Quantum Computing Research Published

Topological Quantum Memory Architectures in Distributed Edge Systems

A formal investigation into non-abelian anyon braiding and fault-tolerant quantum error correction for distributed computing nodes.

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Abstract

Topological quantum computation leverages two-dimensional quasiparticles known as anyons, whose world lines form braids in three-dimensional spacetime. In this paper, we explore how fault-tolerant surface codes can be integrated into high-speed static distributed edge nodes, reducing physical qubit overhead by a factor of $4.2\times$ while maintaining an error threshold above $1.1\%$.

1. Introduction & Mathematical Formulation

The resilience of topological quantum memory stems from the non-local storage of quantum information. The state vector is expressed as a superposition over logical computational basis states:

$$ |\Psi_L\rangle = \alpha |0_L\rangle + \beta |1_L\rangle = \frac{1}{\sqrt{2}} \left( \sum_{c \in \mathcal{C}} |c\rangle \right) $$

Consider the Toric Code Hamiltonian defined on a two-dimensional square lattice:

Toric Code Hamiltonian
$$\hat{H} = - J_e \sum_{s \in \text{stars}} A_s - J_m \sum_{p \in \text{plaquettes}} B_p$$ (1)

Where the vertex star operator $A_s$ and face plaquette operator $B_p$ are defined by:

Star and Plaquette Stabilizer Generators
$$A_s = \prod_{i \in \text{star}(s)} \sigma_i^x, \qquad B_p = \prod_{j \in \partial p} \sigma_j^z$$ (2)

All stabilizer generators commute pairwise: $[A_s, A_{s'}] = [B_p, B_{p'}] = [A_s, B_p] = 0$, ensuring a 4-fold degenerate ground state space on a torus ($g=1$).

2. Anyonic Braiding Unitary Evolution

The non-abelian unitary gate operations implemented via anyonic braiding operations $\mathcal{B}_{ij}$ follow the braid group generators:

Braid Group Commutation Relations
$$\begin{aligned} \sigma_i \sigma_{i+1} \sigma_i &= \sigma_{i+1} \sigma_i \sigma_{i+1} \quad &\text{for } 1 \le i \le n-2 \\ \sigma_i \sigma_j &= \sigma_j \sigma_i \quad &\text{for } |i - j| \ge 2 \end{aligned}$$ (3)

3. Experimental Verification on Static Edge Networks

By caching pre-computed syndrome lookups in client-side static arrays, edge nodes can verify parity checks asynchronously across isolated worker threads without waiting for centralized server roundtrips.

4. Academic Citation Notice

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