Fault-tolerant compiling of classically hard IQP circuits on hypercubes

2024-04-29

arXiv.org

AI Summary

Fault-tolerant implementation of high-complexity Instantaneous Quantum Polynomial (IQP) sampling circuits on noisy neutral-atom arrays remains challenging. Method: We introduce “fault-tolerant compilation”—a novel paradigm that co-designs high-order IQP circuits and tailored quantum error-correcting codes on hypercubic geometries. We construct two scalable color codes: a [[2^D, D, 2]] detection code and an [[O(d^D), D, d]] fault-tolerant code, both supporting transversal gates. We prove that IQP sampling on D ≥ 4 hypercubes is classically intractable and compatible with efficient linear cross-entropy benchmarking (XEB) verification. Results: We experimentally implement fault-tolerant compilation on the Bluvstein group’s neutral-atom hypercubic platform, achieving exponential error suppression and rapid qubit shuffling. This work provides the first systematic solution for scalable, hardware-adapted, and verifiably fault-tolerant quantum sampling.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Security and Privacy: Large-scale security measurements
• Responsible Web: Algorithmic accountability and transparency on the web

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.

Problem

• Develop fault-tolerant quantum circuits for complex sampling tasks.
• Co-design circuits with error-correcting codes for neutral atom arrays.
• Analyze classical hardness and verification of IQP circuit sampling.

Innovation

• Hardware-efficient fault-tolerant quantum circuit design
• Co-design with quantum error correcting codes
• Hypercube geometry for scalable IQP circuits