  A major challenge for quantum computers is the scalable simultaneous
execution of quantum gates. One approach to address this in trapped ion quantum
computers is the implementation of quantum gates based on static magnetic field
gradients and global microwave fields. In this paper, we present the
fabrication of surface ion traps with integrated copper current carrying wires
embedded inside the substrate below the ion trap electrodes, capable of
generating high magnetic field gradients. The copper layer's measured sheet
resistance of 1.12 m$\Omega$/sq at room temperature is sufficiently low to
incorporate complex designs, without excessive power dissipation at high
currents causing a thermal runaway. At a temperature of 40 K the sheet
resistance drops to 20.9 $\mu\Omega$/sq giving a lower limit for the residual
resistance ratio of 100. Continuous currents of 13 A can be applied, resulting
in a simulated magnetic field gradient of 144 T/m at the ion position, which is
125 $\mu$m from the trap surface for the particular anti-parallel wire pair in
our design.
