arXiv subjects

Cory T. Aitchison

Publications and source records attributed to Cory T. Aitchison.

3 recordsLinked to original sources

arXiv2026

Spacetime Spins: Statistical mechanics for error correction with stabilizer circuits

A powerful method for analyzing quantum error-correcting codes is to map them onto classical statistical mechanics models. Such mappings have thus far mostly focused on static codes, possibly subject to repeated syndrome measurements. Recent progress in quantum error correction, however, has prompted new paradigms where codes emerge from stabilizer circuits in spacetime -- a unifying perspective encompassing syndrome extraction circuits of static codes, dynamically generated codes, and logical operations. We show how to construct statistical mechanical models for stabilizer circuits subject to independent Pauli errors, by mapping logical equivalence class probabilities of errors to partition functions using the spacetime subsystem code formalism. We also introduce a modular language of spin diagrams for constructing the spin Hamiltonians, which we describe in detail focusing on independent circuit-level X-Z error channels. With the repetition and toric codes as examples, we use our approach to analytically rank logical error rates and thresholds between code implementations with standard and dynamic syndrome extraction circuits, describe the effect of transversal logical Clifford gates on logical error rates, and perform Monte Carlo simulations to estimate maximum likelihood thresholds. Our framework offers a universal prescription to analyze, simulate, and compare the decoding properties of any stabilizer circuit, while revealing the innate connections between dynamical quantum systems and noise-resilient phases of matter.

quant-ph↗

arXiv2025

Competing automorphisms and disordered Floquet codes

Topological order is a promising basis for quantum error correction, a key milestone towards large-scale quantum computing. Floquet codes provide a dynamical scheme for this while also exhibiting Floquet-enriched topological order (FET) where anyons periodically undergo a measurement-induced automorphism that acts uniformly in space. We study disordered Floquet codes where automorphisms have a spatiotemporally heterogeneous distribution -- the automorphisms "compete". We characterize the effect of this competition, showing how key features of the purification dynamics of mixed codestates can be inferred from anyon and automorphism properties for any Abelian topological order. This perspective can explain the protection or measurement of logical information in a dynamic automorphism (DA) code when subjected to a noise model of missing measurements. We demonstrate this using a DA color code with perturbed measurement sequences. The framework of competing automorphisms captures essential features of Floquet codes and robustness to noise, and may elucidate key mechanisms involving topological order, automorphisms, and fault-tolerance.

quant-ph↗

arXiv2023

No Strings Attached: Boundaries and Defects in the Cubic Code

Haah's cubic code is the prototypical type-II fracton topological order. It instantiates the no string-like operator property that underlies the favorable scaling of its code distance and logical energy barrier. Previously, the cubic code was only explored in translation-invariant systems on infinite and periodic lattices. In these settings, the code distance scales superlinearly with the linear system size, while the number of logical qubits within the degenerate ground space exhibits a complicated functional dependence that undergoes large fluctuations within a linear envelope. Here, we extend the cubic code to systems with open boundary conditions and crystal lattice defects. We characterize the condensation of topological excitations in the vicinity of these boundaries and defects, finding that their inclusion can introduce local string-like operators and enhance the mobility of otherwise fractonic excitations. Despite this, we use these boundaries and defects to define new encodings where the number of logical qubits scales linearly without fluctuations, and the code distance scales superlinearly, with the linear system size. These include a subsystem encoding with open boundary conditions and a subspace encoding using lattice defects.

quant-ph↗