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Acknowledgments and References

Clifft has benefited from open research and software that shaped its algorithms, interfaces, and physical models. We acknowledge the following work and describe how it contributed to Clifft.

Stim

Stim's circuit format and compile-once, sample-many interfaces shaped Clifft's frontend and sampling APIs. Clifft originally used Stim's C++ tableau implementation; current production builds use Clifft's native Clifford implementation. Stim continues to serve as an independent reference for correctness tests and as a source of QEC circuit fixtures.

SOFT and SymFT

SOFT's generalized-stabilizer simulation and released magic-state cultivation circuits informed Clifft's development and provided workloads for its examples and benchmarks.

SymFT, the second-generation successor to SOFT, combines SOFT's generalized-stabilizer simulation with Clifft's original dense active-state representation. Clifft's current sampler adopts SymFT's symbolic Clifford-Pauli-frame factorization, adaptive stabilizer-coordinate planning, and direct multi-coordinate kernels. SymFT's packed cross-shot execution also inspired Clifft's packed sampling path.

SymFT's counts-focused CPU optimization work also motivated skipping unused expectation probes in Clifft's scalar aggregate sampling. This is a Clifft-specific adaptation; SymFT's compiled CPU path falls back for circuits with expectation probes.

The method provenance describes this lineage and the implementation boundaries. The symbolic sampling and packed sampling updates explain the adaptations.

Tsim

Tsim's Stim-compatible approach to universal noisy-circuit simulation informed Clifft's circuit-format and interface design. Its open code and data enabled direct comparisons in Clifft's original performance study.

SqaleSim

Infleqtion's SqaleSim motivated Clifft's leakage/loss instrument design and its five-level neutral-atom modeling. The public schedules and noise model from the Sqale study underpin Clifft's logical Shor noise-sweep tutorial. That tutorial compares matched model assumptions with Clifft's exact conditional back-action.

deltakit-stim

Riverlane's deltakit-stim inspired Clifft's configurable leakage partner effects, including partner noise and leakage spreading. Its binary leakage ledger and status-conditioned Pauli randomization also informed the fixed execution path: Clifft prepares classical status/noise inputs for a shared quantum plan, with separate readout handling to preserve its classifier correlations. The partner-interactions guide describes Clifft's model and API.

TOHPE

Clifft's phase-polynomial optimizer implements Vivien Vandaele's TOHPE algorithm for reducing T count. The author's Rust implementation served as a validation reference. Clifft supplies the surrounding state constraints, non-Clifford core extraction, and Clifford correction.

Merlin

Serban Cercelescu, Mark Koch, and Arthur Pesah's Merlin paper and simulator motivated extending Clifft's existing phase-polynomial optimization to measured code-switching preparations. Their description of states using affine support and cubic phase polynomials informed the investigation of fixed constraints recovered after measurement and feedback, and of cancellations visible only across complete phase regions. This motivated the bounded region expansion and basis-selection work in Clifft's static optimizer. Clifft uses its own Pauli constraint analysis and TOHPE synthesis; this pass does not implement Merlin's DCP simulator or per-history specialization.

Clifft also directly reuses circuits from Merlin's code-switching generator. The BT27 fixture validates measurement-feedback constraint recovery and bounded phase-region expansion. The modified direct-X BT81 fixture validates 87-variable phase collection, basis selection, and measurement-aware squeezing. The BT27 and BT81 fixture headers record the pinned generator revision, construction recipes, and modifications. These generated circuits are included under Apache-2.0; the headers also pin Merlin's upstream license revision.

Triorthogonal circuits

Matthew Cha of Riverlane assembled the triorthogonal circuit collection used to evaluate Clifft's phase-polynomial optimization. The release post reports the results. The code families and distillation protocols are described in:

MQT Bench

Clifft's fixed-input 32-qubit Draper QFT adder fixture was generated with MQT Bench. It provides an arithmetic workload for validating and benchmarking arbitrary-angle rotation simplification, as described in Richer Noise Models, Smaller Active States.

Pauli Frame Sparse Representation

Thomas Tuloup and Thomas Ayral's work informed Clifft's stratified importance-sampling approach to rare-event estimation. Clifft's importance-sampling tutorial follows their cultivation analysis by conditioning on fault count and weighting each stratum by its probability.

Magic-state cultivation

The magic-state cultivation protocol and its released circuits, data, and analysis tools underpin Clifft's cultivation examples and benchmarks. Clifft uses artifacts from the original work as well as T-gate circuits distributed with SOFT; the fixture headers and tutorials record their individual sources.

xoshiro256++

Clifft uses David Blackman and Sebastiano Vigna's xoshiro256++ random-number generator, seeded with SplitMix64, for sampling. The implementation follows the public reference code, providing a small per-shot state and deterministic integer output across platforms.