The Short Version
This claim is false. Quantum computers pose a recognized future threat to certain public-key encryption systems (like RSA and ECC) via Shor's algorithm, but they cannot break "all" currently used encryption. Symmetric algorithms like AES-256 are only marginally weakened by Grover's algorithm and remain secure with appropriate key sizes. Moreover, no quantum computer today has the fault-tolerant hardware needed to break even real-world RSA-2048. NIST itself describes this as a future risk to "many" systems — not a present capability against all encryption.