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arXiv:2311.15973 · Physica Scripta

Quantum simulation of entanglement dynamics in a quantum processor

Sebastian Saavedra-Pino, Cristian Inzulza, Pablo Román, F. Albarrán-Arriagada, J. C. Retamal

Published Jul 11, 2024• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1402-4896/ad624a

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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.
We analyze the basic aspects of the quantum information theory, namely the quantum version of the theory that is behind all the classical implementations like computers and communications. We focus on quantum computation, defining its fundamental unit: the qubit, namely a quantum two-level system that will be described in detail in this thesis. We then concentrate on the possible transformations gates that can be applied to qubits, both unitary and non-unitary ones. The challenges in the construction of qubits are impressive: in particular, it is difficult to isolate the system from the environment. This interaction is modeled by non-unitary transformations. The characteristic times connected to these processes are the relaxation time, the time in which a state decays in another state, and the decoherence time, the time in which quantum coherence is lost. These times are fundamental in quantum computing since they quantify how many operations can be performed on qubits and still obtain reliable results. We measure these characteristic times on the IBM quantum processor ’ibmq_16_melbourne’ performing three different experiments: one for the relaxation time and two for the decoherence time, namely Ramsey and Echo experiments. Finally, we implement a quantum algorithm, an algorithm that uses the resources of quantum mechanics, like entanglement. We focus on finding a protocol to define the quantum version of the elementary cellular automata, the quantum elementary cellular automata, and run it on the IBM processor. They are dynamical systems defined on a lattice in which the evolution is defined using simple local update rules. Comparing the physical results with theoretical expectations and noise-affected simulations we show the performance of the IBM processor.
We investigate the entanglement dynamics of two interacting qubits in a common vacuum environment. The inevitable environment interaction leads to entanglement sudden death (ESD) in a two qubit entangled state system. The entanglement dynamics can be modified by the use of local unitary operations (quantum gates), applied on the system during its evolution. We show that these operations not only delays or avoids the ESD but also advances the entanglement revival with high concurrence value depending on the time of operation. We have analytically found out different time windows for switching with different quantum gates so that the ESD can be completely avoided in the subsequent evolution of the system. Our result offers practical applications in the field of quantum information processing where the entanglement is a necessary resource.
We investigate the entanglement dynamics of the bipartite quantum system between two qubits with the dissipative environment. We begin with the standard Markovian master equation in the Lindblad form and the initial state which is prepared in the extended Werner-like state: ρ Φ AB (0). We examine the conditions for entanglement sudden death (ESD) and calculate the corresponding ESD time by the Wootters concurrence. We observe that ESD is determined by the parameters such as the mean occupation number of the environment N , amount of initial entanglement α and the purity r . For N = 0, we get the analytical expressions of both ESD condition and ESD time. For N > 0 we give a theoretical analysis that ESD always occurs, and simulate the concurrence as a function of γ 0 t and one of the parameters N , α and r .
When an initially entangled pair of qubits undergoes local decoherence processes, there are a number of ways in which the original entanglement can spread throughout the multipartite system consisting of the two qubits and their environments. Here, we report theoretical and experimental results regarding the dynamics of the distribution of entanglement in this system. The experiment employs an all optical setup in which the qubits are encoded in the polarization degrees of freedom of two photons, and each local decoherence channel is implemented with an interferometer that couples the polarization to the path of each photon, which acts as an environment. We monitor the dynamics and distribution of entanglement and observe the transition from bipartite to multipartite entanglement and back, and show how these transitions are intimately related to the sudden death and sudden birth of entanglement. The multipartite entanglement is further analyzed in terms of three- and four-partite entanglement contributions, and genuine four-qubit entanglement is observed at some points of the evolution.
We investigate the sudden birth and sudden death of entanglement of two qubits interacting with un-correlated structured reservoirs. The system is initially prepared in two-qubit extended Werner-like state. We work out the dependence of the entanglement dynamics on both non-Markovian environments and the purity of initial state, and show that non-Markovian environments and the purity can control the time of the two-qubit entanglement sudden death and the reservoirs' entanglement sudden birth. Furthermore, under the conditions of different purity and initial entanglement, the revival of qubits' entanglement can manifest before, simultaneously or even after the disentanglement of their corresponding reservoirs.