Quantum Computer Simulation via Tensor Networks

In recent years lots of efforts have been spent in the realization of quantum computers able to reproduce quantum circuits involving increasing number of qubits with the greatest possible accuracy. The final goal is to reach the limit, the so-called quantum supremacy, where a classical computer is no longer able to reproduce the results of a quantum machine. Indeed, simulating quantum many-body systems is very computationally demanding due to the exponential scaling of the Hilbert space with the number of qubits. In order to perform a classical simulation of a quantum circuit acting on a qubits register, one must choose between two possible approaches: the first is an exact description of the qubits’ state, possible up to a maximum reachable number of qubits. The second, instead, consists of representing the state approximately. But, even quantum processors are not able to reproduce exactly a given quantum circuit: their coupling with the environment, which is minimized but not removed by the experimental implementation, induces errors through quantum channels like decoherence or bit-flip. Therefore an approximate representation of the qubits' state is acceptable as long as its errors are comparable with the experimental ones. The tensor network methods allow one to approximate a quantum state by efficiently compressing its information, introducing a controllable error. In this thesis, these methods will be used to simulate a quantum computer on a large computational cluster, to push as far as possible the classical simulation framework