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International Journal of Theoretical Physics

Fault Tolerant Authenticated Quantum Dialogue Based on Logical Qubits and Controlled-Not Operations

Yan‐Feng Lang

Published Nov 21, 2018• 7 citations
Publisher
DOI
10.1007/s10773-018-3952-7

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The information leakage is a challenge in the design of Controlled quantum dialogue (CQD) protocols and the CQD protocol over noise channel has not been well researched. A CQD protocol without information leakage over an ideal channel is first proposed, where single photons are used to carrying secret information and pre-shared keys are used to authenticate identity and control information decoding for the prevention of information leakage, moreover, a novel kind of the unitary encoding operations with good property on the quantum operation discrimination are adopted to avoid active attacks from outside eavesdropper. By substituting logical qubits for single photons and constructing unitary encoding operations with the same property based on logical qubits, three fault-tolerant versions of the proposed CQD protocol are obtained, which can combat collective-dephasing, collective-rotation and all kinds of unitary collective noise, respectively. The security and efficiency analysis show the proposed protocols are appropriate for secure quantum dialogue in practice.
Encoding of quantum information and carrying out computation on encoded state is an essential requirement for improving the reliability of a quantum computer. Resource limitation in today's noisy intermediate scale quantum (NISQ) processors further restricts carrying out fault-tolerant quantum gate operations on such systems. Recent experiments conducted on physical qubits of superconducting transmon type and trapped atomic ions using the fault-tolerant scheme based on [[4, 2, 2]] code have shown a systematic improvement in the fidelity of all logical quantum gate operations except the logical controlled-NOT (CNOT) operation that requires 3 physical SWAP operations for fault-tolerant realization. In this present work we propose an optimal realization of logical CNOT operations on a single or two separate [[4, 2, 2]] code-words using 4 physical CNOT operations and an additional qubit. We further introduce logical two-qubit positive and negative controlled-phase operations with varying rotation angle, and also propose the fault-tolerant realization of logical 2-controlled-phase (C2Z) and 2-controlled-NOT (C2NOT) operations that are required for universal computation using [[4, 2, 2]] encoding. The implementation requires less number of encoded operations and one additional qubit. Through experiments conducted on the 15-qubit IBM Quantum Experience processor and QASM simulator the fidelity and validity of all these proposed gate operations have been verified.