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Quantum Computer

01 /Quantum Computers 02 /How to build a qubit 03 /Spin qubits (beginner level) 04 /Operations on spin qubits (beginner level) 05 /Electron spin qubits 06 /Capturing a single electron 07 /Quantum dot qubits 08 /Quantum control and readout 09 /Qubit errors 10 /NV center qubits 11 /Operations on NV center qubits 12 /The Transmon Qubit - A basis for the Quantum Computer 13 /Operations on the Transmon Qubit - Circuit QED 14 /Single-qubit operations on the Transmon qubit 15 /Measurements on the Transmon Qubit 16 /Two-qubit operations on the Transmon qubit 17 /Topological qubits: Anyons 18 /Operations on anyons: Braiding 19 /Operations on anyons: Real-life experiments 20 /Topological quantum computing: Majorana fermions and where to find them 21 /Majorana bound states in superconductors 22 /How do you measure Majorana bound states? 23 /A framework for the future Quantum Computer 24 /The Building Blocks of a Quantum Computer 25 /How to build a Quantum Algorithm - Quantum Circuits 26 /How do you program a quantum algorithm? 27 /The compiler of a quantum computer 28 /Micro-architectures 29 /How do we connect our quantum system to a classical interface? 30 /Assembling a Quantum Processor 31 /Microwave drivers for qubits 32 /Implementation of microwave drivers 33 /Quantum error correction 34 /Surface codes 35 /Fault-tolerant Quantum Error Correction with surface codes

Larmor Precession on Bloch Sphere

Larmor precession is a fundamental concept in quantum mechanics that describes the rotation of a quantum state, in an external magnetic field. To understand this phenomenon in the context of qubits, it's essential to visualize the qubit state on a Bloch sphere, where each point on the sphere represents a possible state of the qubit.

Larmor Precession on Bloch Sphere

When a constant external magnetic field B along the z-axis is applied to a qubit, the state of the qubit in Bloch sphere will begin to rotate around the z-axis.

Let us denote a magnetic field that is constant and directed along the z-axis as  Bẑ
. The Hamiltonian describing a quantum state under a magnetic field is given by

where  is the magnetic moment operator. It is related to the spin operator by

where ge is the gyromagnetic ratio, e is the electron charge and m is the mass of the electron.

When the applied magnetic field  is applied to the qubit, the Bloch vector representing the quantum state will precess around the z-axis at a frequency know as the Larmor frequency:

where e is the electron charge and m is the mass of the electron.

Understanding Larmor precession is crucial in the field of quantum computing, particularly in the manipulation and control of qubit states. By applying an external magnetic field, it is possible to precisely manipulate and control the state of qubits.