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- W3200537988 abstract "Quantum low-density parity-check (LDPC) codes are a promising avenue to reduce the cost of constructing scalable quantum circuits. However, it is unclear how to implement these codes in practice. Seminal results of Bravyi et al. [Phys. Rev. Lett. 104, 050503 (2010)] have shown that quantum LDPC codes implemented through local interactions obey restrictions on their dimension $k$ and distance $d$. Here we address the complementary question of how many long-range interactions are required to implement a quantum LDPC code with parameters $k$ and $d$. In particular, in 2D we show that a quantum LDPC code with distance $densuremath{propto}{n}^{1/2+ϵ}$ requires $mathrm{ensuremath{Omega}}({n}^{1/2+ϵ})$ interactions of length $stackrel{texttildelow{}}{mathrm{ensuremath{Omega}}}({n}^{ϵ})$. Further, a code satisfying $kensuremath{propto}n$ with distance $densuremath{propto}{n}^{ensuremath{alpha}}$ requires $stackrel{texttildelow{}}{mathrm{ensuremath{Omega}}}(n)$ interactions of length $stackrel{texttildelow{}}{mathrm{ensuremath{Omega}}}({n}^{ensuremath{alpha}/2})$. As an application of these results, we consider a model called a stacked architecture, which has previously been considered as a potential way to implement quantum LDPC codes. In this model, although most interactions are local, a few of them are allowed to be very long. We prove that limited long-range connectivity implies quantitative bounds on the distance and code dimension." @default.
- W3200537988 created "2021-09-27" @default.
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- W3200537988 date "2022-07-28" @default.
- W3200537988 modified "2023-10-11" @default.
- W3200537988 title "Quantifying Nonlocality: How Outperforming Local Quantum Codes Is Expensive" @default.
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- W3200537988 doi "https://doi.org/10.1103/physrevlett.129.050505" @default.
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