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In this chapter, we use an electron spin qubit under a constant external magnetic field as an example to show how a single-qubit gate, namely, the phase shift gate, can be implemented by turning the external magnetic field on for a given time. This is not a practical approach because turning on and off a large DC magnetic field is difficult and cannot be done very fast. However, the example is very instructive because it clarifies many important concepts in spin qubits by using relatively simple mathematics. In the process, we will also discuss the construction of Hamiltonian, how Larmor precession can be understood on the Block sphere, and how to find the time required to implement a given phase shift gate.

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Spin Qubit—Larmor Precession—Phase Shift Gate

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  • 发表日期：

    2025年

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  • Hiu Yung Wong

摘要

In this chapter, we use an electron spin qubit under a constant external magnetic field as an example to show how a single-qubit gate, namely, the phase shift gate, can be implemented by turning the external magnetic field on for a given time. This is not a practical approach because turning on and off a large DC magnetic field is difficult and cannot be done very fast. However, the example is very instructive because it clarifies many important concepts in spin qubits by using relatively simple mathematics. In the process, we will also discuss the construction of Hamiltonian, how Larmor precession can be understood on the Block sphere, and how to find the time required to implement a given phase shift gate.