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Quantum Computer Solutions

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

The Transmon Qubit - A basis for the Quantum Computer

So for a specific parameter space, the behavior of these superconducting circuits can be simplified to a harmonic oscillator (which operates as a two-level system). Simplifying a complex system to a well-known, smaller system is crucial in many other fields of physics. Can you think of another example?

 

Harmonic oscillators are useful to model diverse systems that oscillate around a point of stable equilibrium. The main idea behind this is to get rid of higher order terms in the physics that describes certain phenomena, to only analyse the terms that matter the most. Hopefully these terms will be enough to describe what you are studying.

Think of describing the movement of the earth around the sun. If you don't need many details, analysing the forces between the earth and the sun from a classical perspective can give you a lot of information already. This way you would conclude the orbit of the earth around the sun is circular, which used to be a pretty good answer back a couple centuries ago.

If you decide to include the moon, then you get a 3 body problem that is not easy to solve, but it helps you describe other phenomena and get more precision in your results.

Of course you could also use general relativity instead of classical mechanics, and then you would be able to describe even more fascinating physics, like black holes.

Another example you may be familiar with are lattice vibrations in solid state systems. Here classical normal modes are used to describe phonons. However, if you wanted to study particular effects, you would need a more complex model to reproduce them.