Analog-to-digital conversion circuits are presented which employ magnetic tunnel junction (MTJ) elements that change state probabilistically in response to application of electrical pulses. Some implementations form a multi-channel analog-to-digital conversion circuit, with each channel comprising a magnetic tunnel junction (MTJ) element, and a pulse generator that determines characteristics of perturbation pulses to be applied to an MTJ element based at least on an analog input. The pulse generator also applies read pulses to the MTJ element to produce indications of magnetization state changes for the MTJ element due to application of the perturbation pulses. Each channel of the multi-channel analog-to-digital conversion circuit can include count circuitry that counts the indications of the magnetization state changes for an associated MTJ element. Outputs from each single-channel analog-to-digital converter are combined to determine a digital output representative of the analog input.