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History of Quantum Error Correction/量子誤り訂正の歴史

History of Quantum Error Correction/量子誤り訂正の歴史
Dr. Simon Devitt is the Chief Science Officer of a quantum computing startup company called Turing Incorporated and he is also the author of an article called ‘Quantum Error Correction for Beginners.’ It’s all a bit advanced for learners in this course so far, but as your studies keep advancing, we might enjoy taking a look at that. Simon is here with us today. Simon, thank you for being with us. Wonderful to be here, Rod. Thanks. So far in the course, our students over the last several steps have learned about extracting parity from a group of qubits, they have learned about the type of errors that can occur in systems, they have learnt a little bit about redundancy in states.
Now, we need to put it all together into a quantum error correction code. Tell us a little bit about those error correction codes. They have had a bit of a long history. They were invented roughly in about 1997 and before their invention, people were really, really worried that we could never build qubits that are good enough at all. Environmental effects, control effects, errors would creep in, and there’s really no way to combat it.
In ’97, Peter Shor, who people may know from Shor’s algorithm actually came up with his second major contribution in quantum computing and presented the first error correction code, which is basically built using two classical error correction codes that are used quite often in telecommunications and signal transfer using the classical internet or radiowaves. With this quantum error correction code, unlike a classical code, you have to protect against two types of errors, you have to protect against the qubits’ bit flipping, so going from 0 to 1 and then back to 0 again, but you also have to protect against what’s called a phase-flip error. We saw those a little bit, just a couple of steps ago here in the course.
Basically, what the trick is for a quantum error correction code is that you embed one code within the other and there are both two classical codes, one deals with the bit-flip errors and one deals with the phase-flip errors. Once you have got that, you can correct for any arbitrary error and that’s what Peter Shor first showed in ’97. After that it was extended by a few other people, notably Andrew Stein at Oxford, Zurek, Ray LaFlamme, people like that, and you started seeing this proliferation of quantum codes come out, and then very, very quickly after that there was a complete general framework about how you do it.
You can take any classical codes that have certain properties and you can do this embedding where you have one code sort of nested within another code, and then you can correct for any arbitrary error that you get on a quantum state. You just said these are built using classical error codes? Yes. Is that true for all quantum error correction codes, are they all based on ideas that come out of classical error correction? The basic framework came out of classical error correction, but there has now been dedicated codes that never existed classically before. They were basically straight adopted for use in quantum computers. The most popular one that’s really gaining traction now with hardware development are topological error correction codes.
Now, these ones are a little bit tricky. They are called topological codes for a reason that we may or may not get into, but they were basically invented by a guy named Alexei Kitaev very, very soon after Peter Shor did his work. Back in 1998, I think it was. Coincidentally, his work then spurred a whole different avenue of research in quantum computing related to what are called topological qubits or anyons – an approach that Microsoft is taking for their hardware.
But these codes have ended up being quite useful now for system’s architects and people who look at quantum architectures for three primary reasons, namely, the experimentalists kind of like them; they are a little bit easier to implement the actual qubits and how they talk to each other and what you need to do to them to perform error correction on the code is remarkably simple compared to some of the more complex codes that exist. They have a very, very high, what we call, fault-tolerant threshold, which I am sure we would talk about at some stage and also make software programming – how to actually implement algorithms on this error corrected computer is actually quite simple.
That becomes sort of the code of choice now that we use for quantum computing design.

このビデオでは、Turing 社 のサイモン・デビット博士をお招きし、QEC(Quantum Error Correction・量子誤り訂正)について 1997年から現在までの歴史について少しお話してもらいます。まず、Peter Shor(ピーター・ショア)が、はじめにビット反転と位相反転の誤り訂正を、いくつかの古典的な誤り訂正符号を特殊な方法で合体させることで実現した時の話から、Alexei Kitaev(アレクセイ・キタエフ)のトポロジカル誤り訂正に至るまでを解説してくれます。その間、Andrew Steane(アンドリュー・スティーン)、Ray Laflamme(レイモンド・ラフラム)、Wojciech Zurekといった物理学者たちの功績についても触れていきます。

ビデオに使われているアニメーションは、私達の同僚である Dominic Horsman博士が開発したものです。サイモンの話にもでてくるトポロジカル誤り訂正のスキームの一つを使って新しい計算手法を提案している私達の論文のために作りました。アニメーション中のボール一つ一つが量子ビットを表しています。大きいボールは量子データを保持しているもので、小さいボールは複数の量子ビットの集合からパリティを抽出する際に使うものです。光が明るくなっているのは、CNOTゲートの実行を示し、パリティの計算をしています。このビデオで紹介しているトポロジカル表面符号では、量子ビットの集合全体が、符号距離4で、一つの論理的な量子ビットを保持しているのがわかります。

デビット博士は、Turing社での仕事の傍ら、Quantum Error Corretion for Beginners” (量子誤り訂正入門)も執筆しました。この本は、量子に関して十分に理解している研究者を対象としていますので、このコースを受講されている皆さんには少し高度な内容が含まれているかもしれません。でも、興味があればぜひ、手にとって見てください。


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