The stabilizer code formalism is presented as a powerful group-theoretic tool for quantum error correction, enabling code construction, analysis of quantum channel capacity, bounds on codes, and fault-tolerant computation.
and Laflamme, R
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abstract
We have previously (quant-ph/9608012) shown that for quantum memories and quantum communication, a state can be transmitted over arbitrary distances with error $\epsilon$ provided each gate has error at most $c\epsilon$. We discuss a similar concatenation technique which can be used with fault tolerant networks to achieve any desired accuracy when computing with classical initial states, provided a minimum gate accuracy can be achieved. The technique works under realistic assumptions on operational errors. These assumptions are more general than the stochastic error heuristic used in other work. Methods are proposed to account for leakage errors, a problem not previously recognized.
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LightStim automates DEM construction for QEC protocols via an augmented Pauli tableau during compilation, matching public tools on detector counts and error rates while enabling new cross-code designs.
Magic state cultivation prepares high-fidelity T states with an order of magnitude fewer qubit-rounds than prior distillation methods by gradually growing them within a surface code under depolarizing noise.
Ancilla-mediated protocols enable deterministic universal logical gates on any stabilizer code without ancilla consumption or code modification.
citing papers explorer
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Stabilizer Codes and Quantum Error Correction
The stabilizer code formalism is presented as a powerful group-theoretic tool for quantum error correction, enabling code construction, analysis of quantum channel capacity, bounds on codes, and fault-tolerant computation.
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LightStim: A Framework for QEC Protocol Evaluation and Prototyping with Automated DEM Construction
LightStim automates DEM construction for QEC protocols via an augmented Pauli tableau during compilation, matching public tools on detector counts and error rates while enabling new cross-code designs.
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Magic state cultivation: growing T states as cheap as CNOT gates
Magic state cultivation prepares high-fidelity T states with an order of magnitude fewer qubit-rounds than prior distillation methods by gradually growing them within a surface code under depolarizing noise.
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Stabilizer Code-Generic Universal Fault-Tolerant Quantum Computation
Ancilla-mediated protocols enable deterministic universal logical gates on any stabilizer code without ancilla consumption or code modification.