Lookup-table decoding is fast and distance preserving, making it attractive for near-term quantum computer architectures with small-distance quantum error-correcting codes. In this work, we develop several optimization tools that can potentially reduce the space and time overhead required for flag fault-tolerant quantum error correction (FTQEC) with lookup-table decoding on Calderbank-Shor-Steane (CSS) codes. Our techniques include the compact lookup-table construction, the meet-in-the-middle technique, the adaptive time decoding for flag FTQEC, the classical processing technique for flag information, and the separate - and -counting technique. We evaluate the performance of our tools using numerical simulation of hexagonal color codes of distances 3, 5, 7, and 9 under circuit-level noise. Combining all tools can result in an increase of more than an order of magnitude in the pseudothreshold for the hexagonal color code of distance 9, from to . Published by the American Physical Society2024
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This content will become publicly available on May 1, 2026
Fault-Tolerant Compiling of Classically Hard Instantaneous Quantum Polynomial Circuits on Hypercubes
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 quantum error-detecting codes whose transversal and permutation gate set can realize arbitrary degree- 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- 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 color codes of increasing distance , 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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- Award ID(s):
- 2012023
- PAR ID:
- 10654713
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- PRX Quantum
- Volume:
- 6
- Issue:
- 2
- ISSN:
- 2691-3399
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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