Fault-tolerant compiling of classically hard IQP circuits on hypercubes

• URL: http://arxiv.org/abs/2404.19005v1
• Date: Mon, 29 Apr 2024 18:00:03 GMT
• Title: Fault-tolerant compiling of classically hard IQP circuits on hypercubes
• Authors: Dominik Hangleiter, Marcin Kalinowski, Dolev Bluvstein, Madelyn Cain, Nishad Maskara, Xun Gao, Aleksander Kubica, Mikhail D. Lukin, Michael J. Gullans,
• Abstract summary: We develop a hardware-efficient, fault-tolerant approach to realizing quantum sampling circuits. We develop a theory of second-moment properties of degree-$D$ IQP circuits for analyzing hardness and verification of random sampling. Our results highlight fault-tolerant compiling as a powerful tool in co-configurable algorithms with specific error-correcting codes and realistic hardware.
• Score: 34.225996865725605
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Realizing computationally complex quantum circuits in the presence of noise and imperfections is a challenging task. While fault-tolerant quantum computing provides a route to reducing noise, it requires a large overhead for generic algorithms. Here, we develop and analyze a hardware-efficient, fault-tolerant approach to realizing complex sampling circuits. We co-design the circuits with the appropriate quantum error correcting codes for efficient implementation in a reconfigurable neutral atom array architecture, constituting what we call a fault-tolerant compilation of the sampling algorithm. Specifically, we consider a family of $[[2^D , D, 2]]$ quantum error detecting codes whose transversal and permutation gate set can realize arbitrary degree-$D$ instantaneous quantum polynomial (IQP) circuits. Using native operations of the code and the atom array hardware, we compile a fault-tolerant and fast-scrambling family of such IQP circuits in a hypercube geometry, realized recently in the experiments by Bluvstein et al. [Nature 626, 7997 (2024)]. We develop a theory of second-moment properties of degree-$D$ IQP circuits for analyzing hardness and verification of random sampling by mapping to a statistical mechanics model. We provide evidence that sampling from hypercube IQP circuits is classically hard to simulate and analyze the linear cross-entropy benchmark (XEB) in comparison to the average fidelity. To realize a fully scalable approach, we first show that Bell sampling from degree-$4$ IQP circuits is classically intractable and can be efficiently validated. We further devise new families of $[[O(d^D),D,d]]$ color codes of increasing distance $d$, permitting exponential error suppression for transversal IQP sampling. Our results highlight fault-tolerant compiling as a powerful tool in co-designing algorithms with specific error-correcting codes and realistic hardware.

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