Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Robust Qubit Mapping Algorithm via Double-Source Optimal Routing on Large Quantum Circuits

Chin-Yi Cheng, Chien-Yi Yang, Yi-Hsiang Kuo, Ren-Chu Wang, Hao-Chung Cheng, Chung-Yang Ric Huang

TL;DR

An innovative qubit mapping algorithm, Duostra, tailored to address the challenge of implementing large-scale quantum circuits on real hardware devices with limited connectivity, yields results of good quality within a reasonable runtime, thereby striving toward achieving quantum advantage.

Abstract

Qubit Mapping is a critical aspect of implementing quantum circuits on real hardware devices. Currently, the existing algorithms for qubit mapping encounter difficulties when dealing with larger circuit sizes involving hundreds of qubits. In this paper, we introduce an innovative qubit mapping algorithm, Duostra, tailored to address the challenge of implementing large-scale quantum circuits on real hardware devices with limited connectivity. Duostra operates by efficiently determining optimal paths for double-qubit gates and inserting SWAP gates accordingly to implement the double-qubit operations on real devices. Together with two heuristic scheduling algorithms, the Limitedly-Exhausitive (LE) Search and the Shortest-Path (SP) Estimation, it yields results of good quality within a reasonable runtime, thereby striving toward achieving quantum advantage. Experimental results showcase our algorithm's superiority, especially for large circuits beyond the NISQ era. For example, on large circuits with more than 50 qubits, we can reduce the mapping cost on an average 21.75% over the virtual best results among QMAP, t|ket>, Qiskit and SABRE. Besides, for mid-size circuits such as the SABRE-large benchmark, we improve the mapping costs by 4.5%, 5.2%, 16.3%, 20.7%, and 25.7%, when compared to QMAP, TOQM, t|ket>, Qiskit, and SABRE, respectively.

Robust Qubit Mapping Algorithm via Double-Source Optimal Routing on Large Quantum Circuits

TL;DR

An innovative qubit mapping algorithm, Duostra, tailored to address the challenge of implementing large-scale quantum circuits on real hardware devices with limited connectivity, yields results of good quality within a reasonable runtime, thereby striving toward achieving quantum advantage.

Abstract

Qubit Mapping is a critical aspect of implementing quantum circuits on real hardware devices. Currently, the existing algorithms for qubit mapping encounter difficulties when dealing with larger circuit sizes involving hundreds of qubits. In this paper, we introduce an innovative qubit mapping algorithm, Duostra, tailored to address the challenge of implementing large-scale quantum circuits on real hardware devices with limited connectivity. Duostra operates by efficiently determining optimal paths for double-qubit gates and inserting SWAP gates accordingly to implement the double-qubit operations on real devices. Together with two heuristic scheduling algorithms, the Limitedly-Exhausitive (LE) Search and the Shortest-Path (SP) Estimation, it yields results of good quality within a reasonable runtime, thereby striving toward achieving quantum advantage. Experimental results showcase our algorithm's superiority, especially for large circuits beyond the NISQ era. For example, on large circuits with more than 50 qubits, we can reduce the mapping cost on an average 21.75% over the virtual best results among QMAP, t|ket>, Qiskit and SABRE. Besides, for mid-size circuits such as the SABRE-large benchmark, we improve the mapping costs by 4.5%, 5.2%, 16.3%, 20.7%, and 25.7%, when compared to QMAP, TOQM, t|ket>, Qiskit, and SABRE, respectively.
Paper Structure (23 sections, 2 theorems, 8 equations, 12 figures, 2 tables, 2 algorithms)

This paper contains 23 sections, 2 theorems, 8 equations, 12 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Qubit Mapping Problem
  3. THE PROPOSED QUBIT MAPPING FRAMEWORK AND ALGORITHM
  4. Initial Placement
  5. Routing: Duostra (Dual-source Dijkstra)
  6. Terminologies
  7. The novelty of Duostra algorithm
  8. Detailed description of the algorithm
  9. Scheduling: Limitedly-Exhaustive (LE) Search and Shortest-Path (SP) Estimation
  10. Limitedly-Exhaustive (LE) Search
  11. Shortest-Path (SP) Estimation
  12. Proof of Duostra Optimality
  13. Experimental Results
  14. Experiment Setup
  15. Compared Methods
  16. ...and 8 more sections

Key Result

lemma 1

The seen set contains the unvisited vertex with the minimum occupied time

Figures (12)

  • Figure 1: The topology of ibmq_washington, retrieved from ibm_ibm_2021
  • Figure 2: An example of the qubit mapping problem
  • Figure 3: Our qubit mapping framework
  • Figure 4: An example of the initial placement strategy for the circuit in Fig. \ref{['fig:Dependency Graph']}
  • Figure 5: Demonstration of the Duostra Procedure for the routing of the double-qubit gate $G6$
  • ...and 7 more figures

Theorems & Definitions (8)

  • definition 1: Dependency Graph (DepG)
  • definition 2: Device Graph (DevG)
  • definition 3: Waitlist
  • definition 4: Ideal Circuit Cost and Mapping Cost
  • definition 5: Occupied Time
  • definition 6: Routing Path
  • lemma 1
  • lemma 2: Duostra Optimality