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Fault-tolerant Coding for Quantum Communication
Quantum Physics · Submitted 15 Sep 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our main results are threshold theorems for the classical and quantum capacity: For every quantum channel $T$ and every $\epsilon>0$ there exists a threshold $p(\epsilon,T)$ for the gate error probability below which rates larger than $C-\epsilon$ are fault-tolerantly achievable with vanishing overall communication error, where $C$ denotes the usual capacity.
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The abstract, sentence by sentence
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 $\epsilon>0$ there exists a threshold $p(\epsilon,T)$ for the gate error probability below which rates larger than $C-\epsilon$ 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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | 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. | background 1.00 | 0.04 | 0.02 | asserted 0.97 |
| s2 | 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. | background 0.89 | 0.06 | 0.02 | hedged possibility 0.55 |
| s3 | As a result, fundamental questions regarding the practical relevance of quantum channel coding remain open. | gap 0.99 | 0.03 | 0.02 | asserted 0.98 |
| s4 | By combining techniques from fault-tolerant quantum computation with techniques from quantum communication, we initiate the study of these questions. | contribution 0.97 | 0.89 | 0.04 | asserted 0.99 |
| s5 | 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. | contribution 1.00 | 0.92 | 0.12 | asserted 0.98 |
| s6 | Our main results are threshold theorems for the classical and quantum capacity: For every quantum channel $T$ and every $\epsilon>0$ there exists a threshold $p(\epsilon,T)$ for the gate error probability below which rates larger than $C-\epsilon$ are fault-tolerantly achievable with vanishing overall communication error, where $C$ denotes the usual capacity. | result 0.99 | 0.95 | 0.97 | asserted 1.00 |
| s7 | 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. | interpretation 1.00 | 0.30 | 0.04 | asserted 0.78 |
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Original abstract
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 $\epsilon>0$ there exists a threshold $p(\epsilon,T)$ for the gate error probability below which rates larger than $C-\epsilon$ 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.
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References
How the literature uses it
2 arXiv papers cite this in 5 sentences
Papers citing it · 4 sentences without a confident label
Cites it as background 1 paper
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How to construct asymptotically good QECCs with positive rates and linear distances, is one of the key problems in quantum coding theory [ref] .
Partially Concatenated Calderbank-Shor-Steane Codes Achieving the Quantum Gilbert-Varshamov Bound Asymptotically · Introduction · 0.81
What it cites · 2 sentences without a confident label
Uses the method or tool of 1 paper
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In the following we will restrict to the concatenations [ref] of the $7$-qubit Steane code for which elementary gadgets have been constructed in [ref] .
Concatenated Quantum Codes · Analyzing noisy quantum circuits · 0.86
Cites as background 4 papers
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A major result on fault-tolerant implementations of quantum circuits using quantum error correcting codes is the threshold theorem by Aharonov and Ben-Or [ref] .
Fault Tolerant Quantum Computation with Constant Error · Concatenated quantum error correcting codes and the threshold theorem · 0.99
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A major result on fault-tolerant implementations of quantum circuits using quantum error correcting codes is the threshold theorem by Aharonov and Ben-Or [ref] .
Fault-Tolerant Quantum Computation With Constant Error Rate · Concatenated quantum error correcting codes and the threshold theorem · 0.99
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In this appendix we review basic facts about concatenated quantum codes [ref] .
Concatenated Quantum Codes · Concatenated quantum error correcting codes · 1.00
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