A new in-situ scheme prepares logical magic states inside arbitrary CSS qLDPC codes using only syndrome-extraction ancillas, with simulations on the [[144,12,12]] BB code and [[225,9,4]] hypergraph-product code showing injection error rates around 10^{-3} or lower under depolarizing and asymmetric噪声
Magic state distillation with low overhead
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
abstract
We propose a new family of error detecting stabilizer codes with an encoding rate 1/3 that permit a transversal implementation of the pi/8-rotation $T$ on all logical qubits. The new codes are used to construct protocols for distilling high-quality `magic' states $T|+>$ by Clifford group gates and Pauli measurements. The distillation overhead has a poly-logarithmic scaling as a function of the output accuracy, where the degree of the polynomial is $\log_2{3}\approx 1.6$. To construct the desired family of codes, we introduce the notion of a triorthogonal matrix --- a binary matrix in which any pair and any triple of rows have even overlap. Any triorthogonal matrix gives rise to a stabilizer code with a transversal $T$-gate on all logical qubits, possibly augmented by Clifford gates. A powerful numerical method for generating triorthogonal matrices is proposed. Our techniques lead to a two-fold overhead reduction for distilling magic states with output accuracy $10^{-12}$ compared with the best previously known protocol.
citation-role summary
background 1
citation-polarity summary
fields
quant-ph 3roles
background 1polarities
background 1representative citing papers
A closed-form resource estimation tool for concatenated quantum error correction reveals that magic-state operations rarely dominate qubit costs, with general optimizations providing orders-of-magnitude larger reductions than magic-specific ones.
A homological framework identifies necessary and sufficient obstruction conditions for transversal logical diagonal gates in quantum CSS codes.
citing papers explorer
-
In-Situ Simultaneous Magic State Injection on Arbitrary CSS qLDPC Codes
A new in-situ scheme prepares logical magic states inside arbitrary CSS qLDPC codes using only syndrome-extraction ancillas, with simulations on the [[144,12,12]] BB code and [[225,9,4]] hypergraph-product code showing injection error rates around 10^{-3} or lower under depolarizing and asymmetric噪声
-
Magic states are rarely the best resource to optimize: An analytical tool for qubit resource estimation in concatenated codes
A closed-form resource estimation tool for concatenated quantum error correction reveals that magic-state operations rarely dominate qubit costs, with general optimizations providing orders-of-magnitude larger reductions than magic-specific ones.
-
Homological origin of transversal implementability of logical diagonal gates in quantum CSS codes
A homological framework identifies necessary and sufficient obstruction conditions for transversal logical diagonal gates in quantum CSS codes.