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arXiv:2105.14581 · Physica Scripta

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

Fereshte Shahbeigi, Mahsa Karimi, Vahid Karimipour

Published Jan 10, 2022• 8 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1402-4896/ac49b0

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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.
We design a quantum circuit in IBM quantum computer that mimics the dynamics of single photon in a coupled cavity system. By suitably choosing the gate parameters in the quantum circuit, we could transfer an unknown qubit state between the qubits. The condition for perfect state transfer is obtained by solving the unitary time dynamics governed by the Hamiltonian of the coupled cavity system. We then demonstrate the dynamics of entanglement between the two-qubits and show violation of Bell's inequality in IBM quantum computer.
Abstract We implement a five-qubit protocol in IBM quantum processors to study entanglement dynamics in a two qubit system in the presence of a simulated environment. Specifically, two qubits represent the main system, while another two qubits serve as the environment. Additionally, we employ an auxiliary qubit to estimate the quantum entanglement. Specifically, we observe the sudden death and sudden birth of entanglement for different inital conditions that were simultaneously implemented on the IBM 127-qubit quantum processor ibm _brisbane. We obtain the quantum entanglement evolution of the main system qubits and the environment qubits averaging over N = 10 independent experiments in the same quantum device. Our experimental data shows the entanglement and disentanglement signatures in system and enviroment qubits, where the noisy nature of current quantum processors produce a shift on times signaling sudden death or sudden birth of entanglement. This work takes relevance showing the usefulness of current noisy quantum devices to test fundamental concepts in quantum information.
Simulating quantum circuits with classical computers requires resources growing exponentially in terms of system size.Real quantum computer with noise, however, may be simulated polynomially with various methods considering different noise models.In this work, we simulate random quantum circuits in one dimension with matrix product density operators (MPDOs), for different noise models such as dephasing, depolarizing, and amplitude damping.We show that the method based on matrix product states (MPSs) fails to approximate the noisy output quantum states for any of the noise models considered, while the MPDO method approximates them well.Compared with the method of matrix product operators (MPOs), the MPDO method reflects a clear physical picture of noise (with inner indices taking care of the noise simulation) and quantum entanglement (with bond indices taking care of two-qubit gate simulation).Consequently, in case of weak system noise, the resource cost of the MPDO will be significantly less than that of the MPO due to a relatively small inner dimension needed for the simulation.In case of strong system noise, a relatively small bond dimension may be sufficient to simulate the noisy circuits, indicating a regime that the noise is large enough for an "easy" classical simulation, which is further supported by a comparison with the experimental results on an IBM cloud device.Moreover, we propose a more effective tensor updates scheme with optimal truncations for both the inner and the bond dimensions, performed after each layer of the circuit, which enjoys a canonical form of the MPDO for improving simulation accuracy.With truncated inner dimension to a maximum value κ and bond dimension to a maximum value χ , the cost of our simulation scales as ∼NDκ 3 χ 3 , for an N-qubit circuit with depth D.
Abstract We simulate the time-dependent dynamics of a three-site spin chain described by the Heisenberg XXX Hamiltonian. The quantum circuit representing the time-dependent wave function is constructed using the Suzuki-Trotter approximation, and is executed on the quantum computer ibm_kawasaki. At each time step, the density matrix of the three-qubit state is reconstructed by state tomography. By applying four different mitigation methods, Clifford data regression, Pauli twirling, density matrix purification, and density matrix orthogonalization, we demonstrate that accurate time-dependent populations and density matrices can be calculated on noisy superconducting-qubit type quantum computers.
In loop quantum gravity approach to Planck scale physics, quantum geometry is represented by superposition of the so-called spin network states. In the recent literature, a class of spin networks promising from the perspective of quantum simulations of quantum gravitational systems has been studied. In this case, the spin network states are represented by graphs with four-valent nodes, and two dimensional intertwiner Hilbert spaces (qubits of space) attached to them. In this article, construction of quantum circuits for a general intertwiner qubit is presented. The obtained circuits are simulated on 5-qubit (Yorktown) and 15-qubit (Melbourne) IBM superconducting quantum computers, giving satisfactory fidelities. The circuits provide building blocks for quantum simulations of complex spin networks in the future. Furthermore, a class of maximally entangled states of spin networks is introduced. As an example of application, attempts to determine transition amplitudes for a monopole and a dipole spin network with the use of superconducting quantum processor are made.