A conditional no-go for resource-free magic-axis measurement on a static surface code

Jiachen Shen; Hui Zhong

Home/Archive/arXiv

arXiv · 2607.16968

A conditional no-go for resource-free magic-axis measurement on a static surface code

Jiachen Shen·Hui Zhong

View original source ↗Read source document ↗Export metadata ↓

Abstract

Under stated assumptions, a static surface-code patch that adds no fold or \mbox{self-dual} structure cannot perform the magic-axis check that magic-state cultivation relies on while still accepting often. This is a conditional no-go. Fault-tolerant machines spend much of their cost making magic states, and cultivation makes them in place by measuring the magic axis, which every known construction does through a fold or \mbox{self-dual} patch that it is folklore to call necessary. We test the folklore. The no-go says that a useful check must pay for the magic axis somewhere. It can add a charge-converting resource, it can leave the dilute regime of its accepted history, or it can accept only exponentially rarely. For a single stabilizer-measurement transcript this is proved outright, from a topological reading of the accepted outcome. For adaptive, post-selected protocols in a bounded-depth (polynomial spacetime-volume) model, it holds under two structural assumptions plus a subcriticality assumption. We isolate the one open assumption, show that protection alone does not force it, and give the threshold any resolution must address. What remains is a single conjecture.

Explore related subjects

eess.SY cs.SY

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Jiachen Shen, Hui Zhong. 2026-07-18. A conditional no-go for resource-free magic-axis measurement on a static surface code. https://arxiv.org/abs/2607.16968

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Failure-Aware Iterative Learning of State-Control Invariant Sets

In this paper, we address the problem of computing maximal state-control invariant sets for deterministic linear systems using failing trajectories. We introduce the concept of state-control invariance, which extends control invariance from the state space to the joint state-control space. The maximal state-control invariant (MSCI) set simultaneously encodes the maximal control invariant set (MCI) and, for each state in the MCI, the set of control inputs that preserve invariance. We prove that the state projection of the MSCI is the MCI and the state-dependent sections of the MSCI are the admissible invariance-preserving inputs. Building on this framework, we develop a Failure-Aware Iterative Learning (FAIL) algorithm for deterministic linear time-invariant systems with polytopic constraints. The algorithm iteratively updates a constraint set in the state-control space by learning predecessor halfspaces from one-step failing state-input pairs, without knowing the dynamics. For each failure, FAIL learns the violated halfspaces of the predecessor of the constraint set by a regression on failing trajectories. We prove that the learned constraint set converges monotonically to the MSCI. Numerical experiments on a double integrator system validate the proposed approach.

eess.SY↗

arXiv2026

Consensus and Synchronization of Multi-agent Systems over Finite Fields - Graph Topologies

This paper presents cooperative protocols for multi-agent systems with agents having a finite state-space. Both scalar single-integrator consensus and general LTI system synchronization are considered. Systems having a finite state-space describe agents with minimal memory capacity processing only a finite alphabet. Such systems are remarkably resilient to communication noise. The crucial problem, however, is to construct the admissible communication topology, which is NP-hard. We address this by efficiently exploring the subsets of admissible graph matrices and propose two new algorithms to generate them. Simulations validate the proposed approach.

eess.SY↗

arXiv2026

Extracting Exact Lie Derivatives Without Backpropagation: A Dual Compiler for Neural Control Barrier Functions

A safety filter based on a neural control barrier function (CBF) deployed in an embedded control loop evaluates, at each control cycle, the trained network and its Lie derivatives along the system vector fields, under the memory and worst-case execution time (WCET) constraints that safety-oriented coding standards impose. Reverse-mode automatic differentiation, by which training frameworks obtain these derivatives, retains an activation cache whose size grows with the sum of the layer widths, and general-purpose differentiation runtimes allocate the computational graph from the heap at each call. This paper presents a compiler that evaluates a neural CBF and its exact Lie derivatives by forward-mode dual-number arithmetic. The compiler emits self-contained C++ code in which a single forward pass, without backpropagation, returns the barrier value and its exact Lie derivative along a given vector field; the drift and input Lie derivatives of the safety constraint are obtained from one such pass per vector field, and a second-order extension based on hyper-dual numbers returns the exact second-order Lie derivatives required by CBFs of relative degree two. The dual forward pass requires a workspace bounded by four times the widest layer, independent of network depth, and the emitted code contains no allocation call sites, so the absence of dynamic allocation is verifiable by inspection of the code. On an ESP32-S3 microcontroller, the compiled filter assembles the complete safety constraint in under one millisecond from statically allocated buffers of at most 768 bytes, and the maximum execution time over 1000 evaluations lies within 5% of the median in all three examples, whereas a heap-allocating reverse-mode baseline shows maxima 33% and 70% above its median in the two first-order examples. The compiler and the embedded experiments are released as open-source software.

eess.SY↗