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Germanium Quantum Technology

01 /What can CMOS technology do for quantum computing? 02 /Semiconductor devices and scaling with industrial approach 03 /Semiconductor foundry facilities: the good and the bad for qubits 04 /IMEC's latest qubit developments 05 /Summary and outlook 06 /Semiconductors for spin qubits 07 /Germanium quantum wells on silicon 08 /Germanium quantum wells on silicon-germanium 09 /Growth methods 10 /Characterization techniques 11 /Electrical characterization of germanium quantum wells 12 /Fabrication of H-FET 13 /Semiconductor qubits: vision and challenges 14 /Quantum materials 15 /Quantum dot qubits and their operation 16 /Types of quantum dot qubits 17 /Qubit Readout 18 /Qubit Control 19 /Qubit Coherence and Fidelity 20 /Multi-qubit control and quantum algorithms 21 /Quantum links and scaling 22 /Physics of holes 23 /Hole spin qubits 24 /Introduction to electronics for quantum computing 25 /Room temperature electronics 26 /Cryogenic qubit chip carriers 27 /Contribution to IGNITE 28 /Quantum Control Stack for Spin Qubits 29 /Auto-tuning a quantum computer 30 /Tuning and operation of arrays 31 /Finding operation points example 32 /What is auto-tuning? 33 /Neural network tuning 34 /Navigating charge stability diagrams 35 /Experimental implementation 36 /Towards universal quantum algorithms 37 /Classical error correction 38 /Quantum error correction 39 /Progress and challenges 40 /Introduction to quantum algorithms 41 /The first algorithms 42 /Quantum annealing 43 /Quantum Machine Learning

Quantum error correction

This video introduces the simplest quantum error correction code, the quantum repetition code. Basic concepts of quantum error correction are exemplified, such as the density matrix, the quantum bitflip channel, redundant encoding of a single qubit in a multi-qubit entangled state, parity-check measurements, quantum bitflip repetition code, and the corresponding error detection and error correction circuits. 

Prerequisite knowledge

  • Basics of quantum mechanics 
  • Density matrix 
  • Qubits, composite (few-qubit) quantum systems 
  • Quantum gates and quantum circuits 

Main takeaways

  • Redundant encoding, as used in the classical repetition code, cannot be generalized directly to quantum error correction due to the no-cloning theorem. 

  • Instead, another type of redundancy can be used: encoding a qubit state into a subspace of a multi-qubit register. 

  • Parity checks are important ingredients to preserve quantum states: they provide information about the physical errors that happened, without causing wave-function collapse. 

  • The concept of the decoder is generalized to quantum error correction: it takes the parity-check results (syndrome) as the input, and outputs an inferred pattern of errors.  

  • One way to do quantum error correction is to perform active error correction based on the decoder’s inferred error pattern. 

Further thinking

True or False: Quantum error correction in the 3-qubit bitflip repetition code is perfect: it does correct any bitflip configurations in the noisy part of the model circuit.

Solution

Further reading

This classic textbook has a chapter on quantum error correction, with a summary of the quantum repetition code and much more:
Michael Nielsen and Isaac Chuang, Quantum Information and Quantum Computation, Cambridge University Press. Chapter 10.1 
https://www.cambridge.org/highereducation/books/quantum-computation-and-quantum-information/01E10196D0A682A6AEFFEA52D53BE9AE#overview 

 

These online lecture notes also provide a pedagogical introduction to quantum error correction:
Dan Browne, Lectures on Topological Codes and Quantum Computation, online notes available at
https://sites.google.com/site/danbrowneucl/teaching/lectures-on-topological-codes-and-quantum-computation