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# Quantum Error Ignoration Revisited

Posted on August 26, 2022, By Brian N. Siegelwax

## A Specific Use Case

My March 10, 2002, article titled “Quantum Error Ignoration” used a quantum walk as a practical example: for two qubits, imagine you have three valid directions of travel and one invalid direction of travel; you simply cannot travel in an invalid direction. So, if environmental noise tells you to go in the impossible fourth direction, you simply ignore that result and run the circuit again and again until you get a valid result. For another example, let’s download and read “Teaching Qubits to Sing: Mission Impossible?” This is actually the algorithm for which I developed the concept of “error ignoration” in the first place.

So, imagine we have a sequence of three notes: A-B-C. For you music aficionados out there, I apologize for the gross oversimplification. But, anyway, imagine we have encoded into the amplitudes of the qubits that whenever we have the three-note sequence A-B-C we want a 70% probability that the next note in our new composition will be a D and a 30% probability that the next note in our new composition will be an E. The source of these probabilities is detailed in the paper, of course.

The problem is that NISQ-era quantum computers are plagued with noise. So, what happens if we get a noise-induced F, for example, instead of a D or an E? We could consider celebrating the inherent creativity of the qubits, sure. But, the problem is that we only have rules in place for the three-note sequences B-C-D and B-C-E. We have no rule in place for the three-note sequence B-C-F because we don’t want F to follow A-B-C, and we don’t want to create a rule for B-C-F because we don’t want B-C-F. Ever.

So, that’s it. With a noise-induced sequence of B-C-F, we’re dead in our tracks. One workaround for this, then, is to ignore the F. In fact, we want to ignore A, B, C, and G, as well. Noise may prohibit us from precisely measuring D 70% of the time and E 30% of the time, but ignoring unauthorized notes allows us to at least ensure that one of the two authorized notes comes next. Our new composition will contain four-note sequences such as A-B-C-D and A-B-C-E so that our new compositions will sound like our “singing” qubits on SoundClick.

For some additional background on QuSing and how it came about, check out my article “Behind The Scenes: My First Paper.” Also, be sure to check out “Quantum Computer: Hello, Music!,” the paper I cited in my book “Dungeons & Qubits: an Adventurer’s Tale Beyond the Quantum Computing Tutorials” as my introduction to the very concept of quantum music. The fact that Professor Miranda and I could use qubits to generate tunes that actually sound good still blows my mind. And, quite frankly, the qubits have had only one singing lesson. We’re just getting started….

In conclusion, we can correct, mitigate, and suppress noise-related errors on quantum computers. In fact, we threw everything we could at QuSing. Nonetheless, errors still happen, and they’re showstoppers. But in quantum show business as in traditional show business, the show must go on. Ignoring errors, just like singers powering through forgotten lyrics, allows our qubits to finish their performances.

Brian N. Siegelwax

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