Representation-Dependent Recoverability in Quantum Compilation
Abstract
Fault-tolerant compilation can disperse high-level structure: schedules split an accumulated phase across rounds, gate synthesis replaces an angle by a Clifford+T word, and randomized compiling spreads rotations over sign-randomized fragments. They preserve the computation but change how cheaply a downstream compiler can recover the aggregate phase data. We formalize this representation-dependent recoverability by charging two channels: output committed before the suffix arrives, and a serialized restart state crossing the cut. For an r-round accumulation of a commuting layer with m generators at accuracy ε (Kε=Θ(1/ε)), any p-pass compiler correct on every valid stream with failure probability at most δ obeys A̅p+(2p−1)S≥(1−δ)mlog2 Kε−h2(δ), where A̅p is committed output and S is the crossing-state cap. The bound covers compile-time randomized compiling; a memory-capped block compiler attains it within a constant factor, and direct semantic aggregation reaches compact output with logarithmic state. The two channels are not always interchangeable. A compiler whose committed prefix is executed at the cut pays a toll the state channel never pays: the entropy log2binommk of the mask naming which k coordinates it commits early. Compilers that defer or buffer pay none of it. We prove both directions and, with instrumented compilers under a preregistered protocol, measure a per-generator toll matching log2binommk/k that vanishes for a public mask and a buffered control. Under a disclosed fixed-total-error Clifford+T and surface-code model, a materialize-first pipeline costs orders of magnitude more logical T states and spacetime volume than a semantic-first one. Phase semantics should therefore be preserved until aggregation whenever the interface permits.
Related
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BibTeX
@misc{yang2026representationdependent,
title = {{Representation-Dependent Recoverability in Quantum Compilation}},
author = {Jinze Yang and Yangyang Li and Xiu-Hao Deng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29210},
eprint = {2609.29210},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29210},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Representation-Dependent Recoverability in Quantum Compilation
AU - Jinze Yang
AU - Yangyang Li
AU - Xiu-Hao Deng
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29210
UR - https://arxiv.org/abs/2609.29210
AB - Fault-tolerant compilation can disperse high-level structure: schedules split an accumulated phase across rounds, gate synthesis replaces an angle by a Clifford+T word, and randomized compiling spreads rotations over sign-randomized fragments. They preserve the computation but change how cheaply a downstream compiler can recover the aggregate phase data. We formalize this representation-dependent recoverability by charging two channels: output committed before the suffix arrives, and a serialized restart state crossing the cut. For an r-round accumulation of a commuting layer with m generators at accuracy ε (K_ε=Θ(1/ε)), any p-pass compiler correct on every valid stream with failure probability at most δ obeys A̅_p+(2p−1)S≥(1−δ)mlog_2 K_ε−h_2(δ), where A̅_p is committed output and S is the crossing-state cap. The bound covers compile-time randomized compiling; a memory-capped block compiler attains it within a constant factor, and direct semantic aggregation reaches compact output with logarithmic state. The two channels are not always interchangeable. A compiler whose committed prefix is executed at the cut pays a toll the state channel never pays: the entropy log_2binommk of the mask naming which k coordinates it commits early. Compilers that defer or buffer pay none of it. We prove both directions and, with instrumented compilers under a preregistered protocol, measure a per-generator toll matching log_2binommk/k that vanishes for a public mask and a buffered control. Under a disclosed fixed-total-error Clifford+T and surface-code model, a materialize-first pipeline costs orders of magnitude more logical T states and spacetime volume than a semantic-first one. Phase semantics should therefore be preserved until aggregation whenever the interface permits.
ER -