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Quantum Error Correction

A major unresolved pain point in second generation and post NISQ era Quantum Computing (QC) is Quantum Error Correction, and for some types of error, there are no practical solutions currently. Commonly manifested errors in QC are due to noise in the physical qubits that result in logical bit flip or logical phase flip errors. A leading candidate to implement fault tolerant hardware is through surface codes, where a logical code is stored as a topological state of an array of physical qubits. Random errors in the states of the physical qubits should be corrected as they proliferate and destroy the logical state. The Quantum Error Correction (QEC) protocols that perform this error correction are termed “decoders”. There are different encoding schemes in addition to the surface codes. By Encoders we mean selection of QEC strategies for arbitrary noise, which is a complex optimization problem.

Noise and errors are inevitable in any Quantum Computer(QC). Commonly manifested errors are due to noise in the physical qubits that result in logical bit flip or logical phase flip errors. There is a need for associated QEC with each implementation, so that these solutions are Robust, Accurate and Fault-Tolerant.

As we emerge from the NISQ era, the Quantum Technology market sector needs solutions in Error Correction. Our envisaged product (TundraQECDL) that will define a niche business need and technological challenge in the form of a modularized embedded QEC solution and can be software fine-tuned in each application. The market is in need for QEC solutions where an End-User such as Quantum hardware solution developer will not have to build-in a complete QEC component but simply adopt TundraQECDL and fine tune it to their requirements. Our off-the-shelf solution will bring about tremendous cost savings and boost in productivity.

While some types of errors can be straight forwardly identified and corrected, determining the QEC strategy for arbitrary noise is a complicated optimization problem. As such a “Syndrome” is defined by a measurement of the end points of an unknown chain of physical qubit errors. TundraSystems is developing a technique to deduce from a given syndrome what errors caused by arbitrary noise have occurred. This robust approach will also address the full range of other errors in the Quantum state. The complete solution is two-fold: Code selection and Error decoding i.e. two optimization tasks performed using Deep Reinforcement.

Shortcomings of Algorithmic approaches: Due to the importance of decoding algorithms for fault-tolerant QC, several approaches have been developed, each of which tries to satisfy as many of the experimentally required criteria as possible. Perhaps most prominent are algorithms based on minimum-weight perfect matching subroutines, although alternative approaches based on techniques such as the renormalization group and locally operating cellular automata have also been put forward. These algorithms solve the problem in principle, but may well be too slow in realistic settings.

Advantages of Machine Learning approaches: Techniques from machine learning have begun to find application in diverse areas of quantum physics. In an attempt to tackle the issue of fast decoding various neural-network based decoders have also been proposed. In particular, previously proposed neural network decoders promise extremely fast decoding times, flexibility with respect to the underlying code and noise model and the potential to scale to large code distances.

Thus, the uniqueness of the Tundra QECDL approach is the synthesis of the following state-of-the-art techniques:

  1. Coherent nanophotonic circuit implementation of a Deep RL framework implementing the DQN algorithm.
  2. Using Deep RL framework above for QEC code optimization. Error and Noise characterization solution.
  3. Using Deep RL code “decoders” to apply the error correction.
  4. Factoring noise at the Syndrome measurement stage.
  5. Using Behavioural Cloning for training the whole system.

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