There is no current threat to our cryptography, and there will not be for a long time.
Most of our cryptography is Public Key based. That means there is a "trap" that is not possible to undo with our current computing power in a reasonable amount of time. An example of a "trap" is the RSA Public key which is computed from a product of 2 large prime numbers that are part of the RSA Private key, and the "trap" is factoring that product is not feasible if a good random number generator was used to produce those primes.
These quantum computers are touted as being able to factor the RSA Public key and thus would break our current algorithms. Fortunately, that isn't true yet. All the papers that have been published on quantum factoring are using cheat methods to do it.
These methods can contain any or all of the following, and other tricks: Pre-computation using classical computers to change the factoring into a physics problem with the answer embedded, and run the physics problem on the quantum computer, picking factors that are within a few bits, so a divide, and bit addition can find it, picking a number that has a bit or three on at the beginning, 1000's of zeros, and a bit or three on at the end.
Peter Gutmann (Austrailian cryptographer) has gone through the papers and found that every one is using these tricks.
Simple version, more
detailed version. Reading though his work, we can see that a quantum computer has yet to factor 35 (prime factors 5 and 7) without cheating. There is a long ways to go before there is any threat to our current public key algorithms that are using 617 digit and larger numbers that would need to be factored. Google and other quantum entities are using the tricks and publishing the hype to get more funding.
As for the Anthropic one linked above, the AES one is attacking our symmetric cryptography. Steve discussed this in the last podcast, and it also is nothing to really be concerned about. The post talks about reduced round AES, which is known to be weaker, and the higher rounds are required to remain strong. The strength of AES increases exponentially with more rounds. No one would use reduced round AES and expect the same protection. The other part of that paper was finding bad implementations in libraries that are used for cryptography, which is a great find, as this will further remove potential attack surface, and ensure the cryptography itself remains strong without a bad implementation bypass.
Also, governments are requiring that cryptography move from the current algorithms to post-quantum cryptography algorithms in the next few years. A lot of us are in the process of migrating to these new algorithms and massive keys, and this would prevent a theoretical quantum computer that won't likely exist for another decade or more from cracking archived copies of our current cryptography protected data.