# Using ZDDs in the Mapping of Quantum Circuits

## TL;DR

This paper explores the use of zero-suppressed decision diagrams (ZDDs) to optimize quantum circuit mapping by partitioning circuits and efficiently representing all possible qubit mappings, reducing the need for additional gates.

## Contribution

It introduces a novel application of ZDDs in quantum circuit mapping, enabling efficient partitioning and mapping of pseudo qubits to physical qubits in NISQ devices.

## Key findings

- ZDDs effectively partition quantum circuits into blocks of adjacent gates.
- ZDDs can represent all possible qubit mappings within each partition.
- The approach reduces the number of additional SWAP gates needed in quantum mapping.

## Abstract

A critical step in quantum compilation is the transformation of a technology-independent quantum circuit into a technology-dependent form for a targeted device. In addition to mapping quantum gates into the supported gate set, it is necessary to map pseudo qubits in the technology-independent circuit into physical qubits of the technology-dependent circuit such that coupling constraints among qubits acting in multiple-qubit gates are satisfied. It is usually not possible to find such a mapping without adding SWAP gates into the circuit. To cope with the technical limitations of NISQ-era quantum devices, it is advantageous to find a mapping that requires as few additional gates as possible. The large search space of possible mappings makes this task a difficult combinatorial optimization problem. In this work, we demonstrate how zero-suppressed decision diagrams (ZDDs) can be used for typical implementation tasks in quantum mapping algorithms. We show how to maximally partition a quantum circuit into blocks of adjacent gates, and if adjacent gates within a circuit do not share common mapping permutations, we attempt to combine them using parallelized SWAP operations represented in a ZDD. Boundaries for the partitions are formed where adjacent gates are unable to be combined. Within each partition block, ZDDs represent all possible mappings of pseudo qubits to physical qubits.