I'd assume that the value intended for public exponent is used as private key exponent. Typically, public key exponent is very small compared to private key exponent. This means that the private key exponent is very small in their scheme, so attacks such as Wiener's attack[0] can be used to break the encryption.
Also, I'd like to add that public exponent is usually fixed to some well-known constant such as 65537, so the attacker might just try brute-forcing when she knows the details of the scheme.
Standard ciphers such as AES and SHA comes into my mind. Some processors even have dedicated hardware instructions speed up computations for such ciphers.
If I remember correctly, the chips in D-Wave machines are for specific problems (optimization problems mostly), so it seems very unlikely they can run the quantum circuits proposed in the article.
[0] https://www.theverge.com/2021/8/18/22630245/google-fuchsia-o...