Measurement-based quantum computation in finite one-dimensional systems: string order implies computational power

• URL: http://arxiv.org/abs/2210.05089v4
• Date: Mon, 25 Dec 2023 09:30:21 GMT
• Title: Measurement-based quantum computation in finite one-dimensional systems: string order implies computational power
• Authors: Robert Raussendorf, Wang Yang, and Arnab Adhikary
• Abstract summary: We present a new framework for assessing the power of measurement-based quantum computation (MBQC) on short-range entangled symmetric resource states. We strengthen the connection between MBQC computational power and string order.
• Score: 2.231201892342328
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a new framework for assessing the power of measurement-based quantum computation (MBQC) on short-range entangled symmetric resource states, in spatial dimension one. It requires fewer assumptions than previously known. The formalism can handle finitely extended systems (as opposed to the thermodynamic limit), and does not require translation-invariance. Further, we strengthen the connection between MBQC computational power and string order. Namely, we establish that whenever a suitable set of string order parameters is non-zero, a corresponding set of unitary gates can be realized with fidelity arbitrarily close to unity.

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