Fault-Tolerant Compiling of Classically Hard Instantaneous Quantum Polynomial Circuits on Hypercubes
Year: 2025
Type: article
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 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 [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 strong evidence that sampling from these hypercube IQP circuits is classically hard to simulate even at relatively low depths. We analyze the linear cross-entropy benchmark (XEB) in comparison to the average fidelity and, depending on the local noise rate, find two different asymptotic regimes. 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.
Source: PRX Quantum
Authors: Dominik Hangleiter, Marcin Kalinowski, Dolev Bluvstein, Madelyn Cain, Nishad Maskara, Xun Gao, Aleksander Kubica, Mikhail D. Lukin, Michael J. Gullans
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,450
Funders: National Science Foundation, U.S. Department of Energy, Defense Advanced Research Projects Agency, Office of Science, University of Colorado Boulder, Intelligence Advanced Research Projects Activity, Multidisciplinary University Research Initiative, Simons Institute for the Theory of Computing, University of California Berkeley, Center for Ultracold Atoms, Massachusetts Institute of Technology, Army Research Office
Awards: G1264789558, G149988304, G1938338418, G2072961586, QLCI-CI: NSF Quantum Leap Challenge Institute for Robust Quantum Simulation, G2916627489, Center: JILA-PFC: Comprehension and Control of Emerging Complexity at the Quantum Frontier, G3719423973, G5188000133, Collaborative Research: FET: Medium: Efficient Compilation for Dynamically Reconfigurable Atom Arrays, G5723341926, G586693022, G5868295057, Physics and Applications of Quantum Nanophotonics Systems, Center for Ultracold Atoms, G7452299184
OpenAlex ID: W4410820249