A Converse for Fault-tolerant Quantum Computation

11/01/2022
by   Uthirakalyani G, et al.
0

With improvements in achievable redundancy for fault-tolerant quantum computing, it is natural to ask: what is the minimum required redundancy? In this paper, we obtain a lower bound on the minimum redundancy required for ϵ-accurate implementation of a large class of operations, which includes unitary operators. For the practically relevant case of sub-exponential (in input size) depth and sub-linear gate size, our bound on redundancy is tighter than the best known lower bound in <cit.>. We obtain this bound by connecting fault-tolerant computation with a set of finite blocklength quantum communication problems whose accuracy requirements satisfy a joint constraint. This bound gives a strictly lower noise threshold for non-degradable noise and captures its dependence on gate size. This bound directly extends to the case where noise at the outputs of a gate are correlated but noise across gates are independent.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
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...
research
03/18/2021

Lower bound the T-count via unitary stabilizer nullity

We introduce magic measures for multi-qubit quantum gates and establish ...
research
09/15/2020

Fault-tolerant Coding for Quantum Communication

Designing encoding and decoding circuits to reliably send messages over ...
research
03/19/2022

A Quantum Algorithm for Network Reliability

Building a network that is resilient to a component failure is vital. Ou...
research
04/25/2023

Scaling W state circuits in the qudit Clifford hierarchy

We identify a novel qudit gate which we call the √(Z) gate. This is an a...
research
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...
research
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...

Please sign up or login with your details

Forgot password? Click here to reset