TENSOR NETWORKS FOR OPEN QUANTUM SYSTEMS

Is it possible to efficiently simulate a quantum physical system on a classical computer? The computational resources needed to manipulate quantum many-body states typically scale exponentially in the number of their constituents, making the simulation very difficult or outright impossible even at modest sizes. Tensor networks provide a powerful mathematical tool to address this issue: by efficiently representing only a low-entanglement subspace of the full space of states, they mitigate the exponential scaling and enable faster computations. Their intuitive diagrammatic language makes them easy to work with in a broad range of settings, including quantum many-body systems and quantum circuits. This thesis explores the simulation of open quantum systems and noisy quantum circuits with tensor networks. It is divided into two main parts. In the first part, we develop a fermionic generalisation of the Markovian closure method originally proposed for bosonic environments. In particular, we address one of the key bottlenecks in simulating open systems coupled to continuous fermionic baths, namely, the linear growth in computational cost with simulation time in standard chain-mapping approaches. Moreover, this method avoids ad-hoc fitting procedures and relies only on mild assumptions on the structure of the environment. In the second part, we explore the interplay between tensor networks and quantum computing, applying tensor-network techniques to noisy intermediate-scale quantum devices both as classical simulators and as building block for an error-mitigation scheme known as Tensor-network Error Mitigation. We introduce a hybrid quantum-classical algorithm that combines quantum computation on noisy devices with classical tensor-network-based post-processing methods. Within this framework, we study a dual-unitary quantum circuit implementing the time evolution of a kicked Ising model, as a way to benchmark the performance of the hybrid approach.