Correlated decoding loses the surface code's effective distance below threshold

César Hernando de la Fuente; Joonas Majaniemi; Evert van Nieuwenburg; Felix Frohnert

Home/Archive/arXiv

arXiv · 2610.26785

Correlated decoding loses the surface code's effective distance below threshold

César Hernando de la Fuente·Joonas Majaniemi·Evert van Nieuwenburg·Felix Frohnert

View original source ↗Read source document ↗Export metadata ↓

Abstract

Correlated decoding improves matching and clustering surface-code decoders by reweighting one decoding subgraph conditioned on the other's correction. We show that standard reweighting can cause correlated decoders to fail on size-$(d-1)/2$ fault configurations that a distance-$d$ code should correct, reducing error suppression deep below threshold. Under circuit-level noise, a single first-pass edge can discount several correlated edges, even though their joint occurrence requires additional independent faults, so the decoder favors an over-discounted correction. Regularizing the reweighting rule restores the nominal distance scaling and a clear correlated-decoding advantage.

Explore related subjects

quant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

César Hernando de la Fuente, Joonas Majaniemi, Evert van Nieuwenburg, Felix Frohnert. 2026-10-19. Correlated decoding loses the surface code's effective distance below threshold. https://arxiv.org/abs/2610.26785

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

KEEP EXPLORING

Related papers

arXiv2026

Quantum superposition of black hole states as a communication resource

The interplay between black holes and quantum information has revealed deep connections between gravity and quantum mechanics. For example, the classical spacetime geometry of a black hole has been shown to degrade quantum entanglement shared by nearby observers, one of whom is in free fall. Here we examine how this picture changes when the black hole's mass degrees of freedom are allowed to exist in a coherent quantum superposition, corresponding to a superposition of distinct spacetime geometries. We show that such quantum coherence can mitigate the loss of entanglement between nearby observers, thereby enhancing the performance of quantum communication protocols operating in the vicinity of the black hole.

quant-ph↗

arXiv2026

Classical simulators as quantum error mitigators via circuit cutting

We introduce a circuit cutting-based error mitigation framework, simulated quantum error mitigation (SQEM), in which an auxiliary error-mitigation subcircuit is simulated classically while the main computation is executed on quantum hardware. For the class of circuits considered here, SQEM can be implemented with polynomial overhead by mitigating one qubit at a time and classically recombining the resulting output distributions. This qubit-wise strategy avoids the exponential overhead of cutting all protected qubits simultaneously, while providing a scalable approximation to joint mitigation. We demonstrate the method using Pauli check sandwiching within VQE hardware-efficient ansätze and obtain ground-state energies close to noiseless ansatz simulations, including chemical accuracy for LiH.

quant-ph↗

arXiv2026

A quantum oscillator interacting with a classical oscillator

We study a quantum oscillator interacting with, and back-reacting on, a classical oscillator. This can be done consistently provided the quantum system decoheres, while the backreaction has a stochastic component which causes the classical system to undergo diffusion. Nonetheless, the state of the quantum oscillator can remain pure conditioned on the trajectory of the classical oscillator. We solve the system using the classical-quantum path integral formulation, and compute the free and bridge correlators of the theory, which we use to find the heating rate. In addition, we explicitly compute the conditioned, and unconditional purity of the system. This serves as a toy model for a number of other systems in which one subsystem can be treated as effectively classical, such as a scalar quantum field interacting with another field undergoing decoherence, or a system emitting radiation, one of which is treated classically.

quant-ph↗