Discussion: The Quantum Error Correction Conundrum

This article is inspired by an interview of Dr. Ivan Deustch of the University of New Mexico’s Center for Quantum Information and Control conducted by Quanta magazine here

In summary, Dr. Deustch briefly described what qubits are and how they function and then went on to discuss a paradox in quantum computing error correction.

Ok, let’s refresh real quick… what is error correction and why is it important?

Say you have one of those old-fashioned two cans and a string phone that you use to communicate with your next door neighbor

Ok, cool. Excited by your can-phone, you hold the can up to your mouth and say “Isn’t this cool?”. Unfortunately, your neighbor (holding the can to her ear), hears you say “Isn’t it cold?”. Confused, as it is July and over 80 degres Fahrenheit out, she then asks if you are well.

The cans and the wire serve as your communication channel. Oftentimes, communication channels introduce some type of interference to the communications they are transmitting, called noise.

This makes sense, right? Communication channels are physical entities that are subject to physical laws. Noise in a channel might be caused by friction, chemical reactions, external factors such as outside temperature, or by simple wear and tear.

In our can example, there was noise in your communication, likely caused by imperfections in the wire. Is it possible for you to devise a method to ensure that the correct information get’s transmitted?

“Yes!” you think to yourself, as you race outside into your side yard. You build a bonfire and, holding your can to your mouth in one hand, you begin to speak your message to your neighbor while also transmitting the same message to your neighbor via smoke signals.

You forgot to charge your phone that day, apparently.

So now you have introduced a second communications channel between yourself and your neighbor. Like the can telephone, the bonfire can transmit a message, but also has noise that could interfere with the end result.

However, your neighbor now has two sources to compare to get your message. If she reads both communications channels and gets the same message from both, then she can be sure with high probability that she has received your message correctly.

To ensure even more accuracy, you could introduce a third communications channel (perhaps you could tell your kid brother the message and then have him run over to her and relay the message. Unfortunately, he is only three years old and does not always remember things very well). If two or more of the messages received are the same, then your neighbor can be sure with high probability that the message received the most times is the correct message.

Computers send messages, in a sense, much the same way that you and your neighbor did. Computers have communications channels that also introduce noise into messages. And for computers, a message might be a video file with hundreds of thousands of pixels that it needs to send accurately. Much like the technique used with your neighbor, computers will oftentimes communicate the same message over multiple channels. The receiving computer will compare all of the messages that it has received and pick the message that appears the most frequently as the correct message.

(Yes, I know this is a simplification of what happens, and that there are techniques such as Hamming encoding to make this process more efficient, but for the purposes of this article we will use the high level analogy outlined above)

So, to bring it back to the interview with Dr. Deutsch, how do quantum computers correct errors?

Well, in short, they currently do not.

This interview actually relates to a recent RT post we did on quantum error correction. In the paper we discussed, the researchers were trying to figure out a way to allow qubits to access any other qubit in the system in constant time. This technique allows for greater error correction.

Due to the properties of entanglement and superposition, Dr. Deutsch states that any sort of error correction of a qubit would destroy much of the information the qubit system is holding.

To refresh, qubits are able to hold more information per unit (where the unit, in this case, is a qubit) as opposed to bits in a traditional computer because the qubits are entangled with their neighbors.

Because of this, if someone were to change the information in even one qubit, a domino effect of sorts would result. This domino effect would cause the information stored in the nearest neighbors of that qubit to change, and the trend would continue throughout the entire system of qubits.

Because of this, it’s pretty hard to see a scenario in which one could correct an error in a qubit.

However, Dr. Deutsch proposes that allowing a certain degree of error (aka a certain amount of noise) in the qubit system might be acceptable. By allowing an acceptable amount of noise in the message, researchers could develop an error correction system much faster by targeting major errors and correcting them in ways that would minimize “domino effect” changes across the system. An algorithm with build-in leniency like this is called a fault tolerant algorithm.

There are currently researchers around the world attempting to create a working quantum computing machine that can successfully bypass the quantum error correction paradox, which is seen in the research community as a critical problem to address in order to have a realistic chance at a fully-functioning quantum computer.

Do you have an idea on how to solve this problem? Do you have questions about the issue or question why it’s important? Let us know in the comments