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Questions tagged [surface-code]

The surfaces codes are a family of quantum error correcting codes defined on a 2D lattice of qubits. Each code within this family has stabilizers that are defined equivalently in the bulk, but they differ in their boundary conditions.

Source: https://quantumcomputing.stackexchange.com/a/2107 (by @JamesWootton)

The surfaces codes are a family of quantum error correcting codes defined on a 2D lattice of qubits. Each code within this family has stabilizers that are defined equivalently in the bulk, but they differ in their boundary conditions.

The members of the surface code family are sometimes also described by more specific names: The toric code is a surface code with periodic boundary conditions, the planar code is one defined on a plane, etc. The term ‘surface code’ is sometimes also used interchangeably with ‘planar code’, since this is the most realistic example of the surface code family.

The surface codes are currently a large research area, so I’ll just point you towards some good entry points (in addition to the Wikipedia article linked to above).

The surface codes can also be generalized to qudits. For more on that, see here.

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What is the "surface code" in the context of quantum error correction?

I am studying Quantum Computing and Information, and have come across the term "surface code", but I can't find a brief explanation of what it is and how it works. Hopefully you guys can help me with this.
Ivanovitch
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Reference that explains how to read 3d topological diagrams for surface code computations

I like making diagrams to describe computations. For the surface code, an excellent tool is 3d topological diagrams. Here is an example diagram (made by me in SketchUp): The basic idea is that white boundaries are places where Z observable chains…
Craig Gidney
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Can you give an intuitive idea behind how the Minimum Weight Perfect Matching (MWPM) decoder work?

The Minimum Weight Perfect Matching (MWPM) decoder seems to be the most popular choice for decoding error syndromes in Surface Code quantum error correction. Can anyone give an intuitive idea of how it works, with an example?
Aubrey Sharansky
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Logical qubit initialization for the surface code

I am reading Fowler et al's paper on the surface code.. I do not understand how to initialize a logical qubit in an arbitrary state with the surface code. I do understand how to initialize the qubit in logical $|{0}\rangle$ and $|{1}\rangle$, but…
Peter-Jan
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If Majorana qubits are analogous to surface codes, why do the diagrams use lines instead of squares?

If you go to some random Majorana paper or talk, you will find a diagram like this one. Note that the diagram is using lines. Making the lines longer should exponentially increase the error suppression: If you go to some random surface code paper…
Craig Gidney
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Magic State Distillation Understanding Check

I'm currently trying to understand the T magic state distillation algorithm described in "Universal Quantum Computation with Ideal Clifford Gates and Noisy Ancillas" [1] (Section V starting on Page 6). I need to understand the basics of magic state…
Malcolm Regan
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What exactly is a subsystem code?

I'm sure I'm just tripping up on terminology here. I'm new to the wonderful field of QEC, and so far am familiar with the stabiliser formalism and basic codes such as the generic surface code. I keep seeing references in the [vast] literature to…
user23402
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What is the definition of Bell state on a n-qubit system?

Question 1: The bell state for a 2-qubit system has been defined in Nielsen and Chuang's book as the set of maximally entangled states spanned by $\{|00\rangle + |11\rangle, |00\rangle - |11\rangle, |01\rangle + |10\rangle, |01\rangle- |10\rangle…
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Why do we need to keep of history of $d$ cycle for surface code in order to resist against data *and* measurement errors

I am trying to understand why we need to keep in memory $d$ clock cycles in order to correct efficiently for the surface code where the syndrome qubits are also faulty ($d$ is the code distance). [edit]: It seems that there is no real "proof" of…
Marco Fellous-Asiani
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What is the quantum bandwidth of a planar array of noisy qubits, assuming free classical communication?

A common task to perform during quantum computation on the surface code is moving qubits from one place to another. There are standard ways to do this within the surface code, but I was wondering what the actual fundamental limits are. If we forget…
Craig Gidney
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Is the common depiction of a surface code to be taken literally as a real-space image of the actual hardware?

I'm currently reading the paper "Surface codes: Towards practical large scale quantum computing" and have a couple of very basic questions that if answered will help me contextualize and organize the information in this paper much better. I…
Malcolm Regan
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In what situation are three rounds of syndrome measurement required for fault-tolerance in the surface code?

I have heard multiple times the claim that three rounds of syndrome measurement required for fault-tolerance in the surface code. I'm not sure what situation would require this, as I think less would suffice. Unfortunately, all these mentions were…
James Wootton
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Simple example for the sub-optimality of MWPM vs Maximum likelihood decoder

I understand that the Minimum Weight Perfect Matching (MWPM) decoder tries to identify the single most probable error configuration, while a maximum likelihood decoder aims to find the most probable coset of errors (those equivalent up to a…
Shoham Jacoby
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Finding all small stabilizer codes

Given some choice of parameters $ [[n,k,d]] $ with $ n $ small, is there any computationally easy way to find all of (or at least many of) the stabilizer codes with those parameters? For certain parameters this is easy, for example it is known that…
Ian Gershon Teixeira
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Getting intuition on the state-injection relations for the generalized $\exp(-iP \pi/8)$ $T$-gates (ideally using ZX calculus)

In Litinsky's paper, there are many circuits relations, like the one below. The left handside represents the "rotation" $\exp(-i P \phi)$ with $\phi=\pi/8$ with similar definitions for the orange ($\phi=\pi/4$) and gray box ($\phi=\pi/2$) on the…
Marco Fellous-Asiani
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