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arXiv:2101.05089 · Condensed Matter Physics

Preparation and study of the entanglement of the Schrödinger cat state on the ibmq-melbourne quantum computer

A.R. Kuzmak, V.M. Tkachuk

Published Dec 1, 2020• 10 citations
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Abstract

We study the entanglement between a certain qubit and the remaining system in the Schrödinger cat state prepared on the ibmq-melbourne quantum computer. The protocol, which we use for this purpose, is based on the determination of the mean value of spin corresponding to a certain qubit. We explore the dependence of the entanglement on a parameter of the Schrödinger cat state which consists of different numbers of qubits. In addition, we explore the entanglement of each qubit with the remaining system in the maximum entangled Schrödinger cat state.

DOI
10.5488/cmp.23.43001

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We study the entanglement between a certain qubit and the remaining system in the Schrödinger cat state prepared on the ibmq-melbourne quantum computer. The protocol, which we use for this purpose, is based on the determination of the mean value of spin corresponding to a certain qubit. We explore the dependence of the entanglement on a parameter of the Schrödinger cat state which consists of different numbers of qubits. In addition, we explore the entanglement of each qubit with the remaining system in the maximum entangled Schrödinger cat state.
Abstract We consider simulation of the high spins on a quantum computer. The protocols which allow one to measure the mean value of spin and correlations between spins are proposed. As a result, we determine the time dependence of the mean values of spin-1 in the magnetic field prepared on the ibmq-santiago quantum computer. In addition, we study the evolution of two interacting spins on the ibmq-lima quantum computer. The time-dependencies of the mean value of spin-1 and correlations between these spins are detected. Finally, we generalize these protocols for the spins of arbitrary values.
The geometric measure of entanglement of variational quantum states is studied on the basis of its relation with the mean value of spin. We examine n-qubit quantum states prepared by a variational circuit with a layer formed by the rotational gates and two-qubit controlled phase gates. The variational circuit is a generalization of that used for preparing quantum Generative Adversarial Network states. The entanglement of a qubit with other qubits in the variational quantum states is determined by the angles of rotational gates that act on the qubit and qubits entangled with it by controlled phase gates and also their parameters. In the case of one layer variational circuit, the states can be associated with graphs with vertices representing qubits and edges corresponding to two-qubit gates. The geometric measure of entanglement of a qubit with other qubits in the quantum graph state depends on the properties of the vertex that represents it in the graph, namely it depends on the vertex degree. The dependence of the geometric measure of entanglement of variational quantum states on their parameters is quantified on IBM's quantum computer.
Entanglement is the quintessential quantum phenomenon and a key enabler of quantum algorithms. The ability to faithfully entangle many distinct particles is often used as a benchmark for the quality of hardware and control in a quantum computer. Greenberger-Horne-Zeilinger (GHZ) states, also known as Schrödinger cat states, are useful for this task. They are easy to verify, but difficult to prepare due to their high sensitivity to noise. In this Letter we report on the largest GHZ state prepared to date consisting of 120 superconducting qubits. We do this via a combination of optimized compilation, low-overhead error detection and temporary uncomputation. We use an automated compiler to maximize error-detection in state preparation circuits subject to arbitrary qubit connectivity constraints and variations in error rates. We measure a GHZ fidelity of 0.56(3) with a post-selection rate of 28%. We certify the fidelity of our GHZ states using multiple methods and show that they are all equivalent, albeit with different practical considerations.
Macroscopic entanglement, or say the Schrödinger's Cat state has attracted much attention for a long time. Recently, the first theoretical work of Fröwis and Dür ( Phys. Rev. Lett. , 106 (2011) 110402) and the first experiment of Lu et al. ( Nat. Photon. , 8 (2014) 364) both showed that, a new type of Schrödinger's Cat state, the logic-qubit entanglement (concatenated Greenberger-Horne-Zeilinger (C-GHZ) state) is immune and robust to the noise, and is possible to be applied in future large-scale quantum networks. In this paper, we describe a protocol of entanglement analysis for this kind of Schrödinger's Cat state. Both the Bell-state type of logic-qubit entanglement and multipartite C-GHZ state can be completely distinguished. Based on the entanglement analysis, an arbitrary unknown macroscopic Schrödinger's Cat superposed state can be teleportated and we can also perform the macroscopic entanglement swapping. Our protocol shows that it is possible to realize long-distance quantum communication and large-scale quantum network based on logic-qubit entanglement.
Quantum entanglement gives rise to a range of non-classical effects, which are extensively exploited in quantum computing and quantum communication. Therefore, detection and quantification of entanglement as well as preparation of highly entangled quantum states remain the fundamental objectives in these fields. Much attention has been devoted to the studies of graph states, which play a role of a central resource in quantum error correction, quantum cryptography and practical quantum metrology in the presence of noise.We examine multi-qubit graph states generated by the action of controlled phase shift operators on a separable quantum state of a system, in which all the qubits are in arbitrary identical states. Analytical expression is obtained for the geometric measure of entanglement of a qubit with other qubits in graph states represented by arbitrary graphs. We conclude that this quantity depends on the degree of the vertex corresponding to the qubit, the absolute values of the parameter of the phase shift gate and the parameter of the initial state the gate is acting on. Moreover, the geometric measure of entanglement of certain types of graph states is quantified on the IBM’s quantum computer ibmq_athens based on the measurements of the mean spin. Namely, we consider states associated with the native connectivity of ibmq_athens, the claw and the complete graphs. Appropriate protocols are proposed to prepare these states on the quantum computer. The results of quantum computations verify our theoretical findings [1].