Problem encoding and quantum annealer performance*

I present ongoing work on experimentally testing the performance of a new way of encoding integer variables onto quantum annealers based on the physics of domain walls as presented in [1]. This encoding is compared to a traditional "one hot" constraint using simple colouring problems. I show experiments performed on the D-Wave Systems Inc. quantum annealers using both the "2000Q" and "advantage" generation of QPU. Preliminary results suggest that the domain wall encoding out performs the traditional method. I discuss a possible explanation in the fact that one hot encodings are susceptable to a mode of failure where the minor embedding chains used to map a graph of higher connectivity in the hardware graph break and decode to a qubit state which does not correspond to a valid problem solution. This work was performed in collaboration with Jie Chen at Durham University and Tobias Stollenwerk at DLR. In addition reporting the new experimental results, I will briefly review the encoding techniques in [1], and discuss applications of the encoding in quantum simulation [2].

[1] Nicholas Chancellor 2019 Quantum Sci. Technol. 4 045004
[2] Steven Abel, Nicholas Chancellor, Michael Spannowsky arXiv:2003.07374; Steven Abel, Michael Spannowsky arXiv:2006.06003