The robot's true position along the tunnel route is known exactly by the simulation, but the robot itself only has a classical inertial measurement unit (IMU): an accelerometer and gyroscope it integrates every step to estimate where it is. That integration accumulates small heading and speed biases into a position error that keeps growing with distance traveled — dead-reckoning drift, unavoidable and unbounded without an outside reference, which is exactly the problem in tunnels, caves and other GPS-denied environments.
A quantum sensor — an atom-interferometer accelerometer or an NV-center magnetometer — measures far more precisely than the classical IMU, but at a much slower rate. Every few meters it delivers one high-precision absolute fix, snapping the position estimate back near the truth. Between fixes the classical IMU is still doing all the fast, continuous work; the quantum sensor only vetoes its accumulated error periodically.
estimate(t) = true(t) + drift(t)
drift(t+dt) = drift(t) + bias·dt + noise·√dt // classical, unbounded
if distanceSinceFix ≥ correctionInterval:
drift ← quantumNoiseFloor // quantum snap, ~mm-cm
distanceSinceFix ← 0
- Quantum correction — toggle it off and the quantum trail drifts exactly like the classical-only one: no free lunch without the sensor.
- Correction interval — how far the robot travels between quantum fixes. Shorter intervals bound the error tighter but assume a sensor that can be read more often; longer intervals let more drift accumulate between snaps.
- IMU drift rate — scales the classical sensor's bias and noise, standing in for cheaper vs. better-calibrated hardware.
- The chart's red curve (classical-only) grows roughly with distance traveled and never resets. The cyan curve (quantum-corrected) saws upward between fixes and drops back to the sensor's tiny noise floor at each one — that sawtooth, not a flat line, is what quantum-aided navigation actually looks like.
Real-world relevance: this fusion pattern — fast/noisy classical dead reckoning kept honest by slow/precise quantum absolute measurements — is the core idea behind quantum-assisted inertial navigation research for submarines, aircraft and mobile robots operating where GPS signals never reach.