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Paper 1

Tensor Decomposition for Non-Clifford Gate Minimization

Kirill Khoruzhii, Patrick Gelß, Sebastian Pokutta

Year

2026

Journal

arXiv preprint

DOI

arXiv:2602.15285

arXiv

2602.15285

Fault-tolerant quantum computation requires minimizing non-Clifford gates, whose implementation via magic state distillation dominates the resource costs. While $T$-count minimization is well-studied, dedicated $CCZ$ factories shift the natural target to direct Toffoli minimization. We develop algebraic methods for this problem, building on a connection between Toffoli count and tensor decomposition over $\mathbb{F}_2$. On standard benchmarks, these methods match or improve all reported results for both Toffoli and $T$-count, with most circuits completing in under a minute on a single CPU instead of thousands of TPUs used by prior work.

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Paper 2

Fast surgery for quantum LDPC codes

Nouédyn Baspin, Lucas Berent, Lawrence Z. Cohen

Year

2025

Journal

arXiv preprint

DOI

arXiv:2510.04521

arXiv

2510.04521

Quantum LDPC codes promise significant reductions in physical qubit overhead compared with topological codes. However, many existing constructions for performing logical operations come with distance-dependent temporal overheads. We introduce a scheme for performing generalized surgery on quantum LDPC codes using a constant number of rounds of syndrome measurement. The merged code in our scheme is constructed by taking the total complex of the base code and a suitably chosen homomorphic chain complex. We demonstrate the applicability of our scheme on an example multi-cycle code and assess the performance under a phenomenological noise model, showing that fast surgery performs comparably to standard generalized surgery with multiple rounds. Our results pave the way towards fault-tolerant quantum computing with LDPC codes with both low spatial and temporal overheads.

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