Local Quantum Codes from Subdivided Manifolds

• URL: http://arxiv.org/abs/2303.06755v3
• Date: Tue, 20 Jun 2023 15:31:04 GMT
• Title: Local Quantum Codes from Subdivided Manifolds
• Authors: Elia Portnoy
• Abstract summary: We demonstrate the existence of quantum codes which are local in dimension $n$ with $V$ qubits, distance $Vfracn-1n$, and dimension $Vfracn-2n$, up to a $polylog(V)$ factor. The proof combines the existence ofally good quantum codes, a procedure to build a manifold from a code by Freedman-Hastings, and a quantitative embedding by Gromov-Guth.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: For $n \ge 3$, we demonstrate the existence of quantum codes which are local in dimension $n$ with $V$ qubits, distance $V^{\frac{n-1}{n}}$, and dimension $V^{\frac{n-2}{n}}$, up to a $polylog(V)$ factor. The distance is optimal up to the polylog factor. The dimension is also optimal for this distance up to the polylog factor. The proof combines the existence of asymptotically good quantum codes, a procedure to build a manifold from a code by Freedman-Hastings, and a quantitative embedding theorem by Gromov-Guth.

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