Nonlinear optical gates are usually considered as fundamental building blocks for universal optical computation. However, the performance is severely limited by small optical nonlinearity, thereby bounding their operation speed, consumption energy, and device size. In this paper, we propose and experimentally demonstrate linear optical logic operations with 3 μm-long Si wire "Ψ" gates consist of 3 × 1 optical combiners including auxiliary bias port, which maximizes the binary contrast of the output in telecom wavelength. We have demonstrated 20 Gbps Boolean "AND" operation with experimentally measured small signal loss (1.6 dB experimentally). A single Ψ gate can perform representative Boolean operations by changing the bias power and relative phases. We have also demonstrated wavelengthindependent operation by seven wavelengths, which leads to wavelength-division multiplexed parallel computation. This ultrashort, highly-integrable, low-loss, and energy-efficient optical logic gates pave the way for ultralow latency optical pattern matching, recognition, and conversion.