Approximate simulation of complex quantum circuits using sparse tensors
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Quantum Physics arXiv:2602.04011 (quant-ph) [Submitted on 3 Feb 2026] Title:Approximate simulation of complex quantum circuits using sparse tensors Authors:Benjamin N. Miller, Peter K. Elgee, Jason R. Pruitt, Kevin C. Cox View a PDF of the paper titled Approximate simulation of complex quantum circuits using sparse tensors, by Benjamin N. Miller and 3 other authors View PDF HTML (experimental) Abstract:The study of quantum circuit simulation using classical computers is a key research topic that helps define the boundary of verifiable quantum advantage, solve quantum many-body problems, and inform development of quantum hardware and software. Tensor networks have become forefront mathematical tools for these tasks. Here we introduce a method to approximately simulate quantum circuits using sparsely-populated tensors. We describe a sparse tensor data structure that can represent quantum states with no underlying symmetry, and outline algorithms to efficiently contract and truncate these tensors. We show that the data structure and contraction algorithm are efficient, leading to expected runtime scalings versus qubit number and circuit depth. Our results motivate future research in optimization of sparse tensor networks for quantum simulation. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2602.04011 [quant-ph] (or arXiv:2602.04011v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.04011 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Benjamin Miller [view email] [v1] Tue, 3 Feb 2026 20:58:32 UTC (4,742 KB) Full-text links: Access Paper: View a PDF of the paper titled Approximate simulation of complex quantum circuits using sparse tensors, by Benjamin N. Miller and 3 other authorsView PDFHTML (experimental)TeX Source view license Ancillary-file links: Ancillary files (details): sparse-circuit_submit/README.md sparse-circuit_submit/local_folder/local.txt sparse-circuit_submit/local_folder/results/10qbit_1layer_naive_bitwise.pkl sparse-circuit_submit/local_folder/results/dense_tree_plot_trunc.pkl sparse-circuit_submit/local_folder/results/diagram_dense.pkl sparse-circuit_submit/local_folder/results/diagram_sparse.pkl sparse-circuit_submit/notebooks/einsum_testing.ipynb sparse-circuit_submit/notebooks/figure_notebook.ipynb sparse-circuit_submit/notebooks/new_paper_results.ipynb sparse-circuit_submit/notebooks/paper_plots.ipynb sparse-circuit_submit/notebooks/paper_testing.ipynb sparse-circuit_submit/notebooks/test_mps.ipynb sparse-circuit_submit/notebooks/test_mps_plot.ipynb sparse-circuit_submit/notebooks/trunc_vs_fidelity.ipynb sparse-circuit_submit/pyproject.toml sparse-circuit_submit/scripts/generate_highest_prob_data.py sparse-circuit_submit/scripts/plot_bitwise_fidelity_v_runtime.py sparse-circuit_submit/scripts/plot_highest_prob_results.py sparse-circuit_submit/scripts/plot_runtimes.py sparse-circuit_submit/scripts/produce_fidelity_v_runtime.py sparse-circuit_submit/scripts/run_fidelity_tests.py sparse-circuit_submit/scripts/run_runtime_tests.py sparse-circuit_submit/src/sparse_circuit/__init__.py sparse-circuit_submit/src/sparse_circuit/benchmark_utils.py sparse-circuit_submit/src/sparse_circuit/bitwise64.py sparse-circuit_submit/src/sparse_circuit/bitwise_circuit.py sparse-circuit_submit/src/sparse_circuit/circuit_utils.py sparse-circuit_submit/src/sparse_circuit/circuits.py sparse-circuit_submit/src/sparse_circuit/np_gates.py sparse-circuit_submit/src/sparse_circuit/quimb_utils.py sparse-circuit_submit/tests/test_batch_time.py sparse-circuit_submit/tests/test_batched_circuit.py sparse-circuit_submit/tests/test_batched_equality.py sparse-circuit_submit/tests/test_bitwise.py sparse-circuit_submit/tests/test_bitwise_circuit.py sparse-circuit_submit/tests/test_fidelity_plot.py sparse-circuit_submit/tests/test_masked_sort.py sparse-circuit_submit/tests/test_topk_trim.py(33 additional files not shown) You must enabled JavaScript to view entire file list. 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