Short answer: Lattice surgery is a technique, introduced in a 2012 paper in the New Journal of Physics, for coupling two planar surface codes without transversal operations, so the encoded computer keeps its two-dimensional nearest-neighbour structure. It works by splitting and merging planar code surfaces, and the authors say it enables universal quantum computation. It is a theoretical proposal, supported by resource analysis in later papers.
Why it was proposed
The 2012 paper says surface codes have become a leading method for quantum error correction in theoretical large-scale computing and communications architecture designs. It says their comparatively high fault-tolerant thresholds and natural two-dimensional nearest-neighbour (2DNN) structure make them an obvious choice for large-scale designs in experimentally realistic systems. It adds that, while based on Kitaev's toric code, there are many variants, two of which are the planar and defect-based codes.
The problem with planar codes
According to the 2012 paper, planar codes require fewer qubits to implement for the same strength of error correction, but are restricted to encoding a single qubit of information. Interactions between encoded qubits are achieved via transversal operations, which destroy the inherent 2DNN nature of the code. A 2017 paper in the same journal explains that a transversal CNOT gate is one where corresponding physical qubits in two logical blocks are interacted via a physical CNOT gate, and that a transversal logic gate eliminates the 2D nearest-neighbour geometry.
What lattice surgery does
The 2012 paper introduces a technique enabling the coupling of two planar codes without transversal operations, maintaining the 2DNN structure of the encoded computer. It says lattice surgery comprises splitting and merging planar code surfaces and enables universal quantum computation. The 2017 paper describes the resulting picture: the computer becomes an array of isolated 2D patches of surface code, each representing a logical qubit, and logical operations come from merge and split operations on them. It says this second approach to universal computation with the surface code does not rely on topological braiding.
How errors are found in the lattice
A 2024 arXiv paper describes the surface code as a lattice where each position represents a qubit crucial to maintaining the logical state, with every qubit monitored by X and Z stabilizers. It says these stabilizers identify phase and bit-flip errors, using combinations of Pauli operators acting on subsets of qubits. An error alters the outcome of the stabilizer checks linked to the affected qubit, and a decoding algorithm can then pinpoint the timing and location of errors. The paper says errors can then be rectified by applying quantum gates to flip the affected qubits back.
What the 2017 paper says about cost
The 2017 paper says the efficiency of state distillation procedures had not yet been investigated in the lattice surgery model, so it gives their translation as an example. It says the resource requirements seem comparable or better to the defect-based state distillation process, and that modularity and eventual implementability allow the lattice surgery model to be viewed favourably. That is the authors' assessment.
What this does not tell you
This article summarises abstracts and introductions of three papers. It describes a proposed method and a resource analysis, and it claims no hardware demonstration.
FAQ
What is lattice surgery?
A technique from a 2012 paper that couples two planar surface codes by splitting and merging code surfaces, without transversal operations.
Why not use transversal operations?
The 2012 paper says transversal operations destroy the inherent two-dimensional nearest-neighbour nature of the code.
Why use planar codes at all?
The paper says planar codes require fewer qubits for the same strength of error correction, but each encodes a single qubit.
How does a logical qubit look in this picture?
A 2017 paper says the computer becomes an array of isolated 2D patches of surface code, each representing a logical qubit.
How are errors detected?
A 2024 paper says X and Z stabilizer checks reveal phase and bit-flip errors, and a decoding algorithm locates them.
All field notes