ABSTRACT
Quantum error correction (QEC) is an effective way to overcome quantum noise and de-coherence, meanwhile the fault tolerance of the encoding circuit, syndrome measurement circuit, and logical gate realization circuit must be ensured so as to achieve reliable quantum computing. Steane code is one of the most famous codes, proposed in 1996, however, the classical encoding circuit based on stabilizer implementation is not fault-tolerant. In this paper, we propose a method to design a fault-tolerant encoding circuit for Calderbank-Shor-Steane (CSS) code based on stabilizer implementation and "flag" bits. We use the Steane code as an example to depict in detail the fault-tolerant encoding circuit design process including the logical operation implementation, the stabilizer implementation, and the "flag" qubits design. The simulation results show that assuming only one quantum gate will be wrong with a certain probability p, the classical encoding circuit will have logic errors proportional to p; our proposed circuit is fault-tolerant as with the help of the "flag" bits, all types of errors in the encoding process can be accurately and uniquely determined, the errors can be fixed. If all the gates will be wrong with a certain probability p, which is the actual situation, the proposed encoding circuit will also be wrong with a certain probability, but its error rate has been reduced greatly from p to p2 compared with the original circuit. This encoding circuit design process can be extended to other CSS codes to improve the correctness of the encoding circuit.
ABSTRACT
In this paper, we propose a distributed secure delegated quantum computation protocol, by which an almost classical client can delegate a (dk)-qubit quantum circuit to d quantum servers, where each server is equipped with a 2k-qubit register that is used to process only k qubits of the delegated quantum circuit. None of servers can learn any information about the input and output of the computation. The only requirement for the client is that he or she has ability to prepare four possible qubits in the state of (|0⟩+eiθ|1⟩)/2, where θ∈{0,π/2,π,3π/2}. The only requirement for servers is that each pair of them share some entangled states (|0⟩|+⟩+|1⟩|-⟩)/2 as ancillary qubits. Instead of assuming that all servers are interconnected directly by quantum channels, we introduce a third party in our protocol that is designed to distribute the entangled states between those servers. This would simplify the quantum network because the servers do not need to share a quantum channel. In the end, we show that our protocol can guarantee unconditional security of the computation under the situation where all servers, including the third party, are honest-but-curious and allowed to cooperate with each other.
