Studies of properties of bipartite graphs with quantum programming

Abstract

Multi-qubit quantum states corresponding to bipartite graphs $G(U,V,E)$ are examined. These states are constructed by applying $CNOT$ gates to an arbitrary separable multi-qubit quantum state. The entanglement distance of the resulting states is derived analytically for an arbitrary bipartite graph structure. A relationship between entanglement and the vertex degree is established. Additionally, we identify how quantum correlators relate to the number of vertices with odd and even degrees in the sets $U$ and $V$. Based on these results, quantum protocols are proposed for quantifying the number of vertices with odd and even degrees in the sets $U$ and $V$. For a specific case where the bipartite graph is a star graph, we analytically calculate the dependence of entanglement distance on the state parameters. These results are also verified through quantum simulations on the AerSimulator, including noise models. Furthermore, we use quantum calculations to quantify the number of vertices with odd degrees in $U$ and $V$. The results agree with the theoretical predictions.

References in corpus (30)

• Quantum entanglement
• Experimental quantum teleportation
• Multi-party entanglement in graph states
• Quantum Cryptography with Entangled Photons
• Quantum Generative Adversarial Networks for Learning and Loading Random Distributions
• Graph States for Quantum Secret Sharing
• Quantum error-correcting codes associated with graphs
• Chip-to-chip quantum teleportation and multi-photon entanglement in silicon
• Bell Inequalities for Graph States
• 16-qubit IBM universal quantum computer can be fully entangled
• Experimental demonstration of a graph state quantum error-correction code
• Recovering Entanglement by Local Operations
• Entanglement in a 20-Qubit Superconducting Quantum Computer
• Graph States as a Resource for Quantum Metrology
• Demonstration of Entanglement Purification and Swapping Protocol to Design Quantum Repeater in IBM Quantum Computer
• Pairwise thermal entanglement in Ising-XYZ diamond chain structure in an external magnetic field
• Quantum circuits for maximally entangled states
• Entanglement in eight-qubit graph states
• Quantum error correction codes and absolutely maximally entangled states
• Efficient quantum pseudorandomness with simple graph states
• Quantifying geometric measure of entanglement by mean value of spin and spin correlations for pure and mixed states
• Identification of networking quantum teleportation on 14-qubit IBM universal quantum computer
• Entanglement of graph states of spin system with Ising interaction and its quantifying on IBM's quantum computer
• Detecting entanglement by the mean value of spin on a quantum computer
• Geometric measure of entanglement of multi-qubit graph states and its detection on a quantum computer
• Efficient Entanglement Measure for Graph States
• Measuring entanglement of a rank-2 mixed state prepared on a quantum computer
• Correlations and projective measurements in maximally entangled multipartite states
• Geometric properties of evolutionary graph states and their detection on a quantum computer
• Entanglement of multi-qubit states representing directed networks and its detection with quantum computing