Fault-tolerant Coding for Quantum Communication

09/15/2020
by   Matthias Christandl, et al.
0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

09/25/2018

Noise Thresholds for Amplification: From Quantum Foundations to Classical Fault-Tolerant Computation

We revisit an old question--fault-tolerant computation by noisy circuits...
09/25/2018

Noise Thresholds for Amplification: Quantum Foundations From Classical Fault-Tolerant Computation

It has long been known that certain superquantum nonlocal correlations c...
12/08/2021

Experimental Characterization of Fault-Tolerant Circuits in Small-Scale Quantum Processors

Experiments conducted on open-access cloud-based IBM Quantum devices are...
03/11/2019

Quantifying the magic of quantum channels

To achieve universal quantum computation via general fault-tolerant sche...
01/31/2022

A lower bound on the space overhead of fault-tolerant quantum computation

The threshold theorem is a fundamental result in the theory of fault-tol...
04/14/2020

Classical Coding Approaches to Quantum Applications

Quantum information science strives to leverage the quantum-mechanical n...
05/30/2021

Computation-aided classical-quantum multiple access to boost network communication speeds

A multiple access channel (MAC) consists of multiple senders simultaneou...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.