On fault tolerant single-shot logical state preparation and robust long-range entanglement

• URL: http://arxiv.org/abs/2411.04405v1
• Date: Thu, 07 Nov 2024 03:51:05 GMT
• Title: On fault tolerant single-shot logical state preparation and robust long-range entanglement
• Authors: Thiago Bergamaschi, Yunchao Liu,
• Abstract summary: We prove that single-shot logical state preparation can be achieved for arbitrary quantum LDPC codes. We also prove single-shot preparation of the encoded GHZ state in arbitrary quantum LDPC codes.
• Score: 1.3408612567129143
• License:
• Abstract: Preparing encoded logical states is the first step in a fault-tolerant quantum computation. Standard approaches based on concatenation or repeated measurement incur a significant time overhead. The Raussendorf-Bravyi-Harrington cluster state offers an alternative: a single-shot preparation of encoded states of the surface code, by means of a constant depth quantum circuit, followed by a single round of measurement and classical feedforward. In this work we generalize this approach and prove that single-shot logical state preparation can be achieved for arbitrary quantum LDPC codes. Our proof relies on a minimum-weight decoder and is based on a generalization of Gottesman's clustering-of-errors argument. As an application, we also prove single-shot preparation of the encoded GHZ state in arbitrary quantum LDPC codes. This shows that adaptive noisy constant depth quantum circuits are capable of generating generic robust long-range entanglement.

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