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Any quantum system can be closely approximated by a quantum circuit with spatially-localized qubits. We analyze such quantum circuits and present evidence that the local weak values comprise a covariant tensor associated with each individual qubit. Even if the state is massively entangled, these tensors do not evolve or collapse when other qubits pass through distant circuit elements. Furthermore, the local tensors always obey covariant dynamical rules. Weak values are subject to both past and future constraints, so these tensors can only be determined by considering the entire circuit "all-at-once" (as in action principles), a known strategy for resolving Bell’s Theorem. These results lend support to the claim that any quantum system can be assigned a realistic, lower-level description fully compatible with classical spacetime.

As quantum processors scale, robust and scalable tools to characterize gate-level noise become indispensable. Randomized benchmarking (RB) and its many variants have emerged as the go-to protocols in practice: they yield a single number to characterize a gate set, the average gate fidelity, per irreducible subspace. It has been argued that RB can in principle be extended into a full tomographic framework (RB tomography), but large-scale practical implementations, even of partial tomographic information, have long been hindered by the need for sequence inversion, explicit gate interleaving, and the required measurement statistics. In this talk, we report on a scalable implementation of a flexible and efficient variant of RB tomography called gate-set shadows, on a 36-qubit superconducting processor. From a single, efficiently implemented randomized-circuit experiment, we reconstruct the one- and two-qubit marginals of the average noise channel, learn classically correlated quantum noise including cross-talk, and infer a variety of diagnostic information and performance metrics. We decompose the reconstructed channels into error-generator rates that separate coherent, stochastic, and correlated contributions, and find cross-talk that is structured but not confined to the chip's physical topology, escaping several standard pairwise cross-talk metrics. We further introduce a way to test how much of this reconstructed noise is explained by mechanisms already assumed in the literature, such as detuning, over-rotation, and decoherence: fitting the reconstructed rates against a library of such models and quantifying what is left over. First results suggest that cross-talk can resist explanation by standard noise models more than commonly assumed.

Quantum inference usually begins by measuring quantum data and converting it into classical information. In this talk, I will consider a different setting in which the desired output remains quantum, allowing coherence to be preserved throughout the inference process. Examples include quantum purity amplification, approximate purification and cloning of mixed states, and density matrix exponentiation. I will show that coherent protocols can use exponentially fewer input copies than any measurement mediated strategy. For quantum purity amplification of a principal eigenstate with an input of dimension d, coherent processing achieves error ε using O(1/ε) copies, while incoherent protocols require Ω(d/ε) copies. More broadly, these results motivate a theory of coherent quantum inference and establish entanglement breaking limits as a natural connection between coherent and incoherent information processing.