Skip to 0 minutes and 3 secondsDr. 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.

Skip to 0 minutes and 45 secondsNow, 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.

Skip to 1 minute and 10 secondsIn ’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.

Skip to 1 minute and 51 secondsBasically, 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.

Skip to 2 minutes and 26 secondsYou 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.

Skip to 3 minutes and 11 secondsNow, 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.

Skip to 3 minutes and 39 secondsBut 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.

Skip to 4 minutes and 21 secondsThat becomes sort of the code of choice now that we use for quantum computing design.

History of Quantum Error Correction

In this video, Dr. Simon Devitt of Turing, Inc. joins us to talk briefly about the history of quantum error correction (QEC) from 1997 through the present. He leads us from Peter Shor’s original insight on how to correct bit flip and phase flip errors using separate classical error correction codes combined in a special way, through Alexei Kitaev’s insight that led to topological methods. Along the way, we meet Andrew Steane, Ray Laflamme, and Wojciech Zurek as well.

The included animation was developed by our colleague, Dr. Dominic Horsman, to accompany our paper introducing a new method of computing using one of the topological error correction schemes mentioned by Simon. Each of the balls represents a qubit. The large ones hold our quantum data, and the small ones are used when we extract the parity of a group of qubits. The glowing light represents execution of the CNOT gates that are used to calculate that parity. In the topological surface code shown in this video, the entire set of qubits shown holds one logical qubit with a code distance of four.

Besides his work at Turing, Dr. Devitt is the author of the review article “Quantum Error Correction for Beginners”. It is targeted at researchers who already have an understanding of many quantum concepts, and so might be a little advanced for most learners here, but check it out if you are interested.

This is the first of three video Steps with Simon that will carry us through the end of QEC. Next we pause for an Exercise in which you will get to try error correction for yourself. The we reconvene with Simon to discuss thresholds and error propagation, then in the final technical Video we discuss numbers and architectures for fault-tolerant, error-corrected quantum computers. After completion of quantum error correction, we will survey the state of the entire quantum computing industry as we wrap up the course.

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This video is from the free online course:

Understanding Quantum Computers

Keio University