Quantum Error Correction with Quantum Autoencoders

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The idea is inspired by this paper ( https://arxiv.org/pdf/2202.00555.pdf)!

Quick Summary:

The authors of this claim that they can make the Autoencoder learn error correction routines. The paper has more results than I described in the call. The key feature of this scheme is the absence of a need to perform operations to send the logical qubit back to the encoded codespace. After an error occurs, the problem of sending the qubits back to the logical codespace is commonly referred to as the decoding problem. The key results of the paper include

• Given an encoding to logical, the ability to perform autonomous error correction.
• The authors also claim, after initializing a QAE on a physical device, it can also learn encodings for the particular device in question.

Possible solutions to the Hackathon

1. Demonstrate QEC with QAEs(Quantum Auto Encoders) by doing any one of the sections from the third one
2. Use this scheme to perform Fault-Tolerant Operations on say IBM's devices.
   • Evaluate the number of logical qubits that can be made with the device in question.
   • Learn QAE given the [[5,1,3]] code for the physical device in question. The problem of noise modeling of the device can be bypassed.
   • Learn both encoding and correction routines using a QAE given a physical device.
3. If we are able to do a bunch of the above stuff, I am fairly confident we can build generalize our code to a given physical qubit graph. and a restricted gate set.
   • Reducing the total amount of resources can be an additional constraint we optimize for. It is not clear from the paper if the authors took note of this constraint.
4. An interesting problem to me would to do this for the surface code, for the encoding and stabilizers are already known. The decoding of surface codes is an unsolved problem right now. The ability of this paper to remove the need for performing active operations for decoding is lucrative. If a QAE can retain the logical codespace information, it could be a useful subroutine in the end-to-end QEC stack.

Bottlenecks/Issues:

• Familiarity with DQNNs: Dissipative Quantum Neural Networks. It is not clear to me how the neural network is implemented. Someone with more experience please comment on this
• As noted by the authors, these can encounter barren plateaus when looking for encoding for a given noise channel.
• It is not clear if the authors ran this on an actual quantum device. In one part they saw classically simulate a DQNNs. In some other parts, they say we used a quantum device. Whatever the case, it needs to be figured out where each of the moving parts of the neural network lies in.

Resources

https://arxiv.org/pdf/1907.11157.pdf - An Introductory Guide to Quantum Error Correction https://arxiv.org/pdf/2012.08331.pdf - Noise Assisted Quantum Autoencoders https://drive.google.com/file/d/1r7PiYOXJjNvEQoJ6QuiWHBtuRzE2kxWj/view?usp=sharing - Review of QEC, last two slides have references in general about QEC

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https://www.youtube.com/watch?v=j_1R5nX7_G0 Talk about this paper