Speaker
Description
The inadequacy of conventional computers in simulating the behavior of many-body quantum systems, due to their limited computational resources, has led to the development of quantum computers, based upon the intrinsic properties of quantum systems themselves. While an ordinary computer operates on classical bits, a quantum computer is built upon qubits, which are two-level quantum systems that can be in states other than "0" and "1", thanks to superposition. However, building a working quantum computer is really challenging due to quantum noise, which is introduced in the simulation by external manipulations of the qubits.
The promise of quantum computers, together with quantum algorithms, is the achievement of a computational speedup with respect to the best known classical algorithm in solving the same task, regardless of the fact that it is related to quantum mechanics.
In parallel with the development of quantum computers, new methods have also been developed in recent years to enable and improve quantum-inspired simulations on classical computers, among which Tensor Networks (TN) methods that allow to simulate with good approximation large many-body quantum systems on classical computers. The key idea of these methods is to efficiently model a composite quantum state by means of a Tensor Network (TN). TNs enable to efficiently represent quantum states by encoding their relevant information into a series of small tensors, representing the individual components of a multi-partite quantum system. Thus, by arranging and connecting the tensors in a specific way, tensor networks allow to capture information about the entanglement structure of the encoded state.
Due to their ability to efficiently, though approximately, simulate large quantum states on ordinary computers, TN methods have gained ground recently in many fields, including applied mathematics, machine learning, chemistry, condensed matter physics and quantum information theory.
In this talk, I will present an overview of TN quantum-inspired simulation methods, focusing especially on matrix product states (MPS), and discuss some applications of these techniques in implementing quantum algorithms (e.g., quantum Fourier transform) and emulating the dynamics of many-body systems (e.g., waveguide QED).
