A Heisenberg scaler reduces noise in quantum metrology and includes: a stimulus source that provides physical stimuli; a physical system including quantum sensors that receive a first and second physical stimuli; produces a measured action parameter; receives an perturbation pulse; and produces modal amplitude; an estimation machine that: receives the measured action parameter and produces a zeroth-order value from the measured action parameter; a gradient analyzer that: receives the measured action parameter and produces the measured action parameter and a gradient; the sensor interrogation unit that: receives the modal amplitude; receives the gradient and the measured action parameter; produces the perturbation pulse; and produces a first-order value from the modal amplitude, the gradient, and the measured action parameter; a Heisenberg determination machine that: receives the zeroth-order value; receives the first-order value; and produces a physical scalar from the zeroth-order value and the first-order value.