Simulating of X-states and the two-qubit XYZ Heisenberg system on IBM quantum computer

Abstract

Two qubit density matrices which are of X-shape, are a natural generalization of Bell Diagonal States (BDSs) recently simulated on the IBM quantum device. We generalize the previous results and propose a quantum circuit for simulation of a general two qubit X-state, implement it on the same quantum device, and study its entanglement for several values of the extended parameter space. We also show that their X-shape is approximately robust against noisy quantum gates. To further physically motivate this study, we invoke the two-spin Heisenberg XYZ system and show that for a wide class of initial states, it leads to dynamical density matrices which are X-states. Due to the symmetries of this Hamiltonian, we show that by only two qubits, one can simulate the dynamics of this system on the IBM quantum computer.

Implementation and measurement of quantum entanglement using IBM quantum platforms

“…IBM, for instance, introduced its 127 quantum processor 'Eagle r3' which is used in three backends called 'Ibm-kyoto', 'Ibm-brisbane' and 'Ibm-osaka', allowing the public to test and verify various theoretical protocols. Large number of researches were done successfully resulting valuable insight to the theoretical framework of different topics including, preparing tunable Bell-diagonal states [42], Werner State Generation [43], simulating of X-states [44], Quantum walks [45], Quantim thermodynamics [46], quantum teleportation [47], simulating Ising interaction [48], verification of entropic uncertainty relations [49], nondestructive discrimination of Bell states [50], and comparing quantum computing architectures [51].…”

Trade-off relations of quantum resource theory in Heisenberg models

“…Owing to the various configurations of spin correlation, spin chain models have significant amounts of quantum resources in entanglement and coherence. This has led to their use in quantum computers and quantum networks [11,[33][34][35][36][37][38]. The two-qubit Heisenberg XYZ model is an example of the smallest yet most general spin chain, which has recently motivated the research community to rapidly adopt the Heisenberg XYZ model [39][40][41][42][43][44][45][46][47].…”