Quantum compiling with variational instruction set for accurate and fast quantum computing

The quantum instruction set (QIS) is defined as the quantum gates that are physically realizable by controlling the qubits in a 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 \R{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 are variationally achieved using the fine-grained time optimization algorithm. Significant reductions on 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 the standard QIS such as \RR{the quantum microinstruction set} (QuMIS, formed by several one- and two-qubit gates including the one-qubit rotations and controlled-NOT gate). With the same requirement on quantum hardware, the time cost by \R{QuVIS} is reduced to be less than one half of that by 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, \R{QuVIS} can be defined for different quantum circuits and adapt to the quantum hardware with different interactions.