The quantum Fourier transform is like a musical instrument that breaks a signal into pure notes. If the instrument is slightly out of tune, the melody sounds wrong. Scientists are checking whether you can spot the detuning by listening to just a few random notes.

Previously, it was thought that if the instrument plays well on average, it would also work for complex pieces. But it turns out that in the quantum world, barely noticeable phase shifts can occur between notes, like an echo that spoils the harmony. A simple check doesn't catch them.

So a new, stricter test was proposed. It monitors such shifts and guarantees that the Harrow–Hassidim–Lloyd (HHL) algorithm will work correctly even in the worst case. It's like a tuner who checks not only individual notes but also their combinations in chords.

Now there's a way to ensure the quantum instrument won't let you down at the most critical moment.