Quantum sensing for robots#

Quantum limits, accelerometer models and a multi-rate Kalman filter that fuses a slow, almost drift-free quantum sensor with a fast, drifting classical one. The equations are on the mathematics page.

Legend: blue inputs, violet internal steps, green outputs, coral people, dashed grey classical baselines. Each entry is labelled by origin: Unique to Quantum Mind designed in this library; it builds on the methods cited with it, Published model, extended implements the cited model as published; Quantum Mind adds the capabilities listed, Published method implements the cited method as published, Software tool infrastructure rather than a model; and by category: Quantum-like quantum probability used to model people; runs on an ordinary computer, Quantum computing quantum circuits; run on the simulator or sent to quantum hardware, Classical classical statistics, decision theory or baselines, Mixed combines parts from more than one of these categories.

Quantum sensing limits#

Published method Quantum computing

The standard quantum limit and the Heisenberg limit of a phase measurement, and the acceleration sensitivity of a light-pulse atom interferometer.

        flowchart LR
    accTitle: Block diagram of Quantum sensing limits
    accDescr: The standard quantum limit and the Heisenberg limit of a phase measurement, and the acceleration sensitivity of a light-pulse atom interferometer.
    n["N atoms · repeats ν"]:::in --> sql["Δφ = 1/√(Nν)<br/>standard quantum limit"]:::op
    n --> h["Δφ = 1/(N√ν)<br/>Heisenberg limit"]:::base
    sql --> a["Δa = Δφ / (C k_eff T²)"]:::out
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API: phase_sensitivity(), atom_interferometer_sensitivity()
Compared with: the Heisenberg limit (needs entangled probes)
Tutorial: Quantum sensing for robot navigation
Origin: Published method: implements the cited method as published.
Category: Quantum computing: quantum circuits; run on the simulator or sent to quantum hardware.
Reference: Kasevich, M., & Chu, S. (1992). Measurement of the gravitational acceleration of an atom with a light-pulse atom interferometer. Applied Physics B, 54, 321-332; Giovannetti, V., Lloyd, S., & Maccone, L. (2004). Quantum-enhanced measurements: beating the standard quantum limit. Science, 306, 1330-1336.

Inertial sensor models#

Published method Mixed

An accelerometer as sample rate, white noise and a drifting bias. A MEMS preset is fast and drifts; an atom-interferometer preset is slow and almost drift-free, with its noise taken from the quantum limit. Values are illustrative.

        flowchart LR
    accTitle: Block diagram of Inertial sensor models
    accDescr: An accelerometer as sample rate, white noise and a drifting bias. A MEMS preset is fast and drifts; an atom-interferometer preset is slow and almost drift-free, with its noise taken from the quantum limit. Values are illustrative.
    a["true acceleration"]:::in --> m["MEMS: fast · noisy · drifting bias"]:::base --> z1["readings"]:::out
    a --> q["atom interferometer: slow · quantum-limited · stable"]:::op --> z2["readings"]:::out
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API: Sensor, mems_accelerometer(), atom_interferometer_accelerometer()
Tutorial: Quantum sensing for robot navigation
Origin: Published method: implements the cited method as published.
Category: Mixed: combines parts from more than one of these categories.
Reference: Kasevich, M., & Chu, S. (1992). Applied Physics B, 54, 321-332.

Multi-rate Kalman dead reckoning#

Published model, extended Mixed

A one-axis robot with an unknown acceleration, several accelerometers at different rates with drifting biases, and optional position fixes, fused by a Kalman filter; whole sensor suites are compared on the same trajectories.

        flowchart LR
    accTitle: Block diagram of Multi-rate Kalman dead reckoning
    accDescr: A one-axis robot with an unknown acceleration, several accelerometers at different rates with drifting biases, and optional position fixes, fused by a Kalman filter; whole sensor suites are compared on the same trajectories.
    tr["simulated trajectory"]:::in --> s1["MEMS 100 Hz"]:::op --> kf["multi-rate Kalman filter<br/>state: p, v, a, biases"]:::op
    tr --> s2["quantum 1 Hz"]:::op --> kf
    fx["position fixes (optional)"]:::in --> kf
    kf --> e["position error<br/>per sensor suite"]:::out
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    classDef hum fill:#3d1414,stroke:#ff7b72,color:#e6edf3
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API: simulate_dead_reckoning(), run_filter(), compare_sensor_suites()
Compared with: each sensor alone; the fused suite against MEMS only (paired test)
Tutorial: Quantum sensing for robot navigation
Origin: Published model, extended: implements the cited model as published; Quantum Mind adds the capabilities listed.
Category: Mixed: combines parts from more than one of these categories.
Quantum Mind adds: several accelerometers with their own rates and bias walks in one filter, and a paired comparison of sensor suites.
Reference: Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 82, 35-45.