Optimal Compilation of Syndrome Extraction Circuits for General Quantum LDPC Codes

• URL: http://arxiv.org/abs/2603.21499v1
• Date: Mon, 23 Mar 2026 02:43:38 GMT
• Title: Optimal Compilation of Syndrome Extraction Circuits for General Quantum LDPC Codes
• Abstract summary: We propose Auto-Stabilizer-Check (ASC), a universal compilation framework that generates depth-optimal syndrome extraction circuits for arbitrary qLDPC codes.<n> ASC reduces circuit depth by approximately 50% and achieves an average 7x-8x suppression of the logical error rate for general qLDPC codes.
• Score: 24.459036277770007
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum error correcting codes (QECC) are essential for constructing large-scale quantum computers that deliver faithful results. As strong competitors to the conventional surface code, quantum low-density parity-check (qLDPC) codes are emerging rapidly: they offer high encoding rates while maintaining reasonable physical-qubit connectivity requirements. Despite the existence of numerous code constructions, a notable gap persists between these designs -- some of which remain purely theoretical -- and their circuit-level deployment. In this work, we propose Auto-Stabilizer-Check (ASC), a universal compilation framework that generates depth-optimal syndrome extraction circuits for arbitrary qLDPC codes. ASC leverages the sparsity of parity-check matrices and exploits the commutativity of X and Z stabilizer measurement subroutines to search for optimal compilation schemes. By iteratively invoking an SMT solver, ASC returns a depth-optimal solution if a satisfying assignment is found, and a near-optimal solution in cases of solver timeouts. Notably, ASC provides the first definitive answer to one of IBM's open problems: for all instances of bivariate bicycle (BB) code reported in their work, our compiler certifies that no depth-6 syndrome extraction circuit exists. Furthermore, by integrating ASC with an end-to-end evaluation framework -- one that assesses different compilation settings under a circuit-level noise model -- ASC reduces circuit depth by approximately 50% and achieves an average 7x-8x suppression of the logical error rate for general qLDPC codes, compared with as-soon-as-possible (ASAP) and coloration-based scheduling. ASC thus substantially reduces manual design overhead and demonstrates its strong potential to serve as a key component in accelerating hardware deployment of qLDPC codes.

Related papers

• Quantum Compiler Design for Fault-Tolerant Quantum Computing [14.739903011159207]
  This survey presents a full-stack view of compiler design for QEC-protected quantum computation.<n>We organize existing work into three interacting layers: logical-level QEC compilation, physical-level QEC realization, and runtime integration.
  arXiv  Detail & Related papers  (2026-09-15T17:05:49Z)
• Coset Ensemble Decoder for Quantum Error Correction with Algorithm-Hardware Co-Design [16.143601808851162]
  quantum error correction (QEC) continuously extracts and decodes error syndromes in real time.<n>A critical component in QEC is the decoder, a classical subsystem that must simultaneously deliver high logical accuracy and ultra-low latency.<n>This paper presents a novel algorithm-hardware co-design that improves the accuracy-latency trade-off over existing approaches.
  arXiv  Detail & Related papers  (2026-06-09T16:37:13Z)
• GeneCS: Synthesizing Resource-Efficient Code Surgery for Arbitrary Quantum Stabilizer Codes [3.088254741965685]
  GeneCS is a resource-efficient compiler for synthesizing code surgery protocols for arbitrary stabilizer codes.<n> Experimental results show that GeneCS achieves an average reduction of over $85%$ in ancillary qubits.
  arXiv  Detail & Related papers  (2026-05-20T21:17:42Z)
• Synthesis and Optimization of Encoding Circuits for Fault-Tolerant Quantum Computation [4.561664406615985]
  We develop methods for synthesizing efficient encoders for arbitrary stabilizer codes.<n>For families with a modular structure, such as tableaud and holographic codes, we show how large encoders can be assembled from optimized local constituent encoders.<n>We obtain improvements of up to 43% in two-qubit gate count and up to 70% in depth.
  arXiv  Detail & Related papers  (2026-05-14T18:00:01Z)
• Focus Session: LLM4PQC -- An Agentic Framework for Accurate and Efficient Synthesis of PQC Cores [12.18204758079849]
  The design of post-quantum cryptography (PQC) hardware is a complex and hierarchical process.<n>A primary bottleneck is the conversion of PQC reference codes from C to high-level synthesis (HLS) specifications.<n>Here, we propose LLM4PQC, an agentic framework that synthesizes high-level PQC specifications and reference C codes into synthesizable C code.
  arXiv  Detail & Related papers  (2026-02-10T15:53:37Z)
• Continual Quantum Architecture Search with Tensor-Train Encoding: Theory and Applications to Signal Processing [68.35481158940401]
  CL-QAS is a continual quantum architecture search framework.<n>It mitigates challenges of costly encoding amplitude and forgetting in variational quantum circuits.<n>It achieves controllable robustness expressivity, sample-efficient generalization, and smooth convergence without barren plateaus.
  arXiv  Detail & Related papers  (2026-01-10T02:36:03Z)
• Bosonic quantum computing with near-term devices and beyond [0.0]
  This thesis investigates scalable fault-tolerant quantum computation.<n>We develop bosonic quantum codes, quantum LDPC codes, and decoding protocols that connect continuous-variable and discrete-variable error correction.
  arXiv  Detail & Related papers  (2025-12-17T04:01:54Z)
• Constraint-Optimal Driven Allocation for Scalable QEC Decoder Scheduling [3.7768601360100647]
  Fault-tolerant quantum computing requires fast and accurate decoding of Quantum Error Correction syndromes.<n>In large-scale systems, the number of available decoders is much smaller than the number of logical qubits, leading to a fundamental resource shortage.<n>To address this limitation, Virtualized Quantum Decoder (VQD) architectures have been proposed to share a limited pool of decoders across multiple qubits.
  arXiv  Detail & Related papers  (2025-12-02T09:07:00Z)
• Fast correlated decoding of transversal logical algorithms [67.01652927671279]
  Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead.<n>Recent advances have shown that by jointly decoding logical qubits in algorithms composed of logical gates, the number of syndrome extraction rounds can be reduced.<n>Here, we reform the problem of decoding circuits by directly decoding relevant logical operator products as they propagate through the circuit.
  arXiv  Detail & Related papers  (2025-05-19T18:00:00Z)
• QUITS: A modular Qldpc code circUIT Simulator [0.6383572393537065]
  QUITS is a modular and flexible circuit-level simulator for QLDPC codes.<n>We introduce a syndrome extraction circuit improved from Tremblay, Delfosse, and Beverland.<n>We evaluate the performance of state-of-the-art QLDPC codes and decoders under various settings.
  arXiv  Detail & Related papers  (2025-04-03T15:14:13Z)
• Near-optimal decoding algorithm for color codes using Population Annealing [44.99833362998488]
  We implement a decoder that finds the recovery operation with the highest success probability. We study the decoder performance on a 4.8.8 color code lattice under different noise models.
  arXiv  Detail & Related papers  (2024-05-06T18:17:42Z)
• Modular decoding: parallelizable real-time decoding for quantum computers [55.41644538483948]
  Real-time quantum computation will require decoding algorithms capable of extracting logical outcomes from a stream of data generated by noisy quantum hardware. We propose modular decoding, an approach capable of addressing this challenge with minimal additional communication and without sacrificing decoding accuracy. We introduce the edge-vertex decomposition, a concrete instance of modular decoding for lattice-surgery style fault-tolerant blocks.
  arXiv  Detail & Related papers  (2023-03-08T19:26:10Z)
• Deep Quantum Error Correction [73.54643419792453]
  Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. In this work, we efficiently train novel emphend-to-end deep quantum error decoders. The proposed method demonstrates the power of neural decoders for QECC by achieving state-of-the-art accuracy.
  arXiv  Detail & Related papers  (2023-01-27T08:16:26Z)
• Neural Belief Propagation Decoding of Quantum LDPC Codes Using Overcomplete Check Matrices [60.02503434201552]
  We propose to decode QLDPC codes based on a check matrix with redundant rows, generated from linear combinations of the rows in the original check matrix. This approach yields a significant improvement in decoding performance with the additional advantage of very low decoding latency.
  arXiv  Detail & Related papers  (2022-12-20T13:41:27Z)
• Entanglement Purification with Quantum LDPC Codes and Iterative Decoding [5.5165579223151795]
  We use QLDPC codes to distill GHZ states, as the resulting high-fidelity logical GHZ states can interact directly with the code used to perform distributed quantum computing. Our results apply to larger size GHZ states as well, where we extend our technical result about a measurement property of $3$-qubit GHZ states to construct a scalable GHZ purification protocol.
  arXiv  Detail & Related papers  (2022-10-25T16:42:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.