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Simulating single-spin dynamics on an IBM five-qubit chip: An approach for undergraduate

Hércules S. Santana, Francisco D.S. Gomes, Émerson M. Alves, Alan C. Santos

Published Jun 10, 2019• 0 citations
OpenAlex

Abstract

In this paper we show how the IBM superconducting chips can be a powerful tool for teaching foundations of quantum mechanics for undergraduate students (for graduates as well, in some cases). To this end, we briefly discuss about the main elements of the IBM Quantum Experience platform necessary to understand this paper, i.e., how to implement operations and single-qubit measurements. As the application, we experimentally study the dynamics of single spin systems interacting with static and time-dependent magnetic fields. First, we study the resonant behavior of a single spin coupled to a time-dependent rotating magnetic field. To end, we study the Larmor precession phenomenon. In both cases we show theoretical and real experimental implementation. This article could be useful in introductory courses like quantum mechanics and nuclear magnetic resonance foundations, for example.

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In this paper we show how the IBM superconducting chips can be a powerful tool for teaching foundations of quantum mechanics for undergraduate students (for graduates as well, in some cases). To this end, we briefly discuss about the main elements of the IBM Quantum Experience platform necessary to understand this paper, i.e., how to implement operations and single-qubit measurements. As the application, we experimentally study the dynamics of single spin systems interacting with static and time-dependent magnetic fields. First, we study the resonant behavior of a single spin coupled to a time-dependent rotating magnetic field. To end, we study the Larmor precession phenomenon. In both cases we show theoretical and real experimental implementation. This article could be useful in introductory courses like quantum mechanics and nuclear magnetic resonance foundations, for example.
Abstract In this paper we show how the IBM superconducting chips can be a powerful tool for teaching foundations of quantum mechanics for undergraduate students (for graduates as well, in some cases). To this end, we briefly discuss about the main elements of the IBM Quantum Experience platform necessary to understand this paper, i.e., how to implement operations and single-qubit measurements. We experimentally study the dynamics of single spin systems interacting with static and time-dependent magnetic fields. First, we study the resonant behavior of a single spin coupled to a time-dependent rotating magnetic field. To end, we study the Larmor precession phenomenon. In both cases we show the theoretical and real experimental implementation. This article could be useful in introductory courses on quantum mechanics and nuclear magnetic resonance foundations, for example.
In this paper we show how the IBM superconducting chips can be a powerful tool for teaching foundations of quantum mechanics for undergraduate students (for graduates as well, in some cases). To this end, we briefly discuss about the main elements of the IBM Quantum Experience platform necessary to understand this paper, i.e., how to implement operations and single-qubit measurements. We experimentally study the dynamics of single spin systems interacting with static and time-dependent magnetic fields. First, we study the resonant behavior of a single spin coupled to a time-dependent rotating magnetic field. To end, we study the Larmor precession phenomenon. In both cases we show the theoretical and real experimental implementation. This article could be useful in introductory courses on quantum mechanics and nuclear magnetic resonance foundations, for example.
As superconducting circuits emerge as a leading platform for scalable quantum information processing, building comprehensive bridges from the foundational principles of macroscopic quantum phenomena to the architecture of modern quantum devices is increasingly essential for introducing new researchers to the field. This tutorial provides a self-contained, pedagogical introduction to superconducting quantum circuits at the undergraduate level. Beginning with an overview of superconductivity and the Josephson effect, the tutorial systematically develops the quantization of microwave circuits into the framework of circuit quantum electrodynamics (cQED). The transmon qubit is then introduced as a state-of-the-art application, with a detailed derivation of its Hamiltonian and its interaction with control and readout circuitry. The theoretical formalism is consolidated through a numerical simulation of vacuum Rabi oscillations in a driven transmon-resonator system, a canonical experiment that demonstrates the coherent energy exchange characteristic of the strong coupling regime. This work serves as a foundational guide and first point of contact, equipping students and researchers with the conceptual and mathematical tools necessary to understand and engineer superconducting quantum hardware.
With the rapid progress of quantum information these recent years, it becomes more and more relevant to dedicate efforts in introducing this research topic to undergraduate students. However, as if in various fields of physics the theoretical learning is closely accompanied with experimental illustrations, such a teaching method can be expensive to organise for quantum information. We propose one way to circumvent these difficulties by using the recently made available 5-qubit quantum processor of IBM, in order to illustrate quantum information tasks, by actually implementing them on the superconducting chip through the web interface of the IBM Quantum Experience. We focus on the realization of a quantum teleportation protocol on this device, analyze the results and discuss the issues encountered, providing a complete analysis of this software as a pedagogical tool.
IBM quantum computers are used to simulate the dynamics of small systems of interacting quantum spins. For time-independent systems with fewer than three spins, we compute the exact time evolution at arbitrary times and measure spin expectation values and energy. It is demonstrated that even in such small systems, one can observe the connection between conservation laws and symmetries in the model. Larger systems require approximating the time-evolution operator, and we investigate the case of N=3 spins explicitly. While it is shown to be unfeasible to use such devices to probe such larger systems without more advanced algorithms or reliable error correction, we demonstrate that the quantum circuit simulator is an easy-to-use method for studying spin dynamics in systems with N∼O(10) spins. The computations presented provide an interesting experimental component to the standard treatment of quantum spin in an undergraduate quantum mechanics course.
We present the results of an analytical study and numerical simulation of the dynamics of a superconducting three-Josephson-junction (3JJ) flux qubit magnetically coupled with rapid single-flux quantum (RSFQ) logic circuit, which demonstrate the fundamental possibility of implementing the simplest logic operations at picosecond times, as well as rapid non-destructive readout. It is shown that when solving optimization problems, the qubit dynamics can be conveniently interpreted as a precession of the magnetic moment vector around the direction of the magnetic field. In this case, the role of magnetic field components is played by combinations of the Hamiltonian matrix elements, and the role of the magnetic moment is played by the Bloch vector. Features of the 3JJ qubit model are discussed during the analysis of how the qubit is affected by exposure to a short control pulse, as are the similarities between the Bloch and Landau-Lifshitz-Gilbert equations. An analysis of solutions to the Bloch equations made it possible to develop recommendations for the use of readout RSFQ circuits in implementing an optimal interface between the classical and quantum parts of the computer system, as well as to justify the use of single-quantum logic in order to control superconducting quantum circuits on a chip.