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arXiv:2512.01943

Automated Compilation Including Dropouts: Tolerating Defective Components in Stabiliser Codes

Stasiu Wolanski

quant-phSubmitted Dec 1, 2025• Announced Dec 2, 2025• 0 citations
v1 · Dec 1, 2025v2 · Jan 11, 2026
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Abstract

Utility-scale solid-state quantum devices will need to fabricate quantum devices at scale using imperfect processes. By introducing tolerance to fabrication defects into the design of the quantum devices, we can improve the yield of usable quantum chips and lower the cost of useful systems. Automated Compilation Including Dropouts (ACID) is a framework that works in the ancilla-free (or `middle-out') paradigm, to generate syndrome extraction circuits for general stabiliser codes in the presence of defective couplers or qubits. In the ancilla-free paradigm, we do not designate particular qubits as measurement ancillas, instead measuring stabilisers using any of the data qubits in their support. This approach leads to a great deal of flexibility in how syndrome extraction circuits can be implemented. ACID works by constructing and solving an optimisation problem within the ancilla-free paradigm to find a short syndrome extraction circuit. Applied to the surface code, ACID produces syndrome-extraction circuits of depth between $1\times$ (no overhead) and $1.5\times$ relative to the depth of defect-free circuits. The LUCI algorithm, the best prior art, yielded a $2 \times$ overhead, so ACID offers a significant time saving. The yield of surface code chips with a logical error rate at most $10\times$ the dropout-free baseline is up to $3\times$ higher using ACID than using LUCI. I demonstrate the broad applicability of ACID by compiling syndrome extraction circuits for bivariate bicycle codes and the colour code. For these circuits, we incur a circuit-depth overhead of between $1\times$ (no overhead) and $2.5\times$ relative to defect-free circuits. I believe this work is the first to simulate both of these families of codes in the presence of fabrication defects.

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Utility-scale solid-state quantum devices will need to fabricate quantum devices at scale using imperfect processes. By introducing tolerance to fabrication defects into the design of the quantum devices, we can improve the yield of usable quantum chips and lower the cost of useful systems. Automated Compilation Including Dropouts (ACID) is a framework that works in the ancilla-free (or `middle-out') paradigm, to generate syndrome extraction circuits for general stabiliser codes in the presence of defective couplers or qubits. In the ancilla-free paradigm, we do not designate particular qubits as measurement ancillas, instead measuring stabilisers using any of the data qubits in their support. This approach leads to a great deal of flexibility in how syndrome extraction circuits can be implemented. ACID works by constructing and solving an optimisation problem within the ancilla-free paradigm to find a short syndrome extraction circuit. Applied to the surface code, ACID produces syndrome-extraction circuits of depth between 1×1\times1× (no overhead) and 1.5×1.5\times1.5× relative to the depth of defect-free circuits. The LUCI algorithm, the best prior art, yielded a 2×2 \times2× overhead, so ACID offers a significant time saving. The yield of surface code chips with a logical error rate at most 10×10\times10× the dropout-free baseline is up to 3×3\times3× higher using ACID than using LUCI. I demonstrate the broad applicability of ACID by compiling syndrome extraction circuits for bivariate bicycle codes and the colour code. For these circuits, we incur a circuit-depth overhead of between 1×1\times1× (no overhead) and 2.5×2.5\times2.5× relative to defect-free circuits. I believe this work is the first to simulate both of these families of codes in the presence of fabrication defects.
Recently, usage of detecting regions facilitated the discovery of new circuits for fault-tolerantly implementing the surface code. Building on these ideas, we present LUCI, a framework for constructing fault-tolerant circuits flexible enough to construct aperiodic and anisotropic circuits, making it a clear step towards quantum error correction beyond static codes. We show that LUCI can be used to adapt surface code circuits to lattices with imperfect qubit and coupler yield, a key challenge for fault-tolerant quantum computers using solid-state architectures. These circuits preserve spacelike distance for isolated broken couplers or isolated broken measure qubits in exchange for halving timelike distance, substantially reducing the penalty for dropout compared to the state of the art and creating opportunities in device architecture design. For qubit and coupler dropout rates of 1% and a patch diameter of 15, LUCI achieves an average spacelike distance of 13.1, compared to 9.1 for the best method in the literature. For a SI1000(0.001) circuit noise model, this translates to a 36x improvement in median logical error rate per round, a factor which increases with device performance. At these dropout and error rates, LUCI requires roughly 25% fewer physical qubits to reach algorithmically relevant one-in-a-trillion logical codeblock error rates.
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.
Long-lived logical qubits are essential for fault-tolerant quantum computation. However, the practical performance of traditional error correction protocols relies on performing specific syndrome circuits, causing vulnerability to hardware defects and imposing rigid connectivity constraints. Recent theoretical findings have proposed that flexible subroutine circuits within the LUCI framework can maintain space-time distance in the presence of isolated or broken components, albeit at the expense of temporal distance. However, these approaches have solely targeted defect avoidance and have not yet been demonstrated to suppress errors with reduced temporal distances on physical hardware. In this work, we propose a reset-free scenario for the LUCI framework and experimentally benchmark it on IBM quantum hardware. By asymmetrically scaling the XXX or ZZZ distance, we compare our reset-free approach against the standard surface code and successfully demonstrate error suppression ratios for targeted logical Pauli errors. Remarkably, despite a nearly halved syndrome density in time, which requires two subroutine rounds for full syndrome extraction, the LUCI framework remains competitive with the rotated surface code implementation. In the LUCI framework, we observe error suppression of 1.75(10)1.75(10)1.75(10) for logical XXX errors and 1.93(12)1.93(12)1.93(12) for logical ZZZ errors, whereas the standard approach yields $ 1.58(13)$ and 2.44(7)2.44(7)2.44(7), respectively. These results demonstrate that dynamic codes outperform standard methods by avoiding highly noisy components, even without physical defects, while preserving logical boundaries. Our findings challenge the conventional dependency on static fault-tolerant architectures by verifying the feasibility and efficacy of the LUCI framework on physical hardware and pave the way for hybrid, hardware-compatible code designs in quantum computing.
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.
Recent work has shown that fabrication defects can be well-handled using a strategy relying on the mid-error-correction-cycle state. In this work we present two improvements to the original prescription. First, we quantify the impact of the choice of a more complete set of gauge operators originally proposed for the hex-grid surface code on the standard square-grid surface code, as well as a new method for excising effectively unused qubits. Second, we leverage the expressivity of the LUCI framework as an intermediate representation, using integer linear programming to find performant physical circuits from the large space of valid LUCI circuits. We show that on the d=11d = 11d=11 surface code at 1%(3%)1\%(3\%)1%(3%) dropout rate for qubits and couplers, these optimizations allow for a total improvement of 14.5%(23.6%)14.5\%(23.6\%)14.5%(23.6%) over 4d4d4d round of syndrome extraction using the SI1000 noise model at 0.1%0.1\%0.1% noise.
We present a fast and effective framework for analysing and designing syndrome extraction circuits (SECs). Our approach is based on left--right circuits, a general SEC design that maintains low depth and avoids gate interleaving constraints by staggering XXX and ZZZ stabiliser checks. Initially proposed for specific classes of codes, we generalise this construction to arbitrary CSS codes and optimise the circuit structure to achieve low qubit idling time, large effective distance, and reduced minimum-weight failure mechanisms. A key component of our framework is the formal notion of residual errors and their associated distance metrics, which form lightweight proxies for capturing error propagation and quantifying the potential harm of circuit-level errors. Applying our automated framework to diverse classes of codes, we observe consistent improvements in logical performance of up to an order of magnitude compared to existing single-ancilla SEC designs. Moreover, by directly applying these proxies, we prove that no non-interleaving SEC can achieve circuit distance 121212 for the gross code, and we identify an explicit circuit that we conjecture achieves distance 111111, exceeding previously known constructions.