Quantum computers are primarily a threat to asymmetric encryption (aka public-key encryption) and other cryptographic operations that rely on certain mathematical operations. Current computers can’t easily conduct prime factorization or solve the discrete logarithm problem. These mathematical problems are the core of RSA, elliptic-curve cryptography, Diffie-Hellman key exchange, DSA etc. These schemes are used by OpenPGP, TLS, SSH, OTR etc. We can expect that these schemes will be insecure. In summary, today’s transport encryption on the internet will be broken.

On the other hand, quantum computers are expected to halve the actual key sizes of symmetric cryptography. So in a post-quantum world AES-256 will offer the security of AES-128, and AES-128 will only offer security similar to AES-64 (which doesn’t exist and should be considered insecure even today).

Besides, all symmetric block ciphers (like AES) use so-called block cipher modes. Several block cipher modes are considered insecure today (like ECB and CBC under certain conditions), and many of today’s secure block cipher modes like GCM will likely become insecure in a post-quantum world. So you not only need to choose AES-256 instead of AES-128, but also use one of the remaining block cipher modes.

You should use symmetric encryption like AES-256.

If we assume that VeraCrypt implemented everything correctly, quantum computers won’t immediately break symmetric crypto, and you chose a sufficiently strong password/passphrase, then your container should be still secure in a post-quantum world.