As a rough way to understand this, take a look at the difference in operation between an analog computer [0] and a digital computer. One of the main difference

As a rough way to understand this, take a look at the difference in operation between an analog computer [0] and a digital computer. One of the main differences is that an analog computer does not achieve a given "operation" (e.g. integration of an input function) via a discrete heurestic (i.e. by executing the calculation in steps using say numerical integration), but rather the analog computer embodies the operation itself via its underlying physics. Essentially, these researchers have proposed a way to tackle integer factorization by creating a quantum system that embodies the calculation itself, rather than performing discrete steps on an input to find its factors as one would via, say, Shor's Algorithm on a "general-purpose" quantum computer. As is mentioned in GP post's link, this is potentially a significant result in both pure math (quantum number theory) and applied cryptography. [0] https://en.wikipedia.org/wiki/Analog_computer https://en.wikipedia.org/wiki/Analog_computer