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arXiv:2603.14641 · Quantum

GPU-Accelerated Quantum Simulation of Stabilizer Circuits

Muhammad Osama, Dimitrios Thanos, Alfons Laarman

quant-phSubmitted Mar 15, 2026• Announced Mar 17, 2026• 0 citations
v1 · Mar 15, 2026v2 · Sep 23, 2026
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Abstract

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.

Journal reference
Quantum 10, 2225 (2026)
DOI
10.22331/q-2026-10-01-2225

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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.
Abstract Equivalence checking plays a crucial role in quantum circuit compilation, optimization, and verification. Stabilizer circuits can be simulated classically by tracking the so-called stabilizer operators in linear time. But the simulation of large stabilizer circuits with thousands of qubits and gates, arising e.g. in the study of novel quantum error-correction protocols, still poses a challenge. In this work, we propose a GPU-based deterministic algorithm for equivalence checking of stabilizer circuits using the stabilizer tableau formalism. We explore various design choices and implement the most efficient version. Our algorithm significantly outperforms the state-of-the-art CCEC checker (which relies on the Stim simulator) in terms of time, memory, and energy. Our approach demonstrates up to two orders of magnitude speedup over existing methods. Notably, previous attempts at GPU acceleration in this area were unsuccessful, making this the first effective implementation.
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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.
Today's quantum processors have tens to hundreds of physical qubits, but reliable execution of arbitrary circuits remains limited to fewer than 30 entangled qubits across hardware modalities. Building upon prior work, we introduce an error- and topology-aware method for mapping multiple independent circuits onto disjoint regions of a single large-scale QPU for parallel circuit execution. For applications with many similarly sized circuits, such as observable estimation for Hamiltonian simulation, this approach can reduce billed QPU execution time, with ideal speedup proportional to the number of usable partitions. We demonstrate the approach on IBM's 156-qubit ibm_boston processor using standard QED-C benchmark and Hamiltonian-based observable-estimation workloads. Compared with standard sequential execution, parallel execution reduces billed execution time by 3.5-5.5x while retaining 83-92% of the sequential fidelity. We further evaluate the scaling of parallel circuit execution using GPU-accelerated classical simulation, distributing measurement circuits across GPUs via MPI. Using CUDA-Q on the NERSC Perlmutter system, we achieve up to 13.8x speedup on 16 GPUs (86% parallel efficiency) for an H2 electronic-structure simulation, with scaling evaluated across multiple Hamiltonians and circuit counts. These results provide an indication of the performance ceiling that parallel execution on future quantum hardware may eventually approach. Both execution modes are implemented as a runtime option within the QED-C Application-Oriented Benchmark suite. Together, the results show that circuit-level parallelism can reduce execution cost on current quantum hardware and simulation time on GPU clusters, with the potential for greater benefits as device quality and qubit counts increase.
In recent years, quantum computing has undergone significant developments and has established its supremacy in many application domains. While quantum hardware is accessible to the public through the cloud environment, a robust and efficient quantum circuit simulator is necessary to investigate the constraints and foster quantum computing development, such as quantum algorithm development and quantum device architecture exploration. In this paper, we observe that most of the publicly available quantum circuit simulators (e.g., QISKit from IBM, QDK from Microsoft, and Qsim-Cirq from Google) suffer from slow simulation and poor scalability when the number of qubits increases. To this end, we systematically investigate the deficiencies in quantum circuit simulation (QCS) and propose Q-GPU, a framework that leverages GPUs with comprehensive optimizations to allow efficient and scalable QCS. Specifically, Q-GPU features i) proactive state amplitude transfer, ii) zero state amplitude pruning, iii) delayed qubit involvement, and iv) lossless nonzero state amplitude compression. Experimental results across nine representative quantum circuits indicate that Q-GPU significantly reduces the execution time of the state-of-the-art GPU-based QCS by 71.89% (3.55× speedup). Q-GPU also outperforms the state-of-the-art OpenMP CPU implementation, the Google Qsim-Cirq simulator, and the Microsoft QDK simulator by 1.49×, 2.02×, and 10.82×, respectively.
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.