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Qimax: Efficient quantum simulation via GPU-accelerated extended stabilizer formalism

Vu Tuan Hai, Bui Cao Doanh, Le Vu Trung Duong, Pham Hoai Luan, Yasuhiko Nakashima

TL;DR

This work tackles the challenge of efficiently classically simulating Clifford and near-Clifford circuits by advancing the extended stabilizer formalism with GPU-accelerated parallelism. The authors introduce Qimax, a three-mode system that uses instruction grouping and base-4 tensor encodings to accelerate stabilizer updates on GPUs, with v3 employing ragged tensors to reduce memory for non-Clifford expansions. Benchmarks show that Qimax, particularly in its v3 form, can outperform GPU-accelerated Qiskit and Pennylane in large-gate-count scenarios, though circuits with high stabilizer rank still scale as $O(4^n)$ versus $O(2^n)$ for state-vector methods. The approach broadens the practicality of stabilizer-based simulation for large Clifford and near-Clifford circuits and lays groundwork for integration with variational quantum algorithms and quantum machine learning workloads, especially where GPU parallelism is beneficial.

Abstract

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.

Qimax: Efficient quantum simulation via GPU-accelerated extended stabilizer formalism

TL;DR

This work tackles the challenge of efficiently classically simulating Clifford and near-Clifford circuits by advancing the extended stabilizer formalism with GPU-accelerated parallelism. The authors introduce Qimax, a three-mode system that uses instruction grouping and base-4 tensor encodings to accelerate stabilizer updates on GPUs, with v3 employing ragged tensors to reduce memory for non-Clifford expansions. Benchmarks show that Qimax, particularly in its v3 form, can outperform GPU-accelerated Qiskit and Pennylane in large-gate-count scenarios, though circuits with high stabilizer rank still scale as versus for state-vector methods. The approach broadens the practicality of stabilizer-based simulation for large Clifford and near-Clifford circuits and lays groundwork for integration with variational quantum algorithms and quantum machine learning workloads, especially where GPU parallelism is beneficial.

Abstract

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.
Paper Structure (18 sections, 9 equations, 5 figures, 2 tables, 2 algorithms)

This paper contains 18 sections, 9 equations, 5 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Extended stabilizer formalism
  4. Gate set
  5. Limitation of extended stabilizer formalism
  6. Proposed techniques
  7. Instruction
  8. Encoding
  9. Gate
  10. 1-qubit gate
  11. 2-qubit gate
  12. Main algorithm
  13. Implementation
  14. Experiments
  15. Conclusion
  16. ...and 3 more sections

Figures (5)

  • Figure 1: The order $n'$ on four generators is shown as four black lines, ranging from 1 to $4^4$. The gate application's order is from qubit $0^{\text{th}}$ to qubit $(n-1)^{\text{th}}$, left to right. We are considering the worst cases by using 4-qubit $|XYZ+\text{chain}\rangle$ ansatz, the circuit representation can be found in Fig. \ref{['fig:operator']} (b).
  • Figure 2: (a) A quantum circuit can be divided into $\{U_k\},\{V_k\}$, and end up with $U_{K-1}$ or $V_{K'-1}$ (b) $XYZ+W_{\text{chain}}$ topology.
  • Figure 3: The average stabilizer rank between circuit, while $|XYZ+chain\rangle$ and max stabilizer rank increase exponential ($\mathcal{O}(2^n)$ and $\mathcal{O}(4^n)$ ), GHZ and Graph are fixed as $1$.
  • Figure 4: The execution time for GHZ circuit and graph circuit on Qimax, these circuits are generated from MQT Bench quetschlich2023mqtbench.
  • Figure 5: Execution time from different versions of Pennylane, Qiskit, and Qimax. The y-axis is plotted on logarithmic scale. The range of #Qubits is 2 to 15.

Theorems & Definitions (3)

  • Example 1
  • Example 2
  • Example 3