Weakly Fault-Tolerant Computation in a Quantum Error-Detecting Code

• URL: http://arxiv.org/abs/2408.14828v1
• Date: Tue, 27 Aug 2024 07:25:36 GMT
• Title: Weakly Fault-Tolerant Computation in a Quantum Error-Detecting Code
• Authors: Christopher Gerhard, Todd A. Brun,
• Abstract summary: Many current quantum error correcting codes that achieve full fault-tolerance suffer from having low ratios of logical to physical qubits and significant overhead. We propose a middle ground: constructions in the [[n,n-2,2]] quantum error detecting code that can detect any error from a single faulty gate.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Many current quantum error correcting codes that achieve full fault-tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale quantum (NISQ) computers and results in the inability to perform quantum algorithms at useful scales with near-term quantum processors. Due to this, calculations are generally done without encoding. We propose a middle ground between these two approaches: constructions in the [[n,n-2,2]] quantum error detecting code that can detect any error from a single faulty gate by measuring the stabilizer generators of the code and additional ancillas at the end of the computation. This achieves what we call weak fault-tolerance. As we show, this demonstrates a significant improvement over no error correction for low enough physical error probabilities and requires much less overhead than codes that achieve full fault-tolerance. We give constructions for a set of gates that achieve universal quantum computation in this error detecting code, while satisfying weak fault-tolerance up to analog imprecision on the physical rotation gate.

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