Qaiji IR: An Eight-Layer Intermediate Representation Family for Hybrid Quantum-Classical Compilation
Abstract
Hybrid quantum-classical compilation relates ideal operations and measurement outcomes to control pulses and device instructions. Existing formats each describe part of this process, and their preservation checks are often specific to one tool rather than to a common intermediate representation (IR). I present Qaiji-IR, an eight-layer IR family organized by a five-axis semantic contract for data, semantics, lowering, runtime, and verification. Its implementation provides typed circuits, an operation-semantics layer (L4) that records operation structure and checks a bounded set of equivalence rules, and a native-scheduling layer (L2) with separate validation. Nine circuit pairs are compared with ideal reference calculations. An aggregate baseline, which compares operation categories and measurement counts, accepts four behavior-changing transformations: gate reordering and changes of rotation angle, operand, or measurement destination. The L4 checker passes none of them. It distinguishes strict equality from equality up to global phase and returns unsupported when its rules cannot decide, as for valid rotation fusion. L2 validation checks native schedules against their source circuits, decomposition rules, local matrices, and configured timing. A single-qubit active-reset program is compiled through the Qaiji-IR frontend, a syntax adapter, and the EmuPlat backend into pulses and device instructions for a virtual pulse processing unit (VPPU). Injected binary outcomes select the conditional drive. Backend predicate tests reveal incorrect execution for equality to zero and for a nonbinary feedback value. This backend path does not use the validated L2 schedule. Physical measurement feedback, calibrated pulse fidelity, and feedback latency require further work.
Related
- A Dynamic Intermediate Representation for Hybrid Quantum-Classical Programs
- Representation-Dependent Recoverability in Quantum Compilation
- Representation Geometry and Inductive Biases in Quantum Classifiers across Classical Visual Benchmarks
- Quantum circuit compilation with constant overhead
- pfoqcompiler: Efficient Compilation of Quantum Control in Recursive First-Order Quantum Programs
BibTeX
@misc{ye2026qaiji,
title = {{Qaiji IR: An Eight-Layer Intermediate Representation Family for Hybrid Quantum-Classical Compilation}},
author = {Jun Ye},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.29305},
eprint = {2609.29305},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29305},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Qaiji IR: An Eight-Layer Intermediate Representation Family for Hybrid Quantum-Classical Compilation
AU - Jun Ye
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2609.29305
UR - https://arxiv.org/abs/2609.29305
AB - Hybrid quantum-classical compilation relates ideal operations and measurement outcomes to control pulses and device instructions. Existing formats each describe part of this process, and their preservation checks are often specific to one tool rather than to a common intermediate representation (IR). I present Qaiji-IR, an eight-layer IR family organized by a five-axis semantic contract for data, semantics, lowering, runtime, and verification. Its implementation provides typed circuits, an operation-semantics layer (L4) that records operation structure and checks a bounded set of equivalence rules, and a native-scheduling layer (L2) with separate validation. Nine circuit pairs are compared with ideal reference calculations. An aggregate baseline, which compares operation categories and measurement counts, accepts four behavior-changing transformations: gate reordering and changes of rotation angle, operand, or measurement destination. The L4 checker passes none of them. It distinguishes strict equality from equality up to global phase and returns unsupported when its rules cannot decide, as for valid rotation fusion. L2 validation checks native schedules against their source circuits, decomposition rules, local matrices, and configured timing. A single-qubit active-reset program is compiled through the Qaiji-IR frontend, a syntax adapter, and the EmuPlat backend into pulses and device instructions for a virtual pulse processing unit (VPPU). Injected binary outcomes select the conditional drive. Backend predicate tests reveal incorrect execution for equality to zero and for a nonbinary feedback value. This backend path does not use the validated L2 schedule. Physical measurement feedback, calibrated pulse fidelity, and feedback latency require further work.
ER -