In a small bowl, combine the smoked paprika, turmeric, ground cumin, kosher salt, and black pepper.
Pat the chicken dry and rub the spice mixture evenly over all sides; set the chicken aside.
Set the Instant Pot to Sauté. Add 2 tablespoons of the olive oil to the inner pot.
Sear the chicken skin-side down (or the first side if skinless) until golden and browned, then flip and brown the other side; remove the chicken to a plate.
Add the remaining 2 tablespoons olive oil to the pot, then sauté the minced garlic, diced onion, and minced ginger for about 2 minutes, stirring, until fragrant and softened.
Stir in the quinoa, drained chickpeas, and dried cherries, then pour in the chicken broth and spread the mixture into an even layer in the pot.
Place the browned chicken on top of the quinoa mixture in a single layer.
Close the Instant Pot lid and set the pressure release valve to SEALING. Select Manual (High Pressure) and set the timer for 10 minutes.
When the cook time finishes, carefully switch the valve to VENTING to quick-release the pressure. When steam stops, press Cancel and open the lid.
Check that the chicken registers 165°F (74°C) with a thermometer. Serve the chicken over the quinoa-chickpea mixture and garnish as desired.