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arXiv:2507.03092

STABSim: A Parallelized Clifford Simulator with Features Beyond Direct Simulation

Sean R. Garner, Liu, Chenxu, Meng Wang, Stein, Samuel, Ang Li

Published Jul 3, 2025• 0 citations
arXivHTMLPDF

Abstract

The quantum stabilizer formalism became foundational for understanding error correction soon after the realization of the first useful quantum error correction codes. Stabilizers provide a way to describe sets of quantum states which are valid codewords within a quantum error correction (QEC) scheme. Existing stabilizer simulators are single threaded applications used to sample larger codes than is possible with other methods. However, there is an outstanding gap in the scaling and accuracy of current simulators for QEC as quantum computing exceeds hundreds of qubits, along with an under-utilization of the capabilities of highly-efficient stabilizer simulation across other quantum domains. In this work, we present the first GPU-accelerated tableau stabilizer simulator to scale better than CPU methods in QEC workloads, by trivializing Clifford gates and exploiting the large parallelism of dedicated GPUs with CUDA warp-level primitives to quickly overcome costly measurement gates. We then implement a new error model that captures non-unitarity in T1/T2 error channels much faster and with exact accuracy for most physical qubits, demonstrate a chemistry use case, and present a new Clifford+T to Pauli-Based Computing (PBC) transpilation optimization through our simulator.

DOI
10.48550/arxiv.2507.03092

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The quantum stabilizer formalism became foundational for understanding error correction soon after the realization of the first useful quantum error correction codes. Stabilizers provide a way to describe sets of quantum states which are valid codewords within a quantum error correction (QEC) scheme. Existing stabilizer simulators are single threaded applications used to sample larger codes than is possible with other methods. However, there is an outstanding gap in the scaling and accuracy of current simulators for QEC as quantum computing exceeds hundreds of qubits, along with an under-utilization of the capabilities of highly-efficient stabilizer simulation across other quantum domains. In this work, we present the first GPU-accelerated tableau stabilizer simulator to scale better than CPU methods in QEC workloads, by trivializing Clifford gates and exploiting the large parallelism of dedicated GPUs with CUDA warp-level primitives to quickly overcome costly measurement gates. We then implement a new error model that captures non-unitarity in T1/T2 error channels much faster and with exact accuracy for most physical qubits, demonstrate a chemistry use case, and present a new Clifford+T to Pauli-Based Computing (PBC) transpilation optimization through our simulator.
We introduce new parallel algorithms for efficiently simulating stabilizer (Clifford) circuits on GPUs, with a focus on data-parallel tableau evolution and scalable handling of projective measurements. Our approach reformulates key bottlenecks in stabilizer simulation -- such as Gaussian elimination and measurement updates -- into GPU-tailored primitives that eliminate sequential dependencies and maximize memory coalescing. We implement these techniques in QuaSARQ, a GPU-accelerated stabilizer simulator designed for large qubit counts and many-shot sampling. Across a broad benchmark suite reaching 180,000 qubits and depth 1,000 (roughly 130M gates), QuaSARQ shows substantial runtime improvements, with up to 105×\times× speedup, and over 80% energy reduction on demanding instances. Moreover, QuaSARQ consistently outperforms Stim, a state-of-the-art CPU-optimized stabilizer simulator, as well as Qiskit-Aer (CPU/GPU), Qibo, Cirq, and PennyLane. Finally, QuaSARQ exhibits a significant advantage in many-shot sampling on large workloads. These results demonstrate that our parallel algorithms can significantly advance the scalability of stabilizer-circuit simulation, particularly for workloads involving extensive measurements and sampling.
Fault-tolerant quantum design relies on simulating noisy quantum error correction (QEC) circuits with hundreds to thousands of physical qubits and large circuit depths. High-throughput stabilizer simulators, such as Stim, are the de facto tools for this regime. However, these simulators typically support only Clifford gates and stochastic Pauli noise. As a result, more realistic device noise models-such as coherent control errors and thermal relaxation-are often approximated using Pauli Twirling. This replacement offers speed but can introduce inaccuracies. To address this, we propose QuasiStim for scalable exact QEC simulation of realistic noise, with QuasiFold as a compiler frontend and DeltaFrame as a sampling backend. QuasiFold lowers sampling overhead by merging equivalent non-Pauli sites in the quantum circuit. DeltaFrame samples the resulting stabilizer trajectories by reusing precomputed predicted references instead of resimulating the full tableau for each shot. QuasiFold can reduce the number of shots by over 100×100\times100× on bivariate-bicycle (BB) codes. Compared to a per-shot tableau simulator, DeltaFrame is 166×166\times166×--1331×1331\times1331× faster on rotated surface-code memory under coherent RZR_ZRZ​ noise as ddd grows from 5 to 35. QuasiStim also makes the PTA bias measurable: the gap is non-negligible and varies with noise strength, decoder, and circuit schedule. QuasiStim will be open-sourced upon publication at https://github.com/isaachyw/QuasiStim
The preparation of high-fidelity logical magic states is a crucial subroutine for universal fault-tolerant quantum computation (FTQC). Predicting the performance of FTQC and developing improved protocols rely on numerical methods to classically simulate logical magic state preparation in the presence of noise. Clifford logic on Pauli-stabilizer codes with circuit-level Pauli errors can be efficiently simulated using Pauli-stabilizer formalism, but the non-Clifford operations required to prepare logical magic states render generic simulation inefficient. We introduce Clifford-stabilizer simulation, an exact and efficient algorithm based on updating a Clifford-stabilizer group to simulate noisy preparation protocols for a broad class of logical magic states used to implement non-Clifford gates in the third level of the Clifford hierarchy under circuit-level Pauli errors. Clifford-stabilizer simulation applies to a range of operations that commonly appear in preparation protocols for such logical magic states, including Pauli-stabilizer measurements, logical Clifford measurements, and transversal non-Clifford gates. Our algorithm for Clifford-stabilizer simulation maps a non-Clifford circuit with sampled circuit-level Pauli errors to a Clifford circuit that exactly reproduces its measurement outcome distribution, achieving time and space complexities polynomial in relevant protocol parameters. We perform exact simulation of magic state cultivation up to fault distance 7 by Clifford-stabilizer simulation. Our method provides a route to perform exact benchmarking of large-scale logical magic state preparation protocols required for useful FTQC.
Simulating Clifford and near-Clifford circuits using the extended stabilizer formalism has become increasingly popular, particularly in quantum error correction. Compared to the state-vector approach, the extended stabilizer formalism can solve the same problems with fewer computational resources, as it operates on stabilizers rather than full state vectors. Most existing studies on near-Clifford circuits focus on balancing the trade-off between the number of ancilla qubits and simulation accuracy, often overlooking performance considerations. Furthermore, in the presence of high-rank stabilizers, performance is limited by the sequential property of the stabilizer formalism. In this work, we introduce a parallelized version of the extended stabilizer formalism, enabling efficient execution on multi-core devices such as GPU. Experimental results demonstrate that, in certain scenarios, our Python-based implementation outperforms state-of-the-art simulators such as Qiskit and Pennylane.
Simulating quantum error correction (QEC) circuits including non-Clifford gates at scale is important to accelerate progress toward fault-tolerant quantum computing. Here we demonstrate that matrix product state (MPS) techniques can handle many QEC circuits exactly and without restriction on gate types. Crucially, we find that MPS efficiency depends sensitively on implementation choices, and we introduce a series of targeted optimizations that reduce bond dimensions and simulation time by several orders of magnitude compared to naive approaches. We illustrate this with examples including: (a) a rotated surface code quantum memory up to distance 11, (b) logical Bell-state preparation up to distance 9, (c) a 15-to-1 magic-state distillation circuit including hundreds of QEC rounds that we optimize to be simulated with only 11 logical qubits (187 physical qubits) and a maximal bond dimension of 64 in under 40 seconds, and (d) a narrow, deep random circuit that scales linearly with the number of T gates. These results demonstrate the importance of circuit-level optimizations and position MPS as a valuable complement to near-Clifford simulators for QEC circuits.
Exact classical simulation of fault-tolerant quantum circuits remains limited by a tradeoff between exponential state vector scaling, exponential TTT-count scaling in stabilizer-rank approaches, and per-shot tracking overhead in sparse generalized stabilizer simulators. In this work, we introduce Clifft, an open-source simulator that shifts the dominant exponential cost from the total qubit count to a dynamic active subspace by factoring the quantum state into an offline Clifford frame, an online Pauli frame, and a dynamically sized active state vector. This architecture resolves deterministic Clifford coordinate transformations ahead of time, generalizing Stim's compile-once, sample-many execution model to circuits with non-Clifford operations. Consequently, exponential simulation costs are determined by the peak active virtual dimension, which expands during non-Clifford operations and contracts during measurements. Clifft remains within a constant factor of standard tools in the pure-Clifford and non-Clifford limits, while delivering up to orders-of-magnitude throughput gains over GPU-accelerated near-Clifford simulators on low-magic fault-tolerant benchmarks. Executing on commodity CPUs and exposing a Stim-like API, Clifft enables, to our knowledge, the first exact end-to-end simulation of magic state cultivation including the escape stage, over hundreds of billions of shots. These simulations show that escape-stage failures suppress the discrepancy between the true TTT-gate circuit and its SSS-proxy at low decoder-gap thresholds, while at high thresholds the full-protocol behavior approaches the larger discrepancy observed in the cultivation stages alone.