software-compensation-quantum-control

name: software-compensation-quantum-control description: "Software-based compensation methodology for AC-line-induced coherent errors in quantum control experiments. Uses line-triggered calibration frames to measure and compensate reproducible mains-synchronous disturbances without hardware modifications. Applicable to trapped-ion qubits, qudits, and precision quantum control. arXiv: 2606.00358" tags: [quantum-control, error-compensation, trapped-ion, qudit, calibration, systems-engineering]

Software-Based Compensation of AC-Line-Induced Control Errors

Source: arXiv:2606.00358 — "Software-based compensation of AC-line-induced control errors in qubits and qudits"

Core Problem

AC mains power line-synchronous disturbances are a common source of coherent, time-dependent error in precision quantum-control experiments. These manifest as magnetic-field-induced shifts in energy level structure, causing time-dependent detunings between ion transitions and local oscillators, plus accumulated phases on superposition states.

Methodology

1. Line-Triggered Calibration Frame

When AC-line disturbances are reproducible with respect to mains phase, measure their effect in a line-triggered frame:

• Trigger measurements synchronized to AC line phase
• Characterize the time-dependent detuning Δ(t) and phase accumulation φ(t)
• Build a calibrated AC contribution model

2. Software Compensation Protocol

Two-level correction applied to control sequences:

Detuning Compensation: Correct for instantaneous oscillator detuning during control pulses

• Update pulse frequencies in real-time based on calibrated AC detuning model
• Achieves 21(9)× reduction in calibrated AC line contribution

Phase Compensation: Correct for accumulated phase between pulses

• Apply compensating phase shifts to control sequences
• Reduces fitted AC phase amplitude below measurement uncertainty

3. Validation Pipeline

• Run randomized benchmarking with and without compensation
• Without compensation: mains-synchronous errors produce time-dependent fluctuations that make standard RB decay model unreliable
• With compensation: recover standard benchmarking decay and extract accurate gate fidelities

4. Qudit Extension Framework

• Extend compensation from qubit to multilevel qudit control
• Apply to algorithms like single-qudit Bernstein-Vazirani
• Demonstrated success probability improvement: 10(7)% → 70(9)% on 16-level qudit

Key Results

Reusable Patterns

Pattern 1: Reproducible Noise → Calibrated Compensation

IF noise is reproducible w.r.t. external reference (AC phase, temperature cycle, etc.)
THEN:
  1. Trigger measurement on reference signal
  2. Build deterministic disturbance model
  3. Apply software correction to control sequences
  4. No additional hardware required

Pattern 2: Control Error Characterization → Compensation

1. Identify coherent error source (magnetic, electric, thermal)
2. Measure error magnitude as function of time/reference
3. Derive compensation function (inverse of error model)
4. Inject compensation into pulse sequence software
5. Validate with randomized benchmarking

Pattern 3: Qubit-to-Qudit Generalization

Qubit compensation framework → extend to qudit by:
- Characterizing multilevel energy structure shifts
- Computing phase accumulation for all relevant transitions
- Applying compensation across all control pulses

Implementation Checklist

• Measure AC line frequency and phase stability
• Build line-triggered calibration measurement sequence
• Fit detuning model Δ(t) = f(phase, amplitude)
• Fit phase accumulation model φ(t) = ∫Δ(t)dt
• Update control software to apply compensation
• Validate with RB (check decay model stability)
• Validate with application-level benchmark
• Extend to qudit if applicable

Activation

ac line compensation, power line noise, mains synchronous error, quantum control error, trapped ion control, qudit control, coherent error compensation, software compensation, line-triggered calibration, randomized benchmarking stability