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Paper 1

Assessing System Capabilities and Bottlenecks of an Early Fault-Tolerant Bicycle Architecture

Kun Liu, Ben Foxman, Gian-Luca R. Anselmetti, Yongshan Ding

Year

2026

Journal

arXiv preprint

DOI

arXiv:2604.20013

arXiv

2604.20013

Early modular fault tolerant quantum computers remain constrained by costly inter-module communication and limited magic state factory service. Understanding such bottlenecks and investigating compiler optimizations most close the gap between algorithm requirements and hardware capabilities is a concrete and practically urgent systems problem. We study the modular architectures based on Bivariate Bicycle codes and identify the dominant bottleneck: inter-module communication induced by non-Clifford operations. We build a compilation pipeline to fill the missing parts of prior works and propose compiler optimizations: synthesizing arbitrary-angle rotations at the factory (syn@fac), transvection based Clifford deferral, and Clifford insertion for critical path duration reduction. We extend the evaluation scope of the prior work to 40+ benchmark categories drawn from PennyLane and MQTBench, including quantum algorithms and Hamiltonian simulations with varying sizes. Under the present instruction cost, syn@fac reduces estimated circuit failure probability by a factor of 9.0 on average across non-Clifford benchmarks. The robustness persists across sweeps of instruction cost ratios, LPU count, and factory count. Besides, transvection reduces Clifford deferral compile time by 77.04\%, while Clifford insertion reduces end-to-end circuit duration by 11.54\% on average on MQTBench, with smaller gains on Hamiltonian simulations. We hope this work inspires the studies on compiler optimizations for early modular FTQC systems.

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Paper 2

Supersymmetric Quantum Mechanics of Hypergeometric-like Differential Operators

Tianchun Zhou

Year

2023

Journal

arXiv preprint

DOI

arXiv:2307.15948

arXiv

2307.15948

Systematic iterative algorithms of supersymmetric quantum mechanics (SUSYQM) type for solving the eigenequation of principal hypergeometric-like differential operator (HLDO) and for generating the eigenequation of associated HLDO itself as well its solutions are developed, without any input from traditional methods. These are initiated by devising two types of active supersymmetrization transformations and momentum operator maps, which work to transform the same eigenequation of HLDO in its two trivial asymmetric factorizations into two distinct supersymmetrically factorized Schrödinger equations. The rest iteration flows are completely controlled by repeatedly performing intertwining action and incorporating some generalized commutator relations to renormalize the superpartner equation of the eigenequation of present level into that of next level. These algorithms therefore provide a simple SUSYQM answer to the question regarding why there exist simultaneously a series of principal as well as associated eigenfunctions for the same HLDO, which boils down to two basic facts: two distinct types of quantum momentum kinetic energy operators and superpotentials are rooted in this operator; each initial superpotential can proliferate into a hierarchy of descendant ones in a shape-invariant fashion. The two active supersymmetrizations establish the isomorphisms between the nonstandard and standard coordinate representations of the SUSYQM algorithm either for principal HLDO or for its associated one, so these algorithms can be constructed in either coordinate representation with equal efficiency. Due to their relatively high efficiency, algebraic elementariness and logical independence, the iterative SUSYQM algorithms developed in this paper could become the hopefuls for supplanting some traditional methods for solving the eigenvalue problems of principal HLDOs and their associated cousins.

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