The title of your question asks for techniques that are impossible to break, to which the One Time Pad (OTP) is the correct answer, as pointed out in the other answers. The OTP is information-theoretically secure, which means that an adversaries computational abilities are inapplicable when it comes to finding the message.
However, despite being perfectly secure in theory, the OTP is of limited use in modern cryptography. It is extremely difficult to use successfully in practice.
The important question really is:
Can we still expect a new cryptographic algorithm which will be hard to crack using even a quantum computer?
Asymmetric cryptography includes Public-Key Encryption (PKE), Digital Signatures, and Key Agreement schemes. These techniques are vital to solve the problems of key distribution and key management. Key distribution and key management are non-negligible problems, they are largely what prevent the OTP from being usable in practice. The internet as we know it today would not function without the ability to create a secured communications channel from an insecure communications channel, which is one of the features that asymmetric algorithms offer.
Shor's algorithm is useful for solving the problems of integer factorization and discrete logarithms. These two problems are what provide the basis for security of widely used schemes such as RSA and Diffie-Hellman.
NIST is currently evaluating submissions for Post-Quantum algorithms - algorithms that are based on problems that are believed to be resistant to quantum computers. These problems include:
It should be noted that classical algorithms for solving the above problems may exist, it's just that the runtime/accuracy of these algorithms is prohibitive for solving large instances in practice. These problems don't appear to be solvable when given the ability to solve the problem of order finding, which is what the quantum part of Shor's algorithm does.
Grover's algorithm provides a quadratic speedup when searching through an unsorted list. This is effectively the problem brute-forcing a symmetric encryption key.
Working around Grover's algorithm is relatively easy compared to working around Shor's algorithm: Simply double the size of your symmetric key. A 256-bit key offers 128-bits of resistance against brute force to an adversary that uses Grover's algorithm.
Grover's algorithm is also usable against hash functions. The solution again is simple: Double the size of your hash output (and capacity if you are using a hash based on a sponge construction).