REVIEW 1 major objections 4 minor 45 references
Aicir: A Full-Stack Quantum Circuit Simulator with AscendNPU Support
T0 review · 1 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash
Pith's one-line read Aicir claims to be the first full-stack quantum circuit simulator with a native Ascend NPU backend, validated without CPU fallback on up to eight NPUs.
desk verdict A careful, honestly scoped systems paper: native Ascend NPU simulation that doesn't oversell speedups, with a validation hole around fallback-detection completeness that the authors themselves document. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing machinery is the paired-real tensor representation: every complex value $z=x+iy$ is stored as two float32 tensors $(x,y)$, and state updates, inner products, probabilities, partial traces, and SVDs are evaluated with real arithmetic. Gates are applied through fixed-rank views—an index table gathers the affected amplitudes, a local matrix multiplication updates them, and scatter writes them back—with the flat path chosen above eight qubits so the working tensor rank no longer grows with qubit count. Custom backward rules keep gate and state gradients in real tensors, avoid complex gradient accumulation, and let the same representation carry distributed sharding and reverse-mode differentiation. The backend contract of 19 methods keeps this hardware-specific machinery below a boundary that circuit construction and algorithm modules do not cross.
What would settle it
With CPU fallback disabled, run one of the claimed-native paths (for example, an $n=14$ Pauli expectation) under device-side tracing that records every host-device transfer and every CPU kernel; if the state tensor is copied to host memory or any operation executes on the CPU during that run, the native-execution claim for that path is false.
Extended reading notes
Core claim
The central claim is that Aicir achieves native Ascend NPU execution across the full simulator stack, and that this is possible because complex numbers are carried as pairs of real tensors and gates are applied through fixed-rank, gather-multiply-scatter views rather than high-rank complex operations. This representation also lets a state vector or density matrix be partitioned across $2^p$ NPUs while reverse-mode differentiation is retained, since the trainable leaves stay real and all collective payloads are real. The paper's experiments establish native execution for the tested paths, check gradients and communication on 2, 4, and 8 NPUs, and explicitly do not claim CPU-to-NPU speedup or multi-NPU scaling.
Load-bearing premise
The claim that the validated paths are truly native rests on the assumption that disabling the explicit CPU fallback and intercepting issued operations catches every hidden host-side path; a silent fallback outside the intercepted surface would not show up in the returned tensor.
Editorial extensions
If this is right
- A researcher on Ascend NPUs can run a complete quantum workflow—circuit construction, state evolution, measurement, expectation values, and gradients—without writing accelerator kernels by hand.
- The paired-real representation lets a state be split across $2^p$ NPUs while gradients still flow, so exact simulation can reach states larger than one device holds.
- Algorithm modules such as variational eigensolvers, quantum machine learning, and architecture search can all reuse the same native backend rather than each needing a separate accelerator port.
- CPU execution remains competitive with established simulators for fused layered circuits, so the NPU capability does not come at a runaway CPU cost.
Reading between the lines
- An extension the paper does not pursue: the paired-real design should transfer to other accelerators whose software stacks lack full complex-tensor kernels.
- The interception-based validation protocol could be reused as a general test for silent CPU fallback in any accelerator backend.
- The row-sharded distributed state with real collectives suggests a hybrid CPU/NPU mode, where part of the state lives in host memory, as a natural next step.
- Readers should treat any workflow outside the paper's validated backend surface as potentially host-assisted until separately checked.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper presents Aicir, a quantum circuit simulator with a native Huawei Ascend NPU backend. It spans circuit construction, state-vector, density-matrix, tensor-network, and MPS engines, measurement, differentiation, variational algorithms, quantum machine learning, quantum architecture search, and distributed state simulation. The NPU backend uses paired real tensors, fixed-rank gate views, and hardware-specific formulas to keep state operations on the device, and the paper validates native execution by disabling CPU fallback and intercepting operations. CPU benchmarks against Qiskit Aer, Cirq, Qiskit referenceStatevector, and PennyLane are reported, along with NPU correctness runs and distributed gradient/communication checks on 2, 4, and 8 NPUs. The abstract and conclusion state that Aicir's CPU runtime is within 0.97--1.28x of Aer and 0.76--1.10x of Cirq for the tested fused layered circuits, and that the NPU tests establish correct native execution without claiming CPU-to-NPU speedup.
Significance. If the claims hold, Aicir fills a real gap: a full-stack simulator with a native Ascend NPU backend, validated with a machine-checkable protocol rather than mere tensor placement checks. Strengths include the explicit scoping of validated paths, independent gradient oracles (parameter-shift and finite difference), a machine-checked communication contract for distributed runs, and honest reporting of both favorable and unfavorable benchmark results. The paper also contributes a detailed account of NPU-specific numerical constraints and their design response. The main risk is that the native-execution validation relies on the completeness of a manually curated interception list, which is a limitation made explicit in the text but not independently audited; this is a methodological concern rather than an internal inconsistency.
major comments (1)
- [Section 5.3 and Section 11] The native-execution claim rests on the completeness of the host-only path interception list. The paper's own bitwise-shift Pauli incident (Section 5.3) shows that an operation can silently execute on the host, produce a correct output tensor, and evade checks based on tensor placement; the interception list is therefore a manually curated set whose completeness is assumed. Since Section 11 states that the experiments 'establish native NPU execution,' I recommend either (i) adding device-level profiling evidence (e.g., Ascend profiling traces showing kernel execution on the device for the representative workloads) or (ii) softening the conclusion to say that the experiments validate native execution for the interception-covered operations, with the completeness assumption explicitly listed as a limitation.
minor comments (4)
- [Appendix B] Please provide a commit hash or exact version identifier for the Aicir release that was measured; the open-source URL alone does not pin the code state and prevents independent reproduction of the reported numbers.
- [Section 9.2, Table 9] The 'Qiskit' column in Table 9 corresponds to Qiskit's referenceStatevector path, not the Aer simulator; the table caption should state this explicitly to avoid confusion with the Aer column.
- [Section 9.4, Table 13] The first row of Table 13 reports '0.0 (at most 2.4×10^-7)', which is ambiguous; please clarify whether the maximum observed error is exactly 0.0 or up to 2.4×10^-7, and state how the two values were obtained.
- [Section 5.2] The claim that constructing gate matrices at the widest precision 'reduced the norm deviation of a nominally double-precision path from about 10^-8 to 10^-16' would benefit from a brief description of the test circuit and measurement procedure so that the reader can assess the relevance of this improvement.
Circularity Check
No significant circularity: the central NPU-execution and gradient claims are validated against external baselines and independent numerical oracles, not against the paper's own fitted inputs.
full rationale
The paper's central claims are system-construction and empirical-validation claims rather than derived predictions. The CPU efficiency comparison is measured against Qiskit Aer and Cirq under matched parity checks, including state-vector agreement before timing, so Aicir's time ratios are not defined into existence by its own inputs. The native-NPU claim is operationalized as dispatch through an explicit NPU implementation with CPU fallback disabled, and the experiments report the workloads that passed under that protocol, with the paper explicitly narrowing coverage to the validated backend surface. 'Native execution' is an operational definition plus a per-path test record, not a quantity fitted from data and then renamed as a prediction. Distributed gradients are checked against parameter-shift and finite-difference references that share no implementation path with the native backward rule, so the gradient results have independent content. The QAS scoring formulas are hand-chosen structural proxies and are explicitly labeled as not the final ranking signal, so no benchmark result is forced by their weights. The only self-citations, such as QuantumDARTS, are used as a literature source for one QAS search method and are not load-bearing for the simulator's correctness, performance, or hardware claims. The known limitation that the host-fallback interception list is manually curated and not independently audited is a validation-completeness risk, not a circular derivation; the paper itself discloses the earlier silent bitwise-shift fallback, which supports rather than refutes its honest per-path validation model.
Assumptions & free parameters
free parameters (3)
- QAS structural expressibility weights =
0.45, 0.35, 0.20 (hand-chosen)
- QAS trainability proxy weights =
0.4, 0.4, 0.2 (hand-chosen)
- QAS hardware efficiency weights =
0.4, 0.3, 0.3 (hand-chosen)
assumptions (6)
- standard math State-vector evolution U|ψ⟩ and density-matrix evolution UρU† define simulator semantics.
- standard math Parameter-shift rule for Pauli rotations gives analytic gradients.
- domain assumption The Ascend NPU lacks complete complex64 kernel support.
- domain assumption HCCL collective communication is available for distributed runs and does not support complex payloads directly.
- ad hoc to paper Distributed layout uses power-of-two sharding with contiguous state blocks and row-sharded density matrices.
- ad hoc to paper Complex trainable leaves are rejected; gradients must flow through paired real leaves.
Cite this review
Pith. "Pith review of Aicir: A Full-Stack Quantum Circuit Simulator with AscendNPU Support." pith.science (2026). https://pith.science/paper/7WIPF2DQ
@misc{pith2026260809733,
author = {Pith},
title = {Pith review of: Aicir: A Full-Stack Quantum Circuit Simulator with AscendNPU Support},
year = {2026},
howpublished = {\url{https://pith.science/paper/7WIPF2DQ}},
note = {Machine review of arXiv:2608.09733}
}
abstract
Quantum computing is a promising way to study problems that are difficult for classical methods, but current quantum hardware still faces limits in scale, noise, and fidelity. Running quantum algorithms on physical machines can also be costly. Quantum circuit simulators therefore remain important because they let researchers design and test algorithms on classical computers before using quantum hardware. Most high-performance simulators provide GPU backends, while few offer native support for NPUs. This gap limits the computing platforms available for quantum-algorithm research. We developed Aicir to provide a full-stack quantum circuit simulator with a native Huawei Ascend NPU backend. Aicir connects circuit construction, several state representations, measurement, differentiation, variational algorithms, quantum machine learning, and quantum architecture search through one programming model. It also supports noise simulation, tensor-network and matrix-product-state engines, and distributed state simulation. On the NPU, paired real tensors, fixed-rank gate views, and hardware-specific formulas keep the tested simulation paths on the device. The same representation lets Aicir partition a state across $2^{p}$ NPUs while retaining reverse-mode differentiation. We validated native execution with CPU fallback disabled and checked distributed communication and gradients on 2, 4, and 8 NPUs. For the tested fused layered circuits, Aicir's CPU runtime is within $0.97$--$1.28\times$ that of Qiskit Aer and $0.76$--$1.10\times$ that of Cirq. These results place its CPU execution in the same range as established simulators for this workload, while the NPU tests establish correct native execution rather than CPU-to-NPU speedup.
Reference graph
Works this paper leans on
-
[1]
Quantum computing in the NISQ era and beyond,
J. Preskill, “Quantum computing in the NISQ era and beyond,”Quantum, vol. 2, p. 79,
-
[2]
AER Development Team, “Qiskit Aer,” Python software package, 2025. [Online]. Available: https://pypi.org/project/qiskit-aer/0.17.2/
work page 2025
-
[3]
Qulacs: a fast and versatile quantum circuit simulator for research purpose,
Y. Suzuki, Y. Kawase, Y. Masumura, Y. Hiraga, M. Nakadai, J. Chen, K. M. Nakanishi, K. Mitarai, R. Imai, S. Tamiya, T. Yamamoto, T. Yan, T. Kawakubo, Y. O. Nakagawa, Y. Ibe, Y. Zhang, H. Yamashita, H. Yoshimura, A. Hayashi, and K. Fujii, “Qulacs: a fast and versatile quantum circuit simulator for research purpose,”Quantum, vol. 5, p. 559,
-
[4]
QuEST and high performance simulation of quantum computers,
T. Jones, A. Brown, I. Bush, and S. C. Benjamin, “QuEST and high performance simulation of quantum computers,”Scientific Reports, vol. 9, p. 10736, 2019. [Online]. Available: https://doi.org/10.1038/s41598-019-47174-9
-
[5]
cuQuantum SDK: A high-performance library for accelerating quantum science,
H. Bayraktar, A. Charara, D. Clark, S. Cohen, T. Costa, Y.-L. L. Fang, Y. Gao, J. Guan, J. Gunnels, A. Haidar, A. Hehn, M. Hohnerbach, M. Jones, T. Lubowe, D. Lyakh, S. Morino, P. Springer, S. Stanwyck, I. Terentyev, S. Varadhan, J. Wong, and T. Yamaguchi, “cuQuantum SDK: A high-performance library for accelerating quantum science,” in2023 IEEE Internatio...
arXiv 2023
-
[6]
TensorCircuit: a quantum software framework for the NISQ era,
S.-X. Zhang, J. Allcock, Z.-Q. Wan, S. Liu, J. Sun, H. Yu, X.-H. Yang, J. Qiu, Z. Ye, Y.-Q. Chen, C.-K. Lee, Y.-C. Zheng, S.-K. Jian, H. Yao, C.-Y. Hsieh, and S. Zhang, “TensorCircuit: a quantum software framework for the NISQ era,”Quantum, vol. 7, p. 912,
-
[7]
mindquantum.simulator.Simulator,
MindSpore Community, “mindquantum.simulator.Simulator,” MindSpore Quantum documentation, 2026, accessed: Aug. 10, 2026. [Online]. Available: https://www.mindspore. cn/mindquantum/docs/en/master/simulator/mindquantum.simulator.Simulator.html
work page 2026
-
[8]
Quantum-inspired algorithm NPU backend tutorial,
——, “Quantum-inspired algorithm NPU backend tutorial,” MindSpore Quantum documentation, 2026, english translation of the official Chinese page title; accessed: Aug. 10,
work page 2026
Show all 45 references
-
[9]
Realified tensor networks: Quantum circuit simulation on real-valued matrix accelerators,
Y. Zhao, X. Pan, E. Xiong, C. Zhu, and J. Liu, “Realified tensor networks: Quantum circuit simulation on real-valued matrix accelerators,” arXiv:2608.03987, 2026. [Online]. Available: https://arxiv.org/abs/2608.03987
2026 arXiv
-
[10]
Quantum computing with Qiskit,
A. Javadi-Abhari, M. Treinish, K. Krsulich, C. J. Wood, J. Lishman, J. Gacon, S. Martiel, P. D. Nation, L. S. Bishop, A. W. Cross, B. R. Johnson, and J. M. Gambetta, “Quantum computing with Qiskit,” arXiv:2405.08810, 2024. [Online]. Available: https://arxiv.org/abs/2405.08810
2024 arXiv
-
[11]
[Online]
Cirq Developers, “Cirq,” Software release, 2026. [Online]. Available: https://doi.org/10. 5281/zenodo.21080138
2026
-
[12]
cirq.Simulator,
Google Quantum AI, “cirq.Simulator,” Cirq documentation, 2026, accessed: Aug. 10, 2026. [Online]. Available: https://quantumai.google/reference/python/cirq/Simulator
2026
-
[13]
Intel quantum simulator: a cloud-ready high-performance simulator of quantum circuits,
G. G. Guerreschi, J. Hogaboam, F. Baruffa, and N. P. D. Sawaya, “Intel quantum simulator: a cloud-ready high-performance simulator of quantum circuits,” Quantum Science and Technology, vol. 5, no. 3, p. 034007, 2020. [Online]. Available: https://doi.org/10.1088/2058-9565/ab8505
2020 doi
-
[14]
Simulating quantum systems with NWQ-Sim on HPC,
I.-S. Suh and A. Li, “Simulating quantum systems with NWQ-Sim on HPC,” in 2023 IEEE International Conference for High Performance Computing, Networking, Storage, and Analysis (SC), 2023, pp. 1–3, research poster rpost195. [Online]. Available: https://www.ornl.gov/publication/s...
2023
-
[15]
PennyLane: Automatic differentiation of hybrid quantum-classical computations,
V. Bergholm, J. Izaac, M. Schuld, C. Gogolin, S. Ahmed, V. Ajith, M. S. Alam, G. Alonso-Linaje, B. AkashNarayanan, A. Asadi, J. M. Arrazola, U. Azad, S. Banning, C. Blank, T. R. Bromley, B. A. Cordier, J. Ceroni, A. Delgado, O. Di Matteo, A. Dusko, T. Garg, D. Guala, A. Hayes,...
2018 arXiv
-
[16]
Yao.jl: Extensible, efficient framework for quantum algorithm design,
X.-Z. Luo, J.-G. Liu, P. Zhang, and L. Wang, “Yao.jl: Extensible, efficient framework for quantum algorithm design,”Quantum, vol. 4, p. 341, 2020. [Online]. Available: https://doi.org/10.22331/q-2020-10-11-341
2020 doi
-
[17]
MindSpore Quantum: A user-friendly, high-performance, and AI-compatible quantum computing framework,
X. Xu, J. Cui, Z. Cui, R. He, Q. Li, X. Li, Y. Lin, J. Liu, W. Liu, J. Lu, M. Luo, C. Lyu, S. Pan, P. Mosharev, R. Shu, J. Tang, R. Xu, S. Xu, K. Yang, F. Yu, Q. Zeng, H. Zhao, Q. Zheng, J. Zhou, X. Zhou, Y. Zhu, Z. Zou, A. Bayat, X. Cao, W. Cui, Z. Li, G. Long, Z. Su, X. Wang...
2024 arXiv
-
[18]
quimb: A python package for quantum information and many-body calculations,
J. Gray, “quimb: A python package for quantum information and many-body calculations,” Journal of Open Source Software, vol. 3, no. 29, p. 819, 2018. [Online]. Available: https://doi.org/10.21105/joss.00819
2018 doi
-
[19]
Hyper-optimized tensor network contraction,
J. Gray and S. Kourtis, “Hyper-optimized tensor network contraction,”Quantum, vol. 5, p. 410, 2021. [Online]. Available: https://doi.org/10.22331/q-2021-03-15-410
2021 doi
-
[20]
Quantum circuit architecture search for variational quantum algorithms,
Y. Du, T. Huang, S. You, M.-H. Hsieh, and D. Tao, “Quantum circuit architecture search for variational quantum algorithms,”npj Quantum Information, vol. 8, p. 62, 2022. [Online]. Available: https://doi.org/10.1038/s41534-022-00570-y
2022 doi
-
[21]
Differentiable quantum architecture search,
S.-X. Zhang, C.-Y. Hsieh, S. Zhang, and H. Yao, “Differentiable quantum architecture search,”Quantum Science and Technology, vol. 7, no. 4, p. 045023, 2022. [Online]. Available: https://doi.org/10.1088/2058-9565/ac87cd
2022 doi
-
[22]
QuantumDARTS: Differentiable quantum architecture search for variational quantum algorithms,
W. Wu, G. Yan, X. Lu, K. Pan, and J. Yan, “QuantumDARTS: Differentiable quantum architecture search for variational quantum algorithms,” inProceedings of the 40th International Conference on Machine Learning, ser. Proceedings of Machine Learning Research, vol. 202. PMLR, 2023,...
2023
-
[23]
Benchmarking the performance of quantum computing software for quantum circuit creation, manipulation and compilation,
P. D. Nation, A. A. Saki, S. Brandhofer, L. Bello, S. Garion, M. Treinish, and A. Javadi- Abhari, “Benchmarking the performance of quantum computing software for quantum circuit creation, manipulation and compilation,”Nature Computational Science, vol. 5, no. 5, pp. 427–435, 2...
2025 doi
-
[24]
Barren plateaus in quantum neural network training landscapes,
J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, “Barren plateaus in quantum neural network training landscapes,”Nature Communications, vol. 9, no. 1, p. 4812, 2018. [Online]. Available: https://doi.org/10.1038/s41467-018-07090-4
2018 doi
-
[25]
Connecting ansatz expressibility to gradient magnitudes and barren plateaus,
Z. Holmes, K. Sharma, M. Cerezo, and P. J. Coles, “Connecting ansatz expressibility to gradient magnitudes and barren plateaus,”PRX Quantum, vol. 3, no. 1, p. 010313, 2022. [Online]. Available: https://doi.org/10.1103/PRXQuantum.3.010313
2022 doi
-
[26]
Efficient classical simulation of slightly entangled quantum computations,
G. Vidal, “Efficient classical simulation of slightly entangled quantum computations,” Physical Review Letters, vol. 91, no. 14, p. 147902, 2003. [Online]. Available: https://doi.org/10.1103/PhysRevLett.91.147902 32
2003 doi
-
[27]
Evaluating analytic gradients on quantum hardware,
M. Schuld, V. Bergholm, C. Gogolin, J. Izaac, and N. Killoran, “Evaluating analytic gradients on quantum hardware,”Physical Review A, vol. 99, no. 3, p. 032331, 2019. [Online]. Available: https://doi.org/10.1103/PhysRevA.99.032331
2019 doi
-
[29]
Quantum architecture search via truly proximal policy optimization,
X. Zhu and X. Hou, “Quantum architecture search via truly proximal policy optimization,”Scientific Reports, vol. 13, no. 1, p. 5157, 2023. [Online]. Available: https://doi.org/10.1038/s41598-023-32349-2
2023 doi
-
[30]
Quantum architecture search via continual reinforcement learning,
E. Ye and S. Y.-C. Chen, “Quantum architecture search via continual reinforcement learning,” arXiv:2112.05779, 2021. [Online]. Available: https://arxiv.org/abs/2112.05779
2021 arXiv
-
[31]
Curriculum reinforcement learning for quantum architecture search under hardware errors,
Y. J. Patel, A. Kundu, M. Ostaszewski, X. Bonet-Monroig, V. Dunjko, and O. Danaci, “Curriculum reinforcement learning for quantum architecture search under hardware errors,” inThe Twelfth International Conference on Learning Representations, 2024, published online; the proceed...
2024
-
[32]
A variational eigenvalue solver on a photonic quantum processor,
A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’Brien, “A variational eigenvalue solver on a photonic quantum processor,”Nature Communications, vol. 5, no. 1, p. 4213, 2014. [Online]. Available: https://doi.org/10.1038/ncomms5213
2014 doi
-
[33]
An adaptive variational algorithm for exact molecular simulations on a quantum computer,
H. R. Grimsley, S. E. Economou, E. Barnes, and N. J. Mayhall, “An adaptive variational algorithm for exact molecular simulations on a quantum computer,”Nature Communications, vol. 10, no. 1, p. 3007, 2019. [Online]. Available: https://doi.org/10.1038/s41467-019-10988-2
2019 doi
-
[34]
A quantum approximate optimization algorithm,
E. Farhi, J. Goldstone, and S. Gutmann, “A quantum approximate optimization algorithm,” arXiv:1411.4028, 2014. [Online]. Available: https://arxiv.org/abs/1411.4028
2014 arXiv
-
[35]
Variational quantum computation of excited states,
O. Higgott, D. Wang, and S. Brierley, “Variational quantum computation of excited states,” Quantum, vol. 3, p. 156, 2019. [Online]. Available: https://doi.org/10.22331/q-2019-07-01-156
2019 doi
-
[36]
Subspace-search variational quantum eigensolver for excited states,
K. M. Nakanishi, K. Mitarai, and K. Fujii, “Subspace-search variational quantum eigensolver for excited states,”Physical Review Research, vol. 1, no. 3, p. 033062, 2019. [Online]. Available: https://doi.org/10.1103/PhysRevResearch.1.033062
2019 doi
-
[37]
Bit ordering in the Qiskit SDK,
IBM Quantum, “Bit ordering in the Qiskit SDK,” IBM Quantum documentation, 2026, accessed: Aug. 10, 2026. [Online]. Available: https://quantum.cloud.ibm.com/docs/en/ guides/bit-ordering
2026
-
[38]
Function gate::RX,
Qulacs Developers, “Function gate::RX,” Qulacs documentation, 2026, accessed: Aug. 10,
2026
-
[39]
cirq.CZPowGate,
Google Quantum AI, “cirq.CZPowGate,” Cirq documentation, 2026, accessed: Aug. 10,
2026
-
[44]
Available: https://docs.qulacs.org/ja/latest/api/function_gate__factory_ 8hpp_1a2fdbf91783b94a41c93f8402e9158a52.html
[Online]. Available: https://docs.qulacs.org/ja/latest/api/function_gate__factory_ 8hpp_1a2fdbf91783b94a41c93f8402e9158a52.html
-
[46]
rx").generator gate_shift_rule(
[Online]. Available: https://quantumai.google/reference/python/cirq/CZPowGate A API reference We discuss design and behaviour in the main text. Here we list the public calls and give short examples. 33 A.1 Installation pip install -e ".[all]"# torch / viz / sci / tn / chem / d...
-
[2018]
Available: https://doi.org/10.22331/q-2018-08-06-79
[Online]. Available: https://doi.org/10.22331/q-2018-08-06-79
2018 doi
-
[2020]
Available: https://arxiv.org/abs/2007.04424
[Online]. Available: https://arxiv.org/abs/2007.04424
2007 arXiv
-
[2021]
Available: https://doi.org/10.22331/q-2021-10-06-559 30
[Online]. Available: https://doi.org/10.22331/q-2021-10-06-559 30
2021 doi
-
[2023]
Available: https://doi.org/10.22331/q-2023-02-02-912
[Online]. Available: https://doi.org/10.22331/q-2023-02-02-912
2023 doi
-
[2026]
Available: https://www.mindspore.cn/mindquantum/docs/zh-CN/master/ case_library/qaia_npu_tutorial.html
[Online]. Available: https://www.mindspore.cn/mindquantum/docs/zh-CN/master/ case_library/qaia_npu_tutorial.html
Reviewed August 11, 2026 · model on record in the stance chip above.
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