Quantum Encryption of superposition states with Quantum Permutation Pad
  in IBM Quantum Computers
We present an implementation of Kuang and Bettenburg's Quantum Permutation
Pad (QPP) used to encrypt superposition states. The project was conducted on
currently available IBM quantum systems using the Qiskit development kit. This
work extends previously reported implementation of QPP used to encrypt basis
states and demonstrates that application of the QPP scheme is not limited to
the encryption of basis states. For this implementation, a pad of 56 2-qubit
Permutation matrices was used, providing 256 bits of entropy for the QPP
algorithm. An image of a cat was used as the plaintext for this experiment. To
create corresponding superposition states, we applied a novel operator defined
in this paper. These superposition states were then encrypted using QPP,
producing superposition ciphertext states. Due to the lack of a quantum
channel, we omitted the transmission and executed the decryption procedure on
the same IBM quantum system. If a quantum channel existed, the superposition
ciphertext states could be transmitted as qubits, and be directly decrypted on
a different quantum system. We provide a brief discussion of the security,
although the focus of the paper remains on the implementation. Previously we
have demonstrated QPP operating in both classical and quantum computers,
offering an interesting opportunity to bridge the security gap between
classical and quantum systems. This work broadens the applicability of QPP for
the encryption of basis states as well as superposition states.
Maria Perepechaenko Randy Kuang