Noise on quantum devices is much more complex than it is commonly given credit. Far from usual models of decoherence, nearly all quantum devices are plagued both by a continuum of environments and temporal instabilities. These induce noisy quantum and classical correlations at the level of the circuit. The relevant spatiotemporal effects are difficult enough to understand, let alone combat. There is presently a lack of either scalable or complete methods to address the phenomena responsible for scrambling and loss of quantum information. In this talk I will discuss recent work to remedy this problem. We establish a theoretical framework that uniformly incorporates and classifies all non-Markovian phenomena. Our framework is universal, minimal on assumptions, and written entirely in terms of experimentally accessible circuit-level quantities. We formulate an efficient reconstruction using tensor network learning, allowing additionally for easy modularisation and simplification. This is showcased with both numerical studies and experiments on IBM Quantum devices, estimating a comprehensive set of spacetime correlations. As well as forming a detailed description of the noise, the resulting characterisation can be straightforwardly fed into counteracting its effects in each of the contexts of error suppression, mitigation, and correction. This talk will broadly cover the work in arXiv:2312.08454 and as well as some future directions. 

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(Please note the time change for this seminar.)