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 -