For every fixed integers $r \ge 4$ and $2 \le k \le r-2$, we construct $r$-dimensional cubical sheaf complexes whose degree-$k$ CSS codes have positive constant rate, linear distance, and constant soundness, with bounded row and column weights. Taking $r=4$ and $k=2$ gives a family of asymptotically good binary qLTCs....
Ye-Yuan Chen, Mi-Ying Huang, Yin-Chen Liu et al.· 2 citations· ⚡1
We prove the $\Delta$-conjecture, which dates back to Gurvich's 1978 thesis. Specifically, let the edges of a complete graph be colored with colors $1,\ldots,d$, and for each $i$ let $G_i$ be the graph on the same vertex set formed by the edges of color $i$. We prove that if every choice of a maximal stable set $S_i$ o...
An efficient quantum adiabatic algorithm is obtained for the ground energy of any model in this family of Heisenberg-type quantum spin systems, based on a new inequality that relates the spectral gap of a positive semidefinite operator to its Lee-Yang radius.
S. Bravyi, David Gosset, Yin-Chen Liu et al.· 3 citations
The output state of a 2D geometrically local shallow random quantum circuit does not have long range correlations due to its lightcone structure. But this changes if one measures a subset of the qubits: long-range entanglement can be induced by the measurement process, leading to conditional correlations between distan...
Yin-Chen Liu, Max McGinley, T. Schuster et al.· 6 citations
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