Resource-efficient Variational Compilation of Block-Encodings

TL;DR

This paper introduces a resource-efficient variational method for compiling block-encoding operators in quantum algorithms, optimizing gate complexity and leveraging symmetries to reduce parameters, with applications in larger quantum circuits.

Contribution

It presents a variational compilation approach that approaches the input matrix's parameter count and incorporates symmetries to improve efficiency and scalability.

Findings

Near-optimal resource requirements for a wide range of matrices

Parameter count approaches that of input matrices, depending on their properties

Symmetry incorporation reduces parameter count and improves optimization

Abstract

Block-encoding operators are one of the essential components in quantum algorithms based on Quantum Signal Processing. Their gate complexity largely determines the overall gate complexity of the full algorithm. Using variational methods, we compile single-ancilla block-encoding unitaries with near-optimal resource requirements for a large range of input matrices. We find that the number of variational parameters in the parameterized quantum circuit approaches the number of free parameters in the input matrices, depending on whether they are real, complex and/or hermitian. Additionally, symmetries present in the input matrix can be incorporated into the ansatz circuit, reducing the parameter count further and enhancing optimizability. While performing a variational compilation of block-encodings ceases to be computationally feasible for large system sizes, the constructed operators can be used as components of larger block-encodings via a linear combination of block-encodings.