Quantum computing is a model of computing based on the quantum physics, which works differently than classical computers and can do things that classical computers can’t, such
as breaking RSA and ECC efficiently. Quantum computers are not "faster computers" and they are not all-powerful and cannot do any computing job faster. Quantum computers are very efficient for certain problems and quite weak for others.
It is well known in computer science that quantum computers will break some cryptographic algorithms, especially the public-key cryptosystems like RSA, ECC and ECDSA that rely on the IFP (integer factorization problem), the DLP (discrete logarithms problem) and the ECDLP (elliptic-curve discrete logarithm problem). Quantum algorithms will not be the end of cryptography, because:
Only some cryptosystems are quantum-unsafe (like RSA, DHKE, ECC, ECDSA and ECDH).
Some cryptosystems are quantum-safe and will be only slightly affected (like cryptographic hashes, MAC algorithms and symmetric key ciphers).
Let's discuss this in details.
Quantum-Safe and Quantum-Broken Crypto Algorithms
Most cryptographic hashes (like SHA2, SHA3, BLAKE2), MAC algorithms (like HMAC and CMAK), key-derivation functions (bcrypt, Scrypt, Argon2) are basically quantum-safe (only slightly affected by quantum computing).
Use 384-bits or more to be quantum-safe (256-bits should be enough for long time)
Symmetric ciphers (like AES-256, Twofish-256) are quantum-safe.
Use 256-bits or more as key length (don't use 128-bit AES)
Most popular public-key cryptosystems (like RSA, DSA, ECDSA, EdDSA, DHKE, ECDH, ElGamal) are quantum-broken!
Most digital signature algorithms (like RSA, ECDSA, EdDSA) are quantum-broken!
Quantum-safe signature algorithms and public-key cryptosystems are already developed (e.g. lattice-based or hash-based signatures), but are not massively used, because of longer keys and longer signatures than ECC.
The quantum-safe cryptography is still emerging, not mature, and still not widely supported by the most crypto-libraries and tools like Web browsers, OpenSSL, OpenSSH, etc. This is a list of well developed quantum crypto algorithm libraries: