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Concatenated Composite Pulses Beyond Local Residual-Error Preservation

  • Masamitsu Bando
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Abstract

Residual-error preservation (REP) provides a sufficient rule for constructing concatenated composite pulses that compensate multiple systematic errors. We show that local REP is not necessary: deviations from REP can cancel across the full sequence. Using first-order error generators, we derive a necessary and sufficient condition for concatenation to retain the robustness of an outer sequence. A simple sufficient condition is that all inner pulses rescale the corresponding elementary error generators by a common real factor, not necessarily unity. We illustrate this principle using pulse-length and off-resonance errors, two systematic error models commonly considered in magnetic resonance. Short CORPSE and SCROFULOUS each compensate one error without preserving the other locally. Combining these inner pulses with suitable equal-rotation-angle outer sequences yields simultaneous first-order compensation of both errors, extending concatenated composite-pulse design beyond local REP.

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Cite

BibTeXRIS
BibTeX
@misc{bando2026concatenated,
  title = {{Concatenated Composite Pulses Beyond Local Residual-Error Preservation}},
  author = {Masamitsu Bando},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22728},
  eprint = {2609.22728},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22728},
}
RIS
TY  - UNPB
TI  - Concatenated Composite Pulses Beyond Local Residual-Error Preservation
AU  - Masamitsu Bando
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.22728
UR  - https://arxiv.org/abs/2609.22728
AB  - Residual-error preservation (REP) provides a sufficient rule for constructing concatenated composite pulses that compensate multiple systematic errors. We show that local REP is not necessary: deviations from REP can cancel across the full sequence. Using first-order error generators, we derive a necessary and sufficient condition for concatenation to retain the robustness of an outer sequence. A simple sufficient condition is that all inner pulses rescale the corresponding elementary error generators by a common real factor, not necessarily unity. We illustrate this principle using pulse-length and off-resonance errors, two systematic error models commonly considered in magnetic resonance. Short CORPSE and SCROFULOUS each compensate one error without preserving the other locally. Combining these inner pulses with suitable equal-rotation-angle outer sequences yields simultaneous first-order compensation of both errors, extending concatenated composite-pulse design beyond local REP.
ER  -