Fast preparation of quantum error-correcting codes is essential for scalable quantum memories, but geometric locality and $U(1)$ charge conservation impose an unavoidable transport constraint. We combine exact complementary-channel geometry, charge-sector Haar analysis, and a gate-resolved connected-moment expansion to study one-dimensional covariant encoders under flagged erasure. Charge-Haar codes attain the universal adjacent-charge lower bound up to exponentially small corrections, yielding an exact $n^{-1/2}$ extensive-erasure law and a sharp half-erasure transition. For local number-conserving brickwork circuits, diffusion of the logical charge enforces an $\Omega(n^2)$ encoding-time lower bound; we also prove an $O(n^3)$ mixing bound for the classical component and reduce the remaining full-channel upper bound to a source-restricted low-support operator-spreading problem. These results identify diffusion as an operational limit on symmetry-constrained quantum coding and establish a route to its exact formation time.
Local quantum interactions generate dynamics in an exponentially large Hilbert space, yet locality and entanglement restrict the information that can spread and accumulate. Bounds on propagation and entanglement growth, together with tensor networks, exploit these restrictions to discard information unnecessary for des...
H. Mackay, Donghoon Kim, Tan Van Vu et al.· 0 citations
Maximum-probability (MP) decoding selects the most probable microscopic error, whereas degenerate maximum-likelihood (MLD) decoding includes the configurational entropy of an entire logical sector. Using code-capacity Pauli noise to isolate rigidity intrinsic to the code, we determine the first physical error weight $m...
Native 3D geometry can improve both the packing density and executable realization of nonlocal qLDPC codes, making practical performance depend jointly on code structure, optical geometry, transport scheduling, and hardware-level noise.
The results show that precise Haar-like statistics can emerge from sparse commuting dynamics with remarkably low quantum resources, with applications to randomized characterization, quantum metrology, quantum algorithms, and many-body physics.
Qing-Yue Zhang, Jun-Jie Chen, Zhou You et al.· 0 citations
Fermionic platforms offer compelling architectures for quantum computing, ranging from topologically protected Majorana-based qubits to fermionic cold atoms. To achieve scalability, however, they require quantum error correction. In this work, we prove that any exact and sufficiently accurate approximate fermionic quan...
We establish sufficient conditions for preparing quantum thermal states of noncommuting local Hamiltonians with polylogarithmic circuit depth in arbitrary fixed spatial dimension. Our conditions combine locality and stability bounds on the effective interactions of reduced density matrices of a Gibbs state with a quant...
H. Hakoshima, Atsushi Iwaki, N. Yoshioka· 0 citations
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