Universal Fault-Tolerant Quantum Computing with Stabiliser Codes
- URL: http://arxiv.org/abs/2012.05260v2
- Date: Thu, 20 May 2021 03:55:17 GMT
- Title: Universal Fault-Tolerant Quantum Computing with Stabiliser Codes
- Authors: Paul Webster, Michael Vasmer, Thomas R. Scruby, and Stephen D.
Bartlett
- Abstract summary: Quantum computers should have both universal and fault-tolerant logic gates.
A number of no-go theorems constrain the ways in which a set of fault-tolerant logic gates can be universal.
We present a general framework for universal fault-tolerant logic with stabiliser codes.
We show how non-unitary implementations of logic gates provide a general approach to circumvent the no-go theorem.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The quantum logic gates used in the design of a quantum computer should be
both universal, meaning arbitrary quantum computations can be performed, and
fault-tolerant, meaning the gates keep errors from cascading out of control. A
number of no-go theorems constrain the ways in which a set of fault-tolerant
logic gates can be universal. These theorems are very restrictive, and
conventional wisdom holds that a universal fault-tolerant logic gate set cannot
be implemented natively, requiring us to use costly distillation procedures for
quantum computation. Here, we present a general framework for universal
fault-tolerant logic with stabiliser codes, together with a no-go theorem that
reveals the very broad conditions constraining such gate sets. Our theorem
applies to a wide range of stabiliser code families, including concatenated
codes and conventional topological stabiliser codes such as the surface code.
The broad applicability of our no-go theorem provides a new perspective on how
the constraints on universal fault-tolerant gate sets can be overcome. In
particular, we show how non-unitary implementations of logic gates provide a
general approach to circumvent the no-go theorem, and we present a rich
landscape of constructions for logic gate sets that are both universal and
fault-tolerant. That is, rather than restricting what is possible, our no-go
theorem provides a signpost to guide us to new, efficient architectures for
fault-tolerant quantum computing.
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