Effect of correlated errors on quantum memory
Phys. Rev. A 112, 022422 – Published 15 August, 2025
DOI: https://doi.org/10.1103/hg2r-py13
Abstract
Recent results on constant overhead LDPC code-based fault-tolerance against i.i.d. errors naturally lead to the question of fault-tolerance against errors with long-range correlations. Ideally, any correlation can be captured by a joint (system and bath) Hamiltonian. However, an arbitrary joint Hamiltonian is often intractable, and hence, the joint Hamiltonian model with pairwise terms was introduced and developed in a seminal series of papers by Terhal and Burkard [Phys. Rev. A 71, 012336 (2005)], Aliferis, Gottesman, and Preskill [Quantum Inf. Comput. 6, 97 (2005)], and Aharonov, Kitaev, and Preskill [Phys. Rev. Lett. 96, 050504 (2006)]. However, the analysis of the new constant overhead codes in that error model appears to be quite challenging. In this paper, to model correlated errors in quantum memory, we introduce a correlation model which is a generalization of the well-known hidden random fields. This proposed model, which includes stationary and ergodic (and possibly non-Markov) error distributions, is shown to capture correlations not captured by the joint Hamiltonian model with pairwise terms. On the other hand, building on non-i.i.d. measure concentration, we show that for a broad class of (possibly) non-Markov and nonstationary error distributions, quantum Tanner codes ensure an exponential retention time (in the number of physical qubits), when the error rate is below a threshold. An implication of this work is that the rate of decay of the correlation with distance does not necessarily differentiate between good and bad correlations.
