Two-step approach to scheduling quantum circuits

TL;DR

This paper presents a two-step scheduling approach for quantum circuits that separates logical gate scheduling from routing, optimizing for hardware constraints and reducing circuit depth and gate count.

Contribution

It introduces a novel two-step scheduling method that decouples logical gate ordering from hardware routing, with specialized schemes for linear qubit arrays.

Findings

Scheduling reduces the number of gates and circuit depth.

Routing scheme minimizes exchange operations in linear arrays.

Application to QAOA demonstrates improved efficiency.

Abstract

As the effort to scale up existing quantum hardware proceeds, it becomes necessary to schedule quantum gates in a way that minimizes the number of operations. There are three constraints that have to be satisfied: the order or dependency of the quantum gates in the specific algorithm, the fact that any qubit may be involved in at most one gate at a time, and the restriction that two-qubit gates are implementable only between connected qubits. The last aspect implies that the compilation depends not only on the algorithm, but also on hardware properties like connectivity. Here we suggest a two-step approach in which logical gates are initially scheduled neglecting connectivity considerations, while routing operations are added at a later step in a way that minimizes their overhead. We rephrase the subtasks of gate scheduling in terms of graph problems like edge-coloring and maximum subgraph isomorphism. While this approach is general, we specialize to a one dimensional array of qubits to propose a routing scheme that is minimal in the number of exchange operations. As a practical application, we schedule the Quantum Approximate Optimization Algorithm in a linear geometry and quantify the reduction in the number of gates and circuit depth that results from increasing the efficacy of the scheduling strategies.