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Continuous Symmetries and Approximate Quantum Error Correction by Faist, Philippe; Nezami, Sepehr; Albert, Victor V.; Salton, Grant; Pastawski, Fernando; Hayden, Patrick; Preskill, John is a scholarly article available to read on EtoBox.

What is Continuous Symmetries and Approximate Quantum Error Correction about?

Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here we study the compatibility of these two important principles. If a logical quantum system is encoded into $n$ physical subsystems, we say that the code is covariant with respect to a symmetry group $G$ if a $G$ transformation on the logical system can be realized by performing transformations on the individual subsystems. For a $G$-covariant code with $G$ a continuous group, we derive a lower bound on the error correction infidelity following erasure of a subsystem. This bound approaches zero when the number of subsystems $n$ or the dimension $d$ of each subsystem is large. We exhibit codes achieving approximately the same scaling of infidelity with $n$ or $d$ as the lower bound. Leveraging tools from representation theory, we prove an approximate version of the Eastin-Knill theorem: If a code admits a universal set of transversal gates and corrects erasure with fixed accuracy, then, for each logical qubit, we need a number of physical qubits per subsystem that is inversely proportion

Author

Faist, Philippe; Nezami, Sepehr; Albert, Victor V.; Salton, Grant; Pastawski, Fernando; Hayden, Patrick; Preskill, John

Published

2019

Language

EN