Approximate Quantum Circuit Synthesis using Block-Encodings

TL;DR

This paper introduces an approximate quantum circuit synthesis method using block-encodings that relaxes unitarity constraints, enabling efficient synthesis of larger and arbitrary operators with polylogarithmic gate complexity.

Contribution

It presents a novel synthesis technique leveraging block-encodings to approximate operators, extending beyond unitaries and reducing complexity.

Findings

Operators approximable by polyadic expressions are synthesized efficiently.

The method applies to arbitrary operators, not just unitaries.

Polylogarithmic gate complexity achieved for large operators.

Abstract

One of the challenges in quantum computing is the synthesis of unitary operators into quantum circuits with polylogarithmic gate complexity. Exact synthesis of generic unitaries requires an exponential number of gates in general. We propose a novel approximate quantum circuit synthesis technique by relaxing the unitary constraints and interchanging them for ancilla qubits via block-encodings. This approach combines smaller block-encodings, which are easier to synthesize, into quantum circuits for larger operators. Due to the use of block-encodings, our technique is not limited to unitary operators and can also be applied for the synthesis of arbitrary operators. We show that operators which can be approximated by a canonical polyadic expression with a polylogarithmic number of terms can be synthesized with polylogarithmic gate complexity with respect to the matrix dimension.