Quantum error mitigation for physical and logical qubits
Sergey Bravyi
APS March Meeting 2022
We propose a family of error-detecting stabilizer codes with an encoding rate of 1/3 that permit a transversal implementation of the gate T=exp(-iπZ/8) on all logical qubits. These codes are used to construct protocols for distilling high-quality "magic" states T+ by Clifford group gates and Pauli measurements. The distillation overhead scales as O(logγ(1/ε)), where ε is the output accuracy and γ=log2(3)∼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 twofold overhead reduction for distilling magic states with accuracy ε∼10-12 compared with previously known protocols. © 2012 American Physical Society.
Sergey Bravyi
APS March Meeting 2022
Sergey Bravyi, Yash Sharma, et al.
QIP 2023
Sergey Bravyi, Joseph A. Latone, et al.
npj Quantum Information
Sergey Bravyi, David Gosset, et al.
QIP 2020