Close

Filter courses

Level
Subcategories
Show courses Show filters
Close

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

Decoherence on a Bloch Sphere

Decoherence is a mechanism that results in the degradation of the quantum information stored in a qubit over time due to interactions with the environment. One way to visualize and understand decoherence is by using the Bloch sphere representation for the quantum state.

Decoherence on Bloch Sphere

When a constant magnetic field is applied along the z-axis, the Bloch vector representing the quantum state precesses around the z-axis at a frequency given by the equation

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

Initially, the vector lies on the surface of the Bloch sphere representing a pure state. The environmental noise can be thought of as magnetic field fluctuations which results in rotations about a control vector with a component in the xy-plane.

T1 is known as the longitudinal relaxation time, representing the time it takes for the qubit's population to relax to its equilibrium state. It corresponds to the decay of the z-component of the Bloch vector, leading the qubit towards a depolarized state at the sphere's center. T1 inversely relates to the Γ1, which is a measure of how quickly the state loses energy into its environment.

The influence of noise on the qubit can also be described visualized on the Bloch sphere by considering the qubit’s density matrix.

A mathematical equation with black textDescription automatically generated with medium confidence

In this matrix, α and β are the amplitudes of the qubit's state. When the state is a pure state, the trace of this matrix is equal to 1. Γ1 drives the decay of these amplitudes representing the transition into a mixed state.

Decoherence plays a crucial role in implementation of the qubits as it limits the time during which quantum information can be accurately stored and manipulated.