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"Surface code quantum computing by lattice surgery", Dominic Horsman, Austin Fowler, Simon Devitt, Rodney Van Meter, 2012

Reviewed August 24, 2023

Citation: Horsman, Clare, et al. "Surface code quantum computing by lattice surgery." New Journal of Physics 14.12 (2012): 123011.

Web: https://arxiv.org/abs/1111.4022

Tags: Abelian-anyons, Foundational, Universal-scheme, Error-correcting-codes

This paper introduces the lattice surgery paradigm for surface codes. It maintains its 2D lattice based architecture at all times, and is extremely amenable to physical implementation.

The key insight is to store the information not in a high genus surface, but instead in lots of little 1-qubit contractible chunks with no defects. The reasons that these chunks can store information is that they have boundary defects - the boundary switches between smooth and rough. By turning on/off qubits around these chunks, they can change place, separate into Bell pairs, and fuse. The operations end up being sufficient for every Clifford gate - only magic state injection/distillation is needed to complete the gate set.

This technique has since been dramatically refined. John Martinis teamed up with Austin Fowler for such a simplification in

> Fowler, Austin G., et al. "Surface codes: Towards practical large-scale quantum computation." Physical Review A 86.3 (2012): 032324.

A nice quote is as follows. “Distilling complex theories into something we can all understand is an important part of science. [After clarifying surface codes with an expository paper], I then knew how to build a quantum computer, it completely changed the experimental landscape for me” - John Martinis in his “Spring school on quantum error correction lecture”, around 34:00 minutes, in reference to this paper.

A more modern introduction which is perhaps even more pedagogical is Litinski's article,

> Litinski, Daniel. "A game of surface codes: Large-scale quantum computing with lattice surgery." Quantum 3 (2019): 128.