Shao-Ming Fei

Ying Lu, Peng-Fei Zhou, Shao-Ming Fei et al.

The quantum instruction set (QIS) is defined as the quantum gates that are physically realizable by controlling the qubits in quantum hardware. Compiling quantum circuits into the product of the gates in a properly defined QIS is a fundamental step in quantum computing. We here propose the quantum variational instruction set (QuVIS) formed by flexibly designed multi-qubit gates for higher speed and accuracy of quantum computing. The controlling of qubits for realizing the gates in a QuVIS is variationally achieved using the fine-grained time optimization algorithm. Significant reductions in both the error accumulation and time cost are demonstrated in realizing the swaps of multiple qubits and quantum Fourier transformations, compared with the compiling by a standard QIS such as the quantum microinstruction set (QuMIS, formed by several one- and two-qubit gates including one-qubit rotations and controlled-NOT gates). With the same requirement on quantum hardware, the time cost for QuVIS is reduced to less than one half of that for QuMIS. Simultaneously, the error is suppressed algebraically as the depth of the compiled circuit is reduced. As a general compiling approach with high flexibility and efficiency, QuVIS can be defined for different quantum circuits and be adapted to the quantum hardware with different interactions.

Shi-Ju Ran, Zheng-Zhi Sun, Shao-Ming Fei et al.

We propose tensor-network compressed sensing (TNCS) by combining the ideas of compressed sensing, tensor network (TN), and machine learning, which permits novel and efficient quantum communications of realistic data. The strategy is to use the unsupervised TN machine learning algorithm to obtain the entangled state $|Ψ\rangle$ that describes the probability distribution of a huge amount of classical information considered to be communicated. To transfer a specific piece of information with $|Ψ\rangle$, our proposal is to encode such information in the separable state with the minimal distance to the measured state $|Φ\rangle$ that is obtained by partially measuring on $|Ψ\rangle$ in a designed way. To this end, a measuring protocol analogous to the compressed sensing with neural-network machine learning is suggested, where the measurements are designed to minimize uncertainty of information from the probability distribution given by $|Φ\rangle$. In this way, those who have $|Φ\rangle$ can reliably access the information by simply measuring on $|Φ\rangle$. We propose q-sparsity to characterize the sparsity of quantum states and the efficiency of the quantum communications by TNCS. The high q-sparsity is essentially due to the fact that the TN states describing nicely the probability distribution obey the area law of entanglement entropy. Testing on realistic datasets (hand-written digits and fashion images), TNCS is shown to possess high efficiency and accuracy, where the security of communications is guaranteed by the fundamental quantum principles.