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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 understand the requisite info for basic QC topics but have the sneaking feeling I'm missing/misunderstanding some implicit abstraction core to the topic of surface codes. And so, would like to double check my intuitions against someone's actual knowledge.

  1. Is a surface code an architecture onto which logical qubits, logical operations, and their connections are physically implemented? That is, is the common depiction of a surface code (the pattern of the measure qubits and data qubits) to be taken literally as a real-space image of the actual hardware or does it correspond to some abstraction in software that I'm not quite grasping?

  2. Are quantum computers currently designed to compile programs into a surface code implementation or are surface codes still a theoretical framework due to the massive amount of qubits that are needed?

Thank you.

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    $\begingroup$ Welcome to Quantum Computing SE! We don't mind basic questions at all! Having said that, it would be helpful, for ease of searching/telling what the question is at a glance if you could come up with a short description of the question and edit that as the title (it's possible that someone else who's better with titles than I am might do that anyway). On a similar note, I hope you don't mind that I've edited in a link to (what I believe is) the paper you're referring to $\endgroup$ – Mithrandir24601♦ Oct 26 '18 at 20:54
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    $\begingroup$ @Malcolm Regan: Since you have two different questions here, you might want to ask them separately. Your question has already earned you 10 points and it may earn you more if you ask it separately. Also someone that knows the answer to one question but not the other would be able to answer, only if you separate the two questions. $\endgroup$ – user1271772 Oct 27 '18 at 3:52
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is the common depiction of a surface code (the pattern of the measure qubits and data qubits) to be taken literally as a real-space image of the actual hardware?

Correct. The surface code is physically implemented by a planar grid of qubits.

hardware vs diagram

Left image source

are surface codes still a theoretical framework due to the massive amount of qubits that are needed?

Correct. To do error corrected quantum computation you need on the order of a thousand physical qubits per logical qubit. And your physical qubits must have fewer than 1 error per thousand operations (especially the 2-qubit operations). No one has a hundred physical qubits yet, and the best demonstrated error rates are ~5 in a thousand.

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