System and method for simulating quantum computer using tensor networks and related methods

A computational system, comprising:

• a module that receives a quantum computation to be simulated;
• a module that implements a lattice-free tensor network simulation based on the received quantum computation, wherein the tensor network simulation adapts dynamically to an interaction pattern in the quantum computation;
• an initialization submodule that initializes an initial state in the tensor network simulation;
• a gate submodule that applies a quantum gate on two quantum bits in the tensor network simulation, wherein the application of the quantum gate generates a connection in a network structure and truncates numerical values in the network structure using a mathematical decomposition and an update process such that the number of numerical values is smaller than a numerical parameter D;
• a submodule that computes an entropy measure for all connections in the network structure;
• a submodule that truncates the connections with the lowest entropy measure to a dimensional parameter, such that the number of bond indices in the network structure is always smaller than a numerical parameter K;
• and
• a module that computes expectation values of observables at the end of the simulation of the quantum computation, wherein the computation of the expectation values involves quantum bits determined in a submodule determining the quantum bits and uses an approximation method.