RSA encryption is based on the difficulty of factoring large composite numbers into their prime factors. To break RSA encryption, one must factorize the public key, a product of two large prime numbers. The number of qubits required to factorize a number N using Shor's algorithm (a quantum algorithm that can be used to factorize integers) is 2n + 3, where n is the number of bits in N.

For instance, RSA-2048, a common RSA key size used in practice, comprises two 1024-bit prime numbers. To break this, one would need approximately 2*2048 + 3 = 4099 qubits. However, this is a simplification, as the number of qubits required would depend on the specifics of the quantum computer and quantum error correction techniques used, which could significantly increase the number of qubits required.

Having enough qubits isn't the only challenge. The qubits must be interconnected in a way that allows the implementation of the quantum gates needed for Shor's algorithm, and the machine must be able to maintain quantum coherence long enough to complete the operation.