Implementing Quantum Secret Sharing on Current Hardware
Quantum secret sharing is a cryptographic scheme that enables a secure
storage and reconstruction of quantum information. While the theory of secret
sharing is mature in its development, relatively few studies have explored the
performance of quantum secret sharing on actual devices. In this work, we
provide a pedagogical description of encoding and decoding circuits for
different secret sharing codes, and we test their performance on IBM's
127-qubit Brisbane system. We evaluate the quality of implementation by
performing a SWAP test between the decoded state and the ideal one, as well as
by estimating how well the code preserves entanglement with a reference system.
Results indicate that a ((3,5)) threshold secret sharing scheme performs
slightly better overall than a ((5,7)) scheme based on the SWAP test, but is
outperformed by the Steane Code scheme in regards to the entanglement fidelity.
We also investigate one implementation of a ((2,3)) qutrit scheme and find that
it performs the worst of all, which is expected due to the additional number of
multi-qubit gate operations needed to encode and decode qutrits.
Jay Graves Mike Nelson Eric Chitambar