TY - JOUR
T1 - Fault-tolerant Coding for Quantum Communication
AU - Christandl, Matthias
AU - Muller-Hermes, Alexander
N1 - Publisher Copyright:
IEEE
PY - 2024
Y1 - 2024
N2 - Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error it is usually assumed that these circuits can be implemented using noise-free gates. While this assumption is satisfied for classical machines in many scenarios, it is not expected to be satisfied in the near term future for quantum machines where decoherence leads to faults in the quantum gates. As a result, fundamental questions regarding the practical relevance of quantum channel coding remain open. By combining techniques from fault-tolerant quantum computation with techniques from quantum communication, we initiate the study of these questions. We introduce fault-tolerant versions of quantum capacities quantifying the optimal communication rates achievable with asymptotically vanishing total error when the encoding and decoding circuits are affected by gate errors with small probability. Our main results are threshold theorems for the classical and quantum capacity: For every quantum channel T and every ϵ > 0 there exists a threshold p(ϵ, T) for the gate error probability below which rates larger than C-ϵ are fault-tolerantly achievable with vanishing overall communication error, where C denotes the usual capacity. Our results are not only relevant in communication over large distances, but also on-chip, where distant parts of a quantum computer might need to communicate under higher levels of noise than affecting the local gates.
AB - Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error it is usually assumed that these circuits can be implemented using noise-free gates. While this assumption is satisfied for classical machines in many scenarios, it is not expected to be satisfied in the near term future for quantum machines where decoherence leads to faults in the quantum gates. As a result, fundamental questions regarding the practical relevance of quantum channel coding remain open. By combining techniques from fault-tolerant quantum computation with techniques from quantum communication, we initiate the study of these questions. We introduce fault-tolerant versions of quantum capacities quantifying the optimal communication rates achievable with asymptotically vanishing total error when the encoding and decoding circuits are affected by gate errors with small probability. Our main results are threshold theorems for the classical and quantum capacity: For every quantum channel T and every ϵ > 0 there exists a threshold p(ϵ, T) for the gate error probability below which rates larger than C-ϵ are fault-tolerantly achievable with vanishing overall communication error, where C denotes the usual capacity. Our results are not only relevant in communication over large distances, but also on-chip, where distant parts of a quantum computer might need to communicate under higher levels of noise than affecting the local gates.
KW - Capacities of quantum channels
KW - Channel coding
KW - Decoding
KW - Fault tolerance
KW - Fault tolerant systems
KW - fault-tolerance
KW - Logic gates
KW - Quantum channels
KW - quantum error correcting codes
KW - Quantum mechanics
U2 - 10.1109/TIT.2022.3169438
DO - 10.1109/TIT.2022.3169438
M3 - Journal article
AN - SCOPUS:85128616823
VL - 70
SP - 282
EP - 317
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
SN - 0018-9448
IS - 1
ER -