Earlier quoted context omitted.
Key management is how many comply with GDPR today. They encrypt the PII and associate it with the user. Then, when someone requests their info to be "deleted", they zero out the encryption key.
This should continue to work as long as you use systems that do not fall to pieces under quantum attacks. AES is considered "resistant" in that quantum does an effective square-rooting of the brute forcing effort (or if you prefer, halving of the binary key length). So, do not use anything under AES 256. Asymmetric algorithms fall apart though, which is why NIST has had a multi-year effort to select new standardized…
If you're a nation state that needs to protect information for 30+ years, then it's worth considering. For everyone on HN, it's not.