Implementing Entangled States on a Quantum Computer

The study of tensor network theory is an important field and promises a wide range of experimental and quantum information theoretical applications. Matrix product state is the most well-known example of tensor network states, which provides an effective and efficient representation of one-dimensional quantum systems. Indeed, it lies at the heart of density matrix renormalization group (DMRG), a most common method for simulation of one-dimensional strongly correlated quantum systems. It has got attention from several areas varying from solid-state systems to quantum computing and quantum simulators. We have considered maximally entangled matrix product states (GHZ and W). Here, we designed the quantum circuits for implementing the matrix product states. In this paper, we simulated the matrix product states in customized IBM (2-qubit, 3-qubit and 4-qubit) quantum systems and determined the probability distribution among the quantum states.