[Paper Review] Next-Generation Topology of D-Wave Quantum Processors

Kelly Boothby, P. Bunyk+2 more|arXiv (Cornell University)|Feb 29, 2020

Quantum Computing Algorithms and Architecture17 references56 citations

TL;DR

Introduces D-Wave’s Pegasus topology, detailing its structure, embedding advantages over Chimera, and initial performance results for simple Ising models.

ABSTRACT

This paper presents an overview of the topology of D-Wave's next-generation quantum processors. It provides examples of minor embeddings and discusses performance of embedding algorithms for the new topology compared to the existing Chimera topology. It also presents some initial performance results for simple, standard Ising model classes of problems.

Motivation & Objective

• Present the Pegasus family of topologies and how they extend Chimera.
• Describe the graph-theoretic structure, coupler types, and qubit degrees of Pegasus.
• Demonstrate how known Chimera embeddings translate to Pegasus and evaluate embedding efficiency.
• Provide initial performance results on simple Ising-model classes to compare Pegasus with Chimera.

Proposed method

• Define Pegasus topologies P_M with a formulaic description and coordinate system.
• Introduce a third coupler type (odd couplers) and specify the three coupler sets (external, odd, internal).
• Provide a constructive embedding framework for cliques, bicliques, and 3D/2D lattices within Pegasus.
• Compare heuristic embedding performance between Pegasus and Chimera using Minorminer across diverse problem sets.
• Analyze treewidth of Pegasus and contrast with Chimera to discuss algorithmic implications.
• Propose an error-correction scheme leveraging odd couplers to increase logical energy scales.

Experimental results

Research questions

• RQ1 How does the Pegasus topology improve embedding efficiency for structured and unstructured problems compared to Chimera?
• RQ2 What are the embedding limits (cliques, bicliques, lattices) achievable in Pegasus and how do chain lengths scale?
• RQ3 How does Pegasus affect the treewidth and the computational hardness of Ising-model problems?
• RQ4 Can the new odd couplers enable practical error correction and energy-scale gains for logical qubits?
• RQ5 How do standard heuristic embedding and classical optimization benchmarks perform on Pegasus versus Chimera?

Key findings

• Pegasus achieves a ~50-60% reduction in average chain length compared with Chimera across diverse problem sets.
• Pegasus has higher connectivity (degree 15, qubit length 12) and supports new subgraph types (K4 and K6,6) not present in Chimera.
• Pegasus enables embedding of larger cliques up to 12(M-1) with chains of length M or M+1, and bicliques up to K_{12M-20,12M-20} with chain length M-1.
• A cubic lattice embedding in Pegasus scales to (M-1)×(M-1)×12 with chain length 2 in P_M, which is more efficient than in Chimera.
• Pegasus treewidth lies between 12M-11 and 12M-4, larger than Chimera’s 4M, indicating different algorithmic properties and potential hardness.
• Initial error-correction scheme using odd couplers can quadruple the logical energy scale when exclusively using internal couplers for logical interactions.