Scalable embedding of parity constraints in quantum annealing hardware

TL;DR

This paper introduces scalable, fixed embeddings based on an extended parity mapping technique to efficiently embed combinatorial optimization problems into quantum annealing hardware, improving connectivity handling.

Contribution

It presents a novel, scalable embedding method extending parity mapping, compatible with existing quantum annealers for arbitrary Ising Hamiltonians.

Findings

Embeddings are fixed, modular, and scalable.

Embedded Hamiltonians preserve original properties.

Compatible with current quantum annealing hardware.

Abstract

One of the main bottlenecks in solving combinatorial optimization problems with quantum annealers is the qubit connectivity in the hardware. A possible solution for larger connectivty is minor embedding. This techniques makes the geometrical properties of the combinatorial optimization problem, encoded as a Hamiltonian, match the properties of the quantum annealing hardware. The embedding itself is a hard computational problem and therefore heuristic algorithms are required. In this work, we present fixed, modular and scalable embeddings that can be used to embed any combinatorial optimization problem described as an Ising Hamiltonian. These embeddings are the result of an extension of the well-known parity mapping, which has been used in the past to map higher-order Ising Hamiltonians to quadratic Hamiltonians, which are suitable for existing quantum hardware. We show how our new embeddings can be mapped to existing quantum annealers and that the embedded Hamiltonian physical properties match the original Hamiltonian properties.