Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds on stabilizer measurement circuits and obstructions to local
  implementations of quantum LDPC codes   In this work we establish lower bounds on the size of Clifford circuits that
measure a family of commuting Pauli operators. Our bounds depend on the
interplay between a pair of graphs: the Tanner graph of the set of measured
Pauli operators, and the connectivity graph which represents the qubit
connections required to implement the circuit. For local-expander quantum
codes, which are promising for low-overhead quantum error correction, we prove
that any syndrome extraction circuit implemented with local Clifford gates in a
2D square patch of $N$ qubits has depth at least $\Omega(n/\sqrt{N})$ where $n$
is the code length. Then, we propose two families of quantum circuits
saturating this bound. First, we construct 2D local syndrome extraction
circuits for quantum LDPC codes with bounded depth using only $O(n^2)$ ancilla
qubits. Second, we design a family of 2D local syndrome extraction circuits for
hypergraph product codes using $O(n)$ ancilla qubits with depth $O(\sqrt{n})$.
Finally, we use circuit noise simulations to compare the performance of a
family of hypergraph product codes using this last family of 2D syndrome
extraction circuits with a syndrome extraction circuit implemented with fully
connected qubits. While there is a threshold of about $10^{-3}$ for a fully
connected implementation, we observe no threshold for the 2D local
implementation despite simulating error rates of as low as $10^{-6}$. This
suggests that quantum LDPC codes are impractical with 2D local quantum
hardware. We believe that our proof technique is of independent interest and
could find other applications. Our bounds on circuit sizes are derived from a
lower bound on the amount of correlations between two subsets of qubits of the
circuit and an upper bound on the amount of correlations introduced by each
circuit gate, which together provide a lower bound on the circuit size.

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The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: eess