Multilevel Circuit Optimization in Quantum Compilers: A Case Study

TL;DR

This paper introduces multilevel circuit optimization (MLCO) for quantum compilers, significantly reducing CX gates in complex circuits by hierarchical simplification and decomposition, demonstrated through a Hamiltonian simulation case study.

Contribution

It presents a novel multilevel optimization framework that enhances circuit simplification and gate decomposition, leading to substantial gate count reduction in quantum circuits.

Findings

Quadratic reduction in CX gates achieved

Higher-level circuit structures reveal effective simplification strategies

Gate cancellations lead to significant circuit size reduction

Abstract

In this paper, we explore multilevel circuit optimization (MLCO), where we deploy multiple gate sets and progressively lower the source circuit through the gate sets to the target circuit. At each level, we first perform an appropriate set of circuit simplifications and then lower the simplified circuit into the next level, decomposing the gates not supported there. We demonstrate its effectiveness, using as a case study the source circuit for Hamiltonian simulation to solve a partial differential equation, which is densely populated with multi-controlled gates and is transformed by the state-of-the-art circuit compiler to the target circuit with the quadratic number of CX gates in the number of qubits. MLCO makes visible higher-level circuit structures, providing us with insights about how to simplify the circuits and how to decompose the gates. By putting the right circuit structure in place and selecting the right decomposition algorithm, we could cause massive cancellation of entangling gates, thereby having achieved the quadratic reduction in the number of CX gates.