Spatial and temporal correlations in quantum noise challenge the local Markovian models commonly used in quantum information processing. We develop a unified operational framework for quantifying temporal, spatial, and total spatiotemporal correlations in general quantum processes. Using process tensors, we define these quantities through optimal distinguishability from Markovian, spatially local, and fully uncorrelated processes. Optimization over admissible probing combs ensures monotonicity under every superprocess that preserves the corresponding free set, while Choi-state functionals and restricted probes provide accessible lower bounds. We establish hierarchy and interpolation relations among the correlation measures and derive dimension-dependent upper bounds on temporal correlations transmitted by quantum memories, with tighter bounds for classical memory, together with universal ceilings imposed by the system dimension. These bounds turn certified lower estimates into witnesses of minimum memory dimension, nonclassicality under a memory-dimension constraint, and inconsistencies in the assumed process model. We illustrate the results with effective superconducting-qubit models featuring \(ZZ\) and \(XY\) interactions, exhibiting saturation of classical-memory, quantum-memory, and system-dimension ceilings. These results pave the way toward practical approaches to characterizing and addressing spatiotemporally correlated errors in quantum devices.
Spatial and temporal correlations in quantum noise challenge the local Markovian models commonly used in quantum information processing. We develop a unified operational framework for quantifying temporal, spatial, and total spatiotemporal correlations in general quantum processes. Using process tensors, we define these quantities through optimal distinguishability from Markovian, spatially local, and fully uncorrelated processes. Optimization over admissible probing combs ensures monotonicity under every superprocess that preserves the corresponding free set, while Choi-state functionals and restricted probes provide accessible lower bounds. We establish hierarchy and interpolation relations among the correlation measures and derive dimension-dependent upper bounds on temporal correlations transmitted by quantum memories, with tighter bounds for classical memory, together with universal ceilings imposed by the system dimension. These bounds turn certified lower estimates into witnesses of minimum memory dimension, nonclassicality under a memory-dimension constraint, and inconsistencies in the assumed process model. We illustrate the results with effective superconducting-qubit models featuring (ZZ) and (XY) interactions, exhibiting saturation of classical-memory, quantum-memory, and system-dimension ceilings. These results pave the way toward practical approaches to characterizing and addressing spatiotemporally correlated errors in quantum devices.
In the dynamics of open quantum systems, information may propagate in time through either the system or the environment, giving rise to Markovian and non-Markovian temporal correlations, respectively. However, despite their notable coexistence in most physical situations, it is not yet clear how these two quantities may limit the existence of one another. Here, we address this issue by deriving several inequalities relating the temporal correlations of general multitime quantum processes. The dynamics are described by process tensors, and the correlations are quantified by the mutual information between subsystems of their Choi states. First, we prove a set of upper bounds to the non-Markovianity of a process given the degree of Markovianity in each of its steps. This immediately implies a nontrivial maximum value for the non-Markovianity of any process, independent of its Markovianity. Finally, we determine how the non-Markovianity limits the amount of total temporal correlations that could be present in a given process. These results show that, although any multitime process must pay a price in total correlations to have a given amount of non-Markovianity, this price vanishes exponentially with the number of steps of the process, while the maximum non-Markovianity grows only linearly. This implies that even a highly non-Markovian process might be arbitrarily close to having the maximum amount of total correlations if it has a sufficiently large number of steps.
Correlated noise is a critical failure mode in quantum error correction (QEC), yet a gap remains between the stochastic Pauli models used for scalable QEC analyses and the microscopic, non-Markovian descriptions of noise in physical devices. We bridge this gap by introducing Spatiotemporal Pauli Processes (SPPs): the natural multi-time generalization of Pauli channels, joint probability distributions over Pauli faults across space and time, obtained exactly from any noise process, however non-Markovian, under standard Pauli-frame randomization. SPPs thereby provide a single language in which correlated noise can be recast, compared, and extended, compatible with both microscopic open systems modeling and the stabilizer workflow of QEC design and analysis. Our central result is constructive: the multi-time Pauli twirl acts by local contractions on a process tensor network, yielding an explicit classical tensor network whose virtual bonds encode memory, bounded by the environment's Liouville-space dimension. Transfer operator diagnostics link memory spectra to correlation decay, and hidden Markov representations enable efficient sampling of correlated Pauli fault trajectories, mapping microscopically derived noise directly into circuit-level QEC simulation. We demonstrate this with surface code memory and stability benchmarks up to distance 19. A temporal "storm" model with tunable correlation time shows that memory alone, at strictly fixed marginal error rates, systematically erodes the exponential error suppression expected from code distance. A genuinely spatiotemporal quantum cellular automaton bath maps exactly, under system twirling, to a nonlinear probabilistic cellular automaton; tuning its coherent interactions drives the noise into a pseudo-critical regime with critical slowing down and macroscopic error avalanches that reverse surface code distance scaling.
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 by both 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. Here, we make deep strides to remedy this problem. We establish a theoretical framework that uniformly incorporates and classifies all non-Markovian phenomena. Our framework is universal, assumes no parameters values, and is written entirely in terms of experimentally accessible circuit-level quantities. We formulate an efficient reconstruction using tensor network learning, allowing also for easy modularization and simplification based on the expected physics of the system. This is then demonstrated through both extensive numerical studies and implementations on IBM Quantum devices, estimating a comprehensive set of spacetime correlations. Finally, we conclude our analysis with applications thereof to the efficacy of control techniques to counteract these effects—including noise-aware circuit compilation and optimized dynamical decoupling. We find significant improvements are possible in the diamond norm and average gate fidelity of arbitrary SU(4) operations, as well as related decoupling improvements in contrast to off-the-shelf schemes.
We develop a framework for characterizing quantum temporal correlations in a general temporal scenario, in which an initial quantum state is measured, sent through a quantum channel, and finally measured again. This framework does not make any assumptions on the system nor on the measurements, namely, it is device independent. It is versatile enough, however, to allow for the addition of further constraints in a semi-device-independent setting. Our framework serves as a natural tool for quantum certification in a temporal scenario when the quantum devices involved are uncharacterized or partially characterized. It can hence also be used for characterizing quantum temporal correlations when one assumes an additional constraint of no-signalling in time, there are upper bounds on the involved systems' dimensions, rank constraints-for which we prove genuine quantum separations over local hidden variable models-or further linear constraints. We present a number of applications, including bounding the maximal violation of temporal Bell inequalities, quantifying temporal steerability, and bounding the maximum successful probability in quantum randomness access codes.
Understanding temporal processes and their correlations in time is of paramount importance for the development of near-term technologies that operate under realistic conditions. Capturing the complete multi-time statistics that define a stochastic process lies at the heart of any proper treatment of memory effects. This is well understood in classical theory, where a hierarchy of joint probability distributions completely characterizes the process at hand. However, attempting to generalize this notion to quantum mechanics is problematic: observing realizations of a quantum process necessarily disturbs the state of the system, breaking an implicit, and crucial, assumption in the classical setting. This issue can be overcome by separating the experimental interventions from the underlying process, enabling an unambiguous description of the process itself and accounting for all possible multi-time correlations for any choice of interrogating instruments. In this paper, using a novel framework for the characterization of quantum stochastic processes, we first solve the long standing question of unambiguously describing the memory length of a quantum processes. This is achieved by constructing a quantum Markov order condition, which naturally generalizes its classical counterpart for the quantification of finite-length memory effects. As measurements are inherently invasive in quantum mechanics, one has no choice but to define Markov order with respect to the interrogating instruments that are used to probe the process at hand: different memory effects are exhibited depending on how one addresses the system, in contrast to the standard classical setting. We then fully characterize the structural constraints imposed on quantum processes with finite Markov order, shedding light on a variety of memory effects that can arise through various examples. Finally, we introduce an instrument-specific notion of memory strength that allows for a meaningful quantification of the temporal correlations between the history and the future of a process for a given choice of experimental intervention. These findings are directly relevant to both characterizing and exploiting memory effects that persist for a finite duration. In particular, immediate applications range from developing efficient compression and recovery schemes for the description of quantum processes with memory to designing coherent control protocols that efficiently perform information-theoretic tasks, amongst a plethora of others.
Abstract Quantum memory—the capacity to faithfully preserve quantum coherence and correlations—is essential for quantum-enhanced technology. There is thus a pressing need for operationally meaningful means to benchmark candidate memories across diverse physical platforms. Here we introduce a universal benchmark distinguished by its relevance across multiple key operational settings, exactly quantifying (1) the memory’s robustness to noise, (2) the number of noiseless qubits needed for its synthesis, (3) its potential to speed up statistical sampling tasks, and (4) performance advantage in non-local games beyond classical limits. The measure is analytically computable for low-dimensional systems and can be efficiently bounded in the experiment without tomography. We thus illustrate quantum memory as a meaningful resource, with our benchmark reflecting both its cost of creation and what it can accomplish. We demonstrate the benchmark on the five-qubit IBM Q hardware, and apply it to witness the efficacy of error-suppression techniques and quantify non-Markovian noise. We thus present an experimentally accessible, practically meaningful, and universally relevant quantifier of a memory’s capability to preserve quantum advantage.