $\lceil \log_2 M \rceil$ qubits by using an amplitude encoding. A general framework for designing and training VQCs, however, has not been proposed, and a fundamental understanding of its power and analytical relationships with classical classifiers are not well understood. An encouraging specific embodiment of VQCs, quantum circuit learning (QCL), utilizes an ansatz: it expresses the quantum evolution operator as a circuit with a predetermined topology and parametrized gates; training involves learning the gate parameters through optimization. In this letter, we first address the open questions about VQCs and then show that they, including QCL, fit inside the well-known kernel method. Based on such correspondence, we devise a design framework of efficient ansatz-independent VQCs, which we call the unitary kernel method (UKM): it directly optimizes the unitary evolution operator in a VQC. Thus, we show that the performance of QCL is bounded from above by the UKM. Next, we propose a variational circuit realization (VCR) for designing efficient quantum circuits for a given unitary operator. By combining the UKM with the VCR, we establish an efficient framework for constructing high-performing circuits. We finally benchmark the relatively superior performance of the UKM and the VCR via extensive numerical simulations on multiple datasets.