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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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General definition for smooth and rough boundaries in surface code

So far, when I was learning surface code the patches on which my qubits were had a "rectangular" shape and they involved stabilizers having either $3$ or $4$ "legs". I was then able to easily identify the smooth or rough boundaries given the…
Marco Fellous-Asiani
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What is a "temporal" or "timelike" logical error in the surface code?

When studying the surface code with phenomenological or circuit noise, the syndrome measurement is noisy, and therefore one has to repeat the syndrome measurement for several rounds before decoding. In all literature about surface code, people…
user109781
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Absorbing Clifford gates in Pauli measurements: we should care about the post-meas quantum state, why no Clifford correction *after* measurement?

I am reading Litinski's paper, in particular the figure 4 shown below: To implement a computation with surface code, we need to "commute" all the Clifford toward the end of the circuit, then we absorb these in the final Pauli measurements. I am…
Marco Fellous-Asiani
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How does moving qubits on the surface code not change the logical state

I am reading this paper, and I do not understand how the process of moving a qubit does not change the logical state. Moving a qubit is done by Extending the logical $ \hat{Z}_L $ operator to include an adjacent measurement-qubit Extending the hole…
Jellybean
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Why are the planar surface codes in articles always of odd distance?

I have been playing around with the qecsim Python library and a question has come to my thoght. Whenever I try to represent the logical error rate dependence with the physical error rate for several planar code distances the even ones do not…
Antoni de Marti
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What is the relation between braiding and CNOT?

According to Fowler, Mariantoni, Martinis, and Cleland, 2012, Surface codes: Towards practical large-scale quantum computation (PRL link, page 29), braiding transformations are doing the same thing that CNOT and its adjacent are doing to 2Q…
Ron Cohen
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Providing a more complete proof on why moving surface code qubits works

A prior Q&A by Jellybean and Lior is instructive on why moving qubits in the surface code works via the hole-based method described in Fowler et al. I'm hoping for more details in why not only the logical operations can transfer, but also that the…
C. Kang
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The definition of physical error rate in the threshold theorem

I was quite confused about the definition of physical error rate in the paper Topological quantum memory, which is famous because it estimate the accurate threshold by using Ising model. In this paper, the author said that Let us imagine that, in a…
Zehong Fan
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What are the logical 0 & 1 states for the 17 qubit (9 data qubit) surface code?

What are the logical 1 and logical 0 states for the 17 qubit (9 data qubit ) surface code given stabilixzers below ? I have read there is an algorithm that calculates the logical 0 and 1 states given the stabilizers . Any more info on this ?
Doug Beveridge
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How to Implement surface Codes for quantum error correction

How would one go about implementing a basic surface code for X and Z error corrections? I have read a bunch of papers, I think I semi-understand its working. But I have absolutely no idea about how to implement it. I have tried implementing it using…
Avimita Chatterjee
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State of matter associated to family of quantum error correcting codes

Is there a sense in which a family of $ [[n,1,d]] $ quantum error correcting codes, where $ d $ increases with $ n $, can always be associated to the ground state of some system? The example I have in mind is the $ [[L^2,1,L]] $ surface code.
Ian Gershon Teixeira
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