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GPU-Accelerated Quantum Simulation of Stabilizer Circuits

Muhammad Osama, Dimitrios Thanos, Alfons Laarman

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.

GPU-Accelerated Quantum Simulation of Stabilizer Circuits

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 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.
Paper Structure (51 sections, 20 equations, 9 figures, 1 table, 9 algorithms)

This paper contains 51 sections, 20 equations, 9 figures, 1 table, 9 algorithms.

Table of Contents

  1. Introduction
  2. Contributions.
  3. Related Work.
  4. Preliminaries
  5. Quantum States and Gates
  6. Circuit Simulation
  7. Stabilizer Circuits
  8. Tableau Formalism
  9. Measurements in the Stabilizer Formalism
  10. The CHP algorithm aaronson2008improved.
  11. Innovations introduced by Stim simulator stim.
  12. GPU Programming
  13. Algorithmic Conventions
  14. Key Challenges for Parallel Measurement and Approach
  15. Identifying Probabilistic Measurements
  16. ...and 36 more sections

Figures (9)

  • Figure 1: GPU architecture hitchHikemultiGPU.
  • Figure 2: Input circuit on the left. Scheduled circuit on the right.
  • Figure 3: Logical and physical formats of a word-aligned tableau.
  • Figure 4: Running example of \ref{['alg:buildTableau']} on 128-qubit system.
  • Figure 5: Compacting pivots on a 6-qubit tableau.
  • ...and 4 more figures

Theorems & Definitions (5)

  • Definition 1: Weak Simulation
  • Example 1
  • Definition 2: Gate Dependency Relation
  • Definition 3: Parallel Gates
  • Definition 4: Maximal Window