Memory effects in open quantum dynamics are often incorporated in the equation of motion through a superoperator known as the memory kernel, which encodes how past states affect future dynamics. However, the usual prescription for determining the memory kernel requires information about the underlying system-environment dynamics. Here, by deriving the transfer tensor method from first principles, we show how a memory kernel master equation, for any quantum process, can be entirely expressed in terms of a family of completely positive dynamical maps. These can be reconstructed through quantum process tomography on the system alone, either experimentally or numerically, and the resulting equation of motion is equivalent to a generalised Nakajima-Zwanzig equation. For experimental settings, we give a full prescription for the reconstruction procedure, rendering the memory kernel operational. When simulation of an open system is the goal, we show how our procedure yields a considerable advantage for numerically calculating dynamics, even when the system is arbitrarily periodically (or transiently) driven or initially correlated with its environment. Namely, we show that the long time dynamics can be efficiently obtained from a set of reconstructed maps over a much shorter time.
 F. A. Pollock, C. Rodríguez-Rosario, T. Frauenheim, M. Paternostro, and K. Modi, Phys. Rev. Lett. 120, 040405 (2018b).
 H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, 2002).
 A. W. Chin, S. F. Huelga, and M. B. Plenio, in Semiconductors and Semimetals, Vol. 85, edited by U. Würfel, M. Thorwart, and E. R. Weber (Elsevier, 2011) pp. 115 – 143.
 J. Cerrillo and J. Cao, Phys. Rev. Lett. 112, 110401 (2014).
 P. Nalbach, A. Ishizaki, G. R. Fleming, and M. Thorwart, New J. Phys. 13, 063040 (2011).
 G. Lindblad, Commun. Math. Phys. 48, 119 (1976).
 M. Ringbauer, C. J. Wood, K. Modi, A. Gilchrist, A. G. White, and A. Fedrizzi, Phys. Rev. Lett. 114, 090402 (2015).
 L. M. Norris, G. A. Paz-Silva, and L. Viola, Phys. Rev. Lett. 116, 150503 (2016).
 J. Jeske, J. H. Cole, C. Müller, M. Marthaler, and G. Schön, New J. Phys. 14, 023013 (2012).
 B. Bellomo, A. De Pasquale, G. Gualdi, and U. Marzolino, J. Phys. A 43, 395303 (2010b).
 R. Rosenbach, J. Cerrillo, S. F. Huelga, J. Cao, and M. B. Plenio, New J. Phys. 18, 023035 (2016).
 H.-P. Breuer and B. Vacchini, Phys. Rev. Lett. 101, 140402 (2008).
 B. Vacchini, Phys. Rev. Lett. 117, 230401 (2016).
 D. Tamascelli, A. Smirne, S. F. Huelga, and M. B. Plenio, Phys. Rev. Lett. 120, 030402 (2018).
 P. Facchi and S. Pascazio, J. Phys. A 41, 493001 (2008).
 T. M. Stace, A. C. Doherty, and D. J. Reilly, Phys. Rev. Lett. 111, 180602 (2013).
 R. Nandkishore and D. A. Huse, Annu. Rev. Condens. Matter Phys. 6, 15 (2015).
 V. Prepeliţă, M. Doroftei, and T. Vasilache, Balkan J. Geom. Appl. 3, 111 (1998).
 S. Alipour, A. T. Rezakhani, A. P. Babu, K. Mølmer, M. Möttönen, and T. Ala-Nissila, "Correlation-Picture Approach to Open-Quantum-System Dynamics", Physical Review X 10 4, 041024 (2020).
 Simon Milz and Kavan Modi, "Quantum Stochastic Processes and Quantum non-Markovian Phenomena", PRX Quantum 2 3, 030201 (2021).
 Mathias R. Jørgensen and Felix A. Pollock, "Exploiting the Causal Tensor Network Structure of Quantum Processes to Efficiently Simulate Non-Markovian Path Integrals", Physical Review Letters 123 24, 240602 (2019).
 Leonardo Banchi, Edward Grant, Andrea Rocchetto, and Simone Severini, "Modelling non-markovian quantum processes with recurrent neural networks", arXiv:1808.01374, New Journal of Physics 20 12, 123030 (2018).
 Yu-Qin Chen, Kai-Li Ma, Yi-Cong Zheng, Jonathan Allcock, Shengyu Zhang, and Chang-Yu Hsieh, "Non-Markovian Noise Characterization with the Transfer Tensor Method", Physical Review Applied 13 3, 034045 (2020).
 Philip Taranto, Felix A. Pollock, Simon Milz, Marco Tomamichel, and Kavan Modi, "Quantum Markov Order", Physical Review Letters 122 14, 140401 (2019).
 Kavan Modi, "George Sudarshan and Quantum Dynamics", Open Systems & Information Dynamics 26 03, 1950013 (2019).
 Rolando Ramirez Camasca and Gabriel T. Landi, "Memory kernel and divisibility of Gaussian collisional models", Physical Review A 103 2, 022202 (2021).
 Philip Taranto, Simon Milz, Felix A. Pollock, and Kavan Modi, "Structure of quantum stochastic processes with finite Markov order", Physical Review A 99 4, 042108 (2019).
 Simon Milz, M. S. Kim, Felix A. Pollock, and Kavan Modi, "Completely Positive Divisibility Does Not Mean Markovianity", Physical Review Letters 123 4, 040401 (2019).
 Francesco Campaioli, Felix A. Pollock, and Kavan Modi, "Tight, robust, and feasible quantum speed limits for open dynamics", Quantum 3, 168 (2019).
 Shlok Nahar and Sai Vinjanampathy, "Preparations and weak-field phase control can witness initial correlations", Physical Review A 100 6, 062120 (2019).
 Pedro Figueroa–Romero, Felix A. Pollock, and Kavan Modi, "Markovianization with approximate unitary designs", Communications Physics 4 1, 127 (2021).
 Michael te Vrugt and Raphael Wittkowski, "Mori-Zwanzig projection operator formalism for far-from-equilibrium systems with time-dependent Hamiltonians", Physical Review E 99 6, 062118 (2019).
 Pedro Figueroa-Romero, Kavan Modi, and Felix A. Pollock, "Almost Markovian processes from closed dynamics", Quantum 3, 136 (2019).
 I. A. Luchnikov, S. V. Vintskevich, D. A. Grigoriev, and S. N. Filippov, "Machine Learning Non-Markovian Quantum Dynamics", Physical Review Letters 124 14, 140502 (2020).
 Mathias R. Jørgensen and Felix A. Pollock, "Discrete memory kernel for multitime correlations in non-Markovian quantum processes", Physical Review A 102 5, 052206 (2020).
 Philip Taranto, "Memory effects in quantum processes", International Journal of Quantum Information 18 02, 1941002 (2020).
 Chu Guo, Kavan Modi, and Dario Poletti, "Tensor-network-based machine learning of non-Markovian quantum processes", Physical Review A 102 6, 062414 (2020).
 Graeme D. Berk, Andrew J. P. Garner, Benjamin Yadin, Kavan Modi, and Felix A. Pollock, "Resource theories of multi-time processes: A window into quantum non-Markovianity", Quantum 5, 435 (2021).
 Felix A. Pollock, César Rodríguez-Rosario, Thomas Frauenheim, Mauro Paternostro, and Kavan Modi, "Non-Markovian quantum processes: Complete framework and efficient characterization", arXiv:1512.00589, Physical Review A 97 1, 012127 (2018).
 Simon Milz, Felix A. Pollock, and Kavan Modi, "An Introduction to Operational Quantum Dynamics", Open Systems and Information Dynamics 24 4, 1740016 (2017).
 Maximilian Buser, Javier Cerrillo, Gernot Schaller, and Jianshu Cao, "Initial system-environment correlations via the transfer-tensor method", Physical Review A 96 6, 062122 (2017).
 Gregory A. L. White, Felix A. Pollock, Lloyd C. L. Hollenberg, Kavan Modi, and Charles D. Hill, "Non-Markovian Quantum Process Tomography", arXiv:2106.11722.
 Shlok Nahar and Sai Vinjanampathy, "Preparations and Weak Quantum Control can Witness non-Markovianity", arXiv:1803.08443.
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