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arXiv:2604.21287

StabilizerBench: A Benchmark for AI-Assisted Quantum Error Correction Circuit Synthesis

Andres Paz, Christian Tarta, Cordelia Yuqiao Li, Mayee Sun, Sarju Patel, Sylvie Lausier

quant-phSubmitted Apr 23, 2026• Announced Apr 24, 2026• 0 citations
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Abstract

As quantum hardware scales toward fault tolerant operation, the demand for correct quantum error correction (QEC) circuits far outpaces manual design capacity. AI agents offer a promising path to automating this synthesis, yet no benchmark exists to measure their progress on the specialized task of generating QEC circuits. We introduce StabilizerBench, a benchmark suite of 192 stabilizer codes spanning 12 families, 4-196 qubits, and distances 2-21, organized into three tasks of increasing difficulty: state preparation circuit generation, circuit optimization under semantic constraints, and fault tolerant circuit synthesis. Although motivated by QEC, stabilizer circuits exercise core competencies required for general quantum programming, including gate decomposition, qubit routing, and semantic preserving transformations, while admitting efficient verification via the Gottesman Knill theorem, enabling the benchmark to scale to large codes without the exponential cost of full unitary comparison. We define a unified generator weighted scoring system with two tiers: a capability score measuring breadth of success and a quality score capturing circuit merit. We also introduce continuous fault tolerance and optimization metrics that grade error resilience and circuit improvements beyond binary pass or fail. Following the design of classical benchmarks such as SWE-bench, StabilizerBench specifies inputs, verification oracles, and scoring but leaves prompts and agent strategies open. We evaluate three frontier AI agents and find the benchmark discriminates across models and tasks with substantial headroom for improvement.

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OmniQEC: discovering practical quantum error-correcting codes by an AI scientist

Ge Yan, Shanchuan Li, Pengyue Ma +5 more

Quantum error correction (QEC) is indispensable for scalable fault-tolerant quantum computing. However, discovering QEC codes that remain effective is challenging, as logical performance depends on the interplay between code structure, hardware, syndrome extraction, and decoding, which often impose competing requirements. Here we introduce OmniQEC, an efficient AI scientist for discovering QEC codes suited to deployment on modern quantum processors. OmniQEC formulates QEC design as an iterative discovery process in which an orchestrator, implemented by advanced large language models (LLMs), coordinates code generation, code-level screening, syndrome-extraction synthesis, and decoder-based circuit evaluation. At its core, OmniQEC combines a self-evolving reasoning mechanism with a slow--fast synergistic workflow: a fast loop explores candidates using inexpensive code-level proxies, whereas a slow loop performs physically grounded circuit-level evaluation and feeds the resulting evidence back into the search. We evaluate OmniQEC across four qLDPC construction families, three LLM backends, and $14$ total-physical-qubit budgets per backend. The discovered codes show steadily improving logical-error suppression with increasing physical-qubit budgets and outperform the BB codes with $[\![72,12,6]\!]$ and $[\![144,12,12]\!]$ under complete-implementation budgets of 98 and 240 physical qubits, respectively. The discovered codes are hardware-friendly and may be of independent interest for practical QEC implementation. These findings pave the way towards LLM-assisted QEC discovery grounded in physically informed code--circuit--decoder co-design.

quant-pharXiv:2607.25865•Jul 29, 2026•0 citations

Automated Synthesis of Fault-Tolerant State Preparation Circuits for Quantum Error Correction Codes

Tom Peham, L. Schmid, Lucas Berent +2 more

A central ingredient in fault-tolerant quantum algorithms is the initialization of a logical state for a given quantum error-correcting code from a set of noisy qubits. A scheme that has demonstrated promising results for small code instances that are realizable on currently available hardware composes a non-fault-tolerant state preparation step with a verification step that checks for spreading errors. Known circuit constructions of this scheme are mostly obtained manually, and no algorithmic techniques for constructing depth- or gate-optimal circuits exist. As a consequence, the current state of the art exploits this scheme only for specific code instances and mostly for the special case of distance 3 codes. In this work, we propose an automated approach for synthesizing fault-tolerant state preparation circuits for arbitrary CSS codes. We utilize methods based on satisfiability solving (SAT) techniques to construct fault-tolerant state preparation circuits consisting of depth- and gate-optimal preparation and verification circuits. We also provide heuristics that can synthesize fault-tolerant state preparation circuits for code instances where no optimal solution can be obtained in an adequate timeframe. Moreover, we give a general construction for non-deterministic state preparation circuits beyond distance 3. Numerical evaluations using $d=3$ and $d=5$ codes confirm that the generated circuits exhibit the desired scaling of the logical error rates. The resulting methods are publicly available as part of the Munich Quantum Toolkit (MQT) at https://github.com/cda-tum/mqt-qecc. Such methods are an important step in providing fault-tolerant circuit constructions that can aid in near-term demonstration of fault-tolerant quantum computing.

arXiv:2408.11894•Aug 21, 2024•0 citations

PropHunt: Automated Optimization of Quantum Syndrome Measurement Circuits

Joshua Viszlai, Satvik Maurya, Swamit Tannu +2 more

Fault-Tolerant Quantum Computing (FTQC) relies on Quantum Error Correction (QEC) codes to reach error rates necessary for large scale quantum applications. At a physical level, QEC codes perform parity checks on data qubits, producing syndrome information, through Syndrome Measurement (SM) circuits. These circuits define a code's logical error rate and must be run repeatedly throughout the entire program. The performance of SM circuits is therefore critical to the success of a FTQC system. While ultimately implemented as physical circuits, SM circuits have challenges that are not addressed by existing circuit optimization tools. Importantly, inside SM circuits themselves errors are expected to occur, and how errors propagate through SM circuits directly impacts which errors are detectable and correctable, defining the code's logical error rate. This is not modeled in NISQ-era tools, which instead optimize for targets such as gate depth or gate count to mitigate the chance that any error occurs. This gap leaves key questions unanswered about the expected real-world effectiveness of QEC codes. In this work we address this gap and present PropHunt, an automated tool for optimizing SM circuits for CSS codes. We evaluate PropHunt on a suite of relevant QEC codes and demonstrate PropHunt's ability to iteratively improve performance and recover existing hand-designed circuits automatically. We also propose a near-term QEC application, Hook-ZNE, which leverages PropHunt's fine-grained control over logical error rate to improve Zero-Noise Extrapolation (ZNE), a promising error mitigation strategy.

quant-pharXiv:2601.17580•Jan 27, 2026•0 citations

Quantum Error Correction: From Stabilizer Codes to Fault-Tolerance Frontiers — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Quantum error correction (QEC) is advancing from theoretical stabilizer codes to practical fault-tolerance thresholds, with continuous-time formulations emerging as a key frontier. MATH: - **Stabilizer formalism**: Pauli group \( \mathcal{P}_n \) on \( n \) qubits; code space \( \mathcal{C} = \{|\psi\rangle : S_i|\psi\rangle = |\psi\rangle \ \forall i\} \), with \( S_i \) generators of an abelian subgroup of \( \mathcal{P}_n \). - **Distance & threshold**: A \([[n,k,d]]\) code corrects \( t = \lfloor (d-1)/2 \rfloor \) errors; fault-tolerance threshold \( p_{\text{th}} \approx 10^{-3} \)–\(10^{-2} \) per gate (surface code). - **Continuous-time QEC (CTQEC)**: Master equation \( \dot{\rho} = -i[H,\rho] + \sum_k \gamma_k \mathcal{D}[L_k]\rho \), with weak measurements and feedback; error rate scales as \( \gamma_k \propto (\text{measurement strength})^2 / \text{noise bandwidth} \). - **QuOps metric**: Reliable quantum operations \( \sim 10^3 \)–\(10^4 \) currently; tar Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

•Aug 23, 2026•0 citations

Synthesis and Optimization of Encoding Circuits for Fault-Tolerant Quantum Computation

Tom Peham, Matthew Steinberg, Robert Wille +1 more

Preparing arbitrary logical states is a central primitive for universal fault-tolerant quantum computation and the cost of encoded-state preparation contributes directly to the overall resource overhead. This makes the synthesis of efficient general-state encoding circuits an important problem, particularly with respect to two-qubit gate count and circuit depth. Yet the synthesis of such encoders has been studied less extensively than general Clifford circuit synthesis or the preparation of specific logical Pauli-eigenstates. In this work, we develop methods for synthesizing efficient encoders for arbitrary stabilizer codes. We formulate encoder synthesis as a search over stabilizer tableaus and introduce greedy and rollout-based algorithms that exploit the freedom among stabilizer-equivalent realizations of the same encoding isometry. For code families with a modular structure, such as generalized concatenated and holographic codes, we show how large encoders can be assembled from optimized local constituent encoders, and we use SMT-based exact synthesis to obtain optimal local circuits for small instances. We further evaluate the proposed methods on a broad set of stabilizer codes, including holographic and quantum low-density parity-check (qLDPC) codes, and compare them against recent encoder-synthesis methods and existing constructions from the literature, obtaining improvements of up to 43% in two-qubit gate count and up to 70% in depth. Our results support the optimization of encoded-state preparation in several fault-tolerant quantum-computing schemes, and all methods are openly available as part of the Munich Quantum Toolkit.

quant-pharXiv:2605.15266•May 18, 2026•0 citations

Quantum Circuit Discovery for Fault-Tolerant Logical State Preparation with Reinforcement Learning

Remmy A. M. Zen, Jan Ollé, Luis Colmenárez +3 more

The realization of large-scale quantum computers requires not only quantum error correction but also fault-tolerant (FT) operations to handle errors that propagate into harmful errors. Recently, flag-based protocols have been introduced that use ancillary qubits to flag harmful errors. However, there is no clear recipe for finding a FT quantum circuit with flag-based protocols, especially when we consider hardware constraints, such as the qubit connectivity and available gate set. This work presents a novel approach to automatically discover compact and hardware-adapted FT quantum circuits to make significant progress towards scalable FT quantum computing. We employ reinforcement learning (RL) as an enabling tool, leveraging a fast, parallelized stabilizer quantum circuit simulator and a nontrivial reward function specifically adapted to the problem. We show that, in the task of FT logical state preparation, RL discovers not only circuits with fewer gates and ancillary qubits than published results but also novel circuits without and with hardware constraints of up to distance-5 codes with 25 physical qubits, and they can be implemented directly in experiments. Furthermore, RL allows for straightforward exploration of different qubit connectivities and the use of transfer learning to accelerate the discovery. More generally, our work sets the framework towards the use of RL or other machine learning techniques for FT quantum circuit discovery with hardware constraints to make real progress towards the realization of large-scale quantum computers, addressing tasks beyond state preparation, including magic state preparation, logical gate synthesis, and syndrome measurement.

Physical Review X•Sep 11, 2025•8 citations
As quantum hardware scales toward fault tolerant operation, the demand for correct quantum error correction (QEC) circuits far outpaces manual design capacity. AI agents offer a promising path to automating this synthesis, yet no benchmark exists to measure their progress on the specialized task of generating QEC circuits. We introduce StabilizerBench, a benchmark suite of 192 stabilizer codes spanning 12 families, 4-196 qubits, and distances 2-21, organized into three tasks of increasing difficulty: state preparation circuit generation, circuit optimization under semantic constraints, and fault tolerant circuit synthesis. Although motivated by QEC, stabilizer circuits exercise core competencies required for general quantum programming, including gate decomposition, qubit routing, and semantic preserving transformations, while admitting efficient verification via the Gottesman Knill theorem, enabling the benchmark to scale to large codes without the exponential cost of full unitary comparison. We define a unified generator weighted scoring system with two tiers: a capability score measuring breadth of success and a quality score capturing circuit merit. We also introduce continuous fault tolerance and optimization metrics that grade error resilience and circuit improvements beyond binary pass or fail. Following the design of classical benchmarks such as SWE-bench, StabilizerBench specifies inputs, verification oracles, and scoring but leaves prompts and agent strategies open. We evaluate three frontier AI agents and find the benchmark discriminates across models and tasks with substantial headroom for improvement.
Quantum error correction (QEC) is indispensable for scalable fault-tolerant quantum computing. However, discovering QEC codes that remain effective is challenging, as logical performance depends on the interplay between code structure, hardware, syndrome extraction, and decoding, which often impose competing requirements. Here we introduce OmniQEC, an efficient AI scientist for discovering QEC codes suited to deployment on modern quantum processors. OmniQEC formulates QEC design as an iterative discovery process in which an orchestrator, implemented by advanced large language models (LLMs), coordinates code generation, code-level screening, syndrome-extraction synthesis, and decoder-based circuit evaluation. At its core, OmniQEC combines a self-evolving reasoning mechanism with a slow--fast synergistic workflow: a fast loop explores candidates using inexpensive code-level proxies, whereas a slow loop performs physically grounded circuit-level evaluation and feeds the resulting evidence back into the search. We evaluate OmniQEC across four qLDPC construction families, three LLM backends, and 141414 total-physical-qubit budgets per backend. The discovered codes show steadily improving logical-error suppression with increasing physical-qubit budgets and outperform the BB codes with [ ⁣[72,12,6] ⁣][\![72,12,6]\!][[72,12,6]] and [ ⁣[144,12,12] ⁣][\![144,12,12]\!][[144,12,12]] under complete-implementation budgets of 98 and 240 physical qubits, respectively. The discovered codes are hardware-friendly and may be of independent interest for practical QEC implementation. These findings pave the way towards LLM-assisted QEC discovery grounded in physically informed code--circuit--decoder co-design.
A central ingredient in fault-tolerant quantum algorithms is the initialization of a logical state for a given quantum error-correcting code from a set of noisy qubits. A scheme that has demonstrated promising results for small code instances that are realizable on currently available hardware composes a non-fault-tolerant state preparation step with a verification step that checks for spreading errors. Known circuit constructions of this scheme are mostly obtained manually, and no algorithmic techniques for constructing depth- or gate-optimal circuits exist. As a consequence, the current state of the art exploits this scheme only for specific code instances and mostly for the special case of distance 3 codes. In this work, we propose an automated approach for synthesizing fault-tolerant state preparation circuits for arbitrary CSS codes. We utilize methods based on satisfiability solving (SAT) techniques to construct fault-tolerant state preparation circuits consisting of depth- and gate-optimal preparation and verification circuits. We also provide heuristics that can synthesize fault-tolerant state preparation circuits for code instances where no optimal solution can be obtained in an adequate timeframe. Moreover, we give a general construction for non-deterministic state preparation circuits beyond distance 3. Numerical evaluations using d=3d=3d=3 and d=5d=5d=5 codes confirm that the generated circuits exhibit the desired scaling of the logical error rates. The resulting methods are publicly available as part of the Munich Quantum Toolkit (MQT) at https://github.com/cda-tum/mqt-qecc. Such methods are an important step in providing fault-tolerant circuit constructions that can aid in near-term demonstration of fault-tolerant quantum computing.
Fault-Tolerant Quantum Computing (FTQC) relies on Quantum Error Correction (QEC) codes to reach error rates necessary for large scale quantum applications. At a physical level, QEC codes perform parity checks on data qubits, producing syndrome information, through Syndrome Measurement (SM) circuits. These circuits define a code's logical error rate and must be run repeatedly throughout the entire program. The performance of SM circuits is therefore critical to the success of a FTQC system. While ultimately implemented as physical circuits, SM circuits have challenges that are not addressed by existing circuit optimization tools. Importantly, inside SM circuits themselves errors are expected to occur, and how errors propagate through SM circuits directly impacts which errors are detectable and correctable, defining the code's logical error rate. This is not modeled in NISQ-era tools, which instead optimize for targets such as gate depth or gate count to mitigate the chance that any error occurs. This gap leaves key questions unanswered about the expected real-world effectiveness of QEC codes. In this work we address this gap and present PropHunt, an automated tool for optimizing SM circuits for CSS codes. We evaluate PropHunt on a suite of relevant QEC codes and demonstrate PropHunt's ability to iteratively improve performance and recover existing hand-designed circuits automatically. We also propose a near-term QEC application, Hook-ZNE, which leverages PropHunt's fine-grained control over logical error rate to improve Zero-Noise Extrapolation (ZNE), a promising error mitigation strategy.
FINDING: Quantum error correction (QEC) is advancing from theoretical stabilizer codes to practical fault-tolerance thresholds, with continuous-time formulations emerging as a key frontier. MATH: - **Stabilizer formalism**: Pauli group Pn \mathcal{P}_n Pn​ on n n n qubits; code space C={∣ψ⟩:Si∣ψ⟩=∣ψ⟩ ∀i} \mathcal{C} = \{|\psi\rangle : S_i|\psi\rangle = |\psi\rangle \ \forall i\} C={∣ψ⟩:Si​∣ψ⟩=∣ψ⟩ ∀i}, with Si S_i Si​ generators of an abelian subgroup of Pn \mathcal{P}_n Pn​. - **Distance & threshold**: A [[n,k,d]][[n,k,d]][[n,k,d]] code corrects t=⌊(d−1)/2⌋ t = \lfloor (d-1)/2 \rfloor t=⌊(d−1)/2⌋ errors; fault-tolerance threshold pth≈10−3 p_{\text{th}} \approx 10^{-3} pth​≈10−3–10−210^{-2} 10−2 per gate (surface code). - **Continuous-time QEC (CTQEC)**: Master equation ρ˙=−i[H,ρ]+∑kγkD[Lk]ρ \dot{\rho} = -i[H,\rho] + \sum_k \gamma_k \mathcal{D}[L_k]\rho ρ˙​=−i[H,ρ]+∑k​γk​D[Lk​]ρ, with weak measurements and feedback; error rate scales as γk∝(measurement strength)2/noise bandwidth \gamma_k \propto (\text{measurement strength})^2 / \text{noise bandwidth} γk​∝(measurement strength)2/noise bandwidth. - **QuOps metric**: Reliable quantum operations ∼103 \sim 10^3 ∼103–10410^4 104 currently; tar Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Preparing arbitrary logical states is a central primitive for universal fault-tolerant quantum computation and the cost of encoded-state preparation contributes directly to the overall resource overhead. This makes the synthesis of efficient general-state encoding circuits an important problem, particularly with respect to two-qubit gate count and circuit depth. Yet the synthesis of such encoders has been studied less extensively than general Clifford circuit synthesis or the preparation of specific logical Pauli-eigenstates. In this work, we develop methods for synthesizing efficient encoders for arbitrary stabilizer codes. We formulate encoder synthesis as a search over stabilizer tableaus and introduce greedy and rollout-based algorithms that exploit the freedom among stabilizer-equivalent realizations of the same encoding isometry. For code families with a modular structure, such as generalized concatenated and holographic codes, we show how large encoders can be assembled from optimized local constituent encoders, and we use SMT-based exact synthesis to obtain optimal local circuits for small instances. We further evaluate the proposed methods on a broad set of stabilizer codes, including holographic and quantum low-density parity-check (qLDPC) codes, and compare them against recent encoder-synthesis methods and existing constructions from the literature, obtaining improvements of up to 43% in two-qubit gate count and up to 70% in depth. Our results support the optimization of encoded-state preparation in several fault-tolerant quantum-computing schemes, and all methods are openly available as part of the Munich Quantum Toolkit.
The realization of large-scale quantum computers requires not only quantum error correction but also fault-tolerant (FT) operations to handle errors that propagate into harmful errors. Recently, flag-based protocols have been introduced that use ancillary qubits to flag harmful errors. However, there is no clear recipe for finding a FT quantum circuit with flag-based protocols, especially when we consider hardware constraints, such as the qubit connectivity and available gate set. This work presents a novel approach to automatically discover compact and hardware-adapted FT quantum circuits to make significant progress towards scalable FT quantum computing. We employ reinforcement learning (RL) as an enabling tool, leveraging a fast, parallelized stabilizer quantum circuit simulator and a nontrivial reward function specifically adapted to the problem. We show that, in the task of FT logical state preparation, RL discovers not only circuits with fewer gates and ancillary qubits than published results but also novel circuits without and with hardware constraints of up to distance-5 codes with 25 physical qubits, and they can be implemented directly in experiments. Furthermore, RL allows for straightforward exploration of different qubit connectivities and the use of transfer learning to accelerate the discovery. More generally, our work sets the framework towards the use of RL or other machine learning techniques for FT quantum circuit discovery with hardware constraints to make real progress towards the realization of large-scale quantum computers, addressing tasks beyond state preparation, including magic state preparation, logical gate synthesis, and syndrome measurement.