Magic tricycles: Efficient magic state generation with finite block-length quantum LDPC codes

• URL: http://arxiv.org/abs/2508.10714v2
• Date: Thu, 06 Nov 2025 19:03:24 GMT
• Title: Magic tricycles: Efficient magic state generation with finite block-length quantum LDPC codes
• Authors: Varun Menon, J. Pablo Bonilla-Ataides, Rohan Mehta, Andi Gu, Daniel Bochen Tan, Mikhail D. Lukin,
• Abstract summary: We introduce a class of finite block-length quantum LDPC codes which we name tricycle codes.<n>These codes can support constant-depth physical circuits that implement logical $CCZ$ gates between three code blocks.<n>We show that tricycle codes enable single-shot state-preparation and error correction, leading to a highly efficient magic-state generation protocol.
• Score: 1.0792624191049491
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The preparation of high-fidelity non-Clifford (magic) states is an essential subroutine for universal quantum computation, but imposes substantial space-time overhead. Magic state factories based on high rate and distance quantum low-density parity check (LDPC) codes equipped with transversal non-Clifford gates can potentially reduce these overheads significantly, by circumventing the need for multiple rounds of distillation and by producing a large number of magic states in a single code-block. As a step towards realizing efficient, fault-tolerant magic state production, we introduce a class of finite block-length quantum LDPC codes which we name tricycle codes, generalizing the well-known bicycle codes to three homological dimensions. These codes can support constant-depth physical circuits that implement logical $CCZ$ gates between three code blocks. To construct these constant-depth $CCZ$ circuits, we develop new analytical and numerical techniques that apply to a broad class of three-dimensional homological and balanced product codes. We further show that tricycle codes enable single-shot state-preparation and error correction, leading to a highly efficient magic-state generation protocol. Numerical simulations of specific codes confirm robust performance under circuit-level noise, demonstrating a high circuit-noise threshold of $>0.5\%$. With modest post-selection, certain tricycle codes of block-lengths of only $50-100$ qubits are shown to achieve logical error-rates of $6\times 10^{-10}$ or lower. Finally, we construct optimal depth syndrome extraction circuits for tricycle codes and present a protocol for implementing them efficiently on a reconfigurable neutral atom platform.

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