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# Pauli gates (cuStateVec)
[[pauli-gate|Pauli gates]] implementation using cuStateVec.

```c
// Compile: nvcc main.cu -o main -lcustatevec
// Run:     ./main

#include <stdio.h>
#include <math.h>
#include <cuda_runtime.h>
#include <custatevec.h>

static void apply_and_print(custatevecHandle_t handle, cuDoubleComplex *d_sv,
                             cuDoubleComplex gate[4], const char *label) {
    cuDoubleComplex h_sv[2] = {{1,0},{0,0}};  // reset to |0>
    cudaMemcpy(d_sv, h_sv, 2 * sizeof(cuDoubleComplex), cudaMemcpyHostToDevice);

    int32_t targets[] = {0};
    custatevecApplyMatrix(
        handle, d_sv, CUDA_C_64F, 1,
        gate, CUDA_C_64F, CUSTATEVEC_MATRIX_LAYOUT_ROW, 0,
        targets, 1, NULL, NULL, 0,
        CUSTATEVEC_COMPUTE_64F, NULL, 0);

    cudaMemcpy(h_sv, d_sv, 2 * sizeof(cuDoubleComplex), cudaMemcpyDeviceToHost);
    printf("%s|0>:  |0>=(%.4f,%.4f)  |1>=(%.4f,%.4f)\n", label,
        cuCreal(h_sv[0]), cuCimag(h_sv[0]),
        cuCreal(h_sv[1]), cuCimag(h_sv[1]));
}

int main() {
    cuDoubleComplex *d_sv;
    cudaMalloc(&d_sv, 2 * sizeof(cuDoubleComplex));

    custatevecHandle_t handle;
    custatevecCreate(&handle);

    cuDoubleComplex i_gate[4] = {{1,0},{0,0},{0,0},{1,0}};
    cuDoubleComplex x_gate[4] = {{0,0},{1,0},{1,0},{0,0}};
    cuDoubleComplex y_gate[4] = {{0,0},{0,-1},{0,1},{0,0}};
    cuDoubleComplex z_gate[4] = {{1,0},{0,0},{0,0},{-1,0}};

    apply_and_print(handle, d_sv, i_gate, "I");
    apply_and_print(handle, d_sv, x_gate, "X");
    apply_and_print(handle, d_sv, y_gate, "Y");
    apply_and_print(handle, d_sv, z_gate, "Z");
    // I|0>:  |0>=(1.0000,0.0000)  |1>=(0.0000,0.0000)
    // X|0>:  |0>=(0.0000,0.0000)  |1>=(1.0000,0.0000)
    // Y|0>:  |0>=(0.0000,0.0000)  |1>=(0.0000,1.0000)
    // Z|0>:  |0>=(1.0000,0.0000)  |1>=(0.0000,0.0000)

    custatevecDestroy(handle);
    cudaFree(d_sv);
    return 0;
}
```