Episode 157 Error mitigation has elevated quantum computing to the scale of hundreds of qubits and tens of layers; however, yet larger scales (deeper circuits) are needed to fully exploit the potential of quantum computing to solve practical problems otherwise intractable. In this talk we will discuss three key results that pave the way for the leap from quantum utility to quantum advantage: (1) we present a thorough derivation of random and systematic errors associated to the most advanced error mitigation strategies, including probabilistic error cancellation (PEC), zero noise extrapolation (ZNE) with probabilistic error amplification, and tensor-network error mitigation (TEM); (2) we prove that TEM (i) has the lowest sampling overhead among all three techniques under realistic noise, (ii) is optimal, in the sense that it saturates the universal lower cost bound for error mitigation, and (iii) is therefore the most promising approach to quantum advantage; (3) we propose a concrete notion of practical quantum advantage in terms of the universality of algorithms, stemming from the commercial need for a problem-independent quantum simulation device. We also establish a connection between error mitigation, relying on additional measurements, and error correction, relying on additional qubits, by demonstrating that TEM with a sufficient bond dimension works similarly to an error correcting code of distance 3. We foresee that the interplay and trade-off between the two resources will be the key to a smooth transition between error mitigation and error correction, and hence between near-term and fault-tolerant quantum computers. Meanwhile, we argue that quantum computing with optimal error mitigation, relying on modest classical computer power for tensor network contraction, has the potential to reach larger scales in accurate simulation than classical methods alone. Sabrina Sabrina Maniscalco is the Professor of Quantum Information, Computing and Logic at the University of Helsinki, Finland. She is the Vice Director of the Finnish Centre of Excellence for Quantum Technologies and serves in the scientific advisory board of several international institutions, such as the Institute for Quantum Optics and Quantum Information (Austria) and the Quantum Technology initiative at CERN. She is CEO and co-founder of Algorithmiq Ltd, a startup focusing on quantum algorithms and software for the Life Sciences. Sabrina obtained her PhD at the University of Palermo (Italy) in 2004. She has held academic research positions around the world, in Sofia (Bulgaria), Durban (South Africa), Turku (Finland) and Edinburgh (UK). She returned to Finland in 2014 to lead the Theoretical Physics Laboratory in Turku. She then moved to the University of Helsinki in November 2020. Sabrina represented Finland’s Quantum National strategy at the White House in May 2022 and is a national figure in quantum for Finland. Sabrina has coordinated several international and interdisciplinary projects and is recognised as one of the leading experts in Quantum Technologies. Guille Guillermo García-Pérez received his PhD in physics from the University of Barcelona in 2018. He then moved to Turku, Finland, to work as a senior researcher in the Turku Centre for Quantum Physics and the Complex Systems Research Group of the University of Turku. In 2020, he co-founded Algorithmiq, where he has also been working as Chief Scientific Officer since then. In 2021 he received a grant from the Academy of Finland to work on emergent geometry from entanglement at the University of Helsinki. Sergei Sergey Filippov holds a PhD in Theoretical Physics from Moscow Institute of Physics and Technology (2012). He did postdoctoral research at Research Center for Quantum Information (Bratislava, 2013) and Russian Quantum Center (Skolkovo, 2014), was a head of Laboratory of Quantum Information Theory and an Associate Professor at MIPT (2014-2022), and worked at Steklov Mathematical Institute RAS (2018-2022). Since 2022 he works as a Senior Researcher at Algorithmiq. With a background in quantum tomography, entanglement dynamics, information capacity of quantum channels, and non-Markovian open quantum systems, his current research is focused on the tensor-network description of quantum dynamical maps and noise mitigation. References: 1) Sergey N. Filippov, Sabrina Maniscalco, Guillermo García-Pérez, “Scalability of quantum error mitigation techniques: from utility to advantage”, arXiv:2403.13542 2) Sergei Filippov, Matea Leahy, Matteo A. C. Rossi, Guillermo García-Pérez, “Scalable tensor-network error mitigation for near-term quantum computing”, arXiv:2307.11740