Robust sparse IQP sampling in constant depth

• URL: http://arxiv.org/abs/2307.10729v4
• Date: Wed, 1 May 2024 11:32:19 GMT
• Title: Robust sparse IQP sampling in constant depth
• Authors: Louis Paletta, Anthony Leverrier, Alain Sarlette, Mazyar Mirrahimi, Christophe Vuillot,
• Abstract summary: NISQ (noisy intermediate scale quantum) approaches without any proof of robust quantum advantage and fully fault-tolerant quantum computation. We propose a scheme to achieve a provable superpolynomial quantum advantage that is robust to noise with minimal error correction requirements.
• Score: 3.670008893193884
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Between NISQ (noisy intermediate scale quantum) approaches without any proof of robust quantum advantage and fully fault-tolerant quantum computation, we propose a scheme to achieve a provable superpolynomial quantum advantage (under some widely accepted complexity conjectures) that is robust to noise with minimal error correction requirements. We choose a class of sampling problems with commuting gates known as sparse IQP (Instantaneous Quantum Polynomial-time) circuits and we ensure its fault-tolerant implementation by introducing the tetrahelix code. This new code is obtained by merging several tetrahedral codes (3D color codes) and has the following properties: each sparse IQP gate admits a transversal implementation, and the depth of the logical circuit can be traded for its width. Combining those, we obtain a depth-1 implementation of any sparse IQP circuit up to the preparation of encoded states. This comes at the cost of a space overhead which is only polylogarithmic in the width of the original circuit. We furthermore show that the state preparation can also be performed in constant depth with a single step of feed-forward from classical computation. Our construction thus exhibits a robust superpolynomial quantum advantage for a sampling problem implemented on a constant depth circuit with a single round of measurement and feed-forward.

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