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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

Inhomogeneous and homogeneous Broadening

Inhomogeneous broadening is a mechanism that results from quasi-static low frequency fluctuations that are constant within one experimental trial, but vary from trial to trial. On the other hand, in homogeneous broadening, the magnetic field fluctuates both within one experiment trial and from trial to trial.

Inhomogeneous broadening

As it was explained earlier in the Larmor precession, the Bloch vector representing the quantum state will precess around the z-axis at a frequency that is directly proportional to the magnitude of B-field. The fluctuations of the magnetic field along the z-axis will result in a different precession frequency in each experiment. This phenomenon can be visualized by the state's projection to the x-axis.

The ensemble average gives a signal decaying over time, characterized by a time constant of T2*. The Fourier transform of this decaying signal demonstrates the spread in precession frequencies. 

Homogeneous broadening

In this case, the magnetic field along z-axis fluctuates within each experimental trial. The magnetic field fluctuation will result in the variation of the precession frequency within one experiment.

The ensemble average of these measurements give a decaying signal which is characterized by a time constant of T2. The Fourier transform of this signal demonstrates the spread of precession frequency resulting from magnetic field fluctuations.

Difference between T2 and T2*

T2 is the time constant characterizing the decay of the qubit state due to the variations in the magnetic field within each experimental trial. One example is the interaction of the spin qubit with the nearby nuclear spins.

On the other hand, T2* is the time constant characterizing the decay of the qubit state both intrinsic spin-spin interactions and the fluctuations in the external magnetic field. For a spin qubit, one mechanism affecting T2* time is charge noise. It is always shorter than T2* time because it encompasses T2 and additional mechanisms degrading the qubit coherence.