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REVIEW 4 major objections 5 minor 31 references

EQNN: Enhanced Quantum Neural Network

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper claims that replacing the baseline feature map with a five-gate Enhanced Feature Map lets a quantum neural network classify mobile data plan choices with 100% accuracy using fewer quantum gates and converging faster under three…

desk verdict Routine angle-encoding variant with a load-bearing arithmetic error in Eq. (19) and a convergence claim contradicted by its own results; not referee-ready. read the letter →

arxiv 2411.17726 v2 pith:5IEX7BRK submitted 2024-11-21 quant-ph cs.ITcs.LGcs.NEmath.IT

Abel C. H. Chen This is my paper · ORCID
classification quant-phcs.ITcs.LGcs.NEmath.IT
keywords quantumneuralnetworkEnhancedFeatureMapvariationalmodelclassificationmobiledatausagepredictionoptimization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes an Enhanced Quantum Neural Network whose key ingredient is a new Enhanced Feature Map (EFM) that encodes each normalized input feature with a small fixed circuit before the trainable part of the network. On a two-class task that recommends mobile data plans from two usage measurements, the paper claims all three EFM-based models reach 100% classification accuracy while the tutorial baseline reaches at most 99.9%, and they do so with 10, 13, or 16 quantum logic gates instead of the baseline's 18. The paper further claims the gains hold across three quantum optimizers and that one variant converges to a flat loss curve faster than the baseline. The paper argues this demonstrates that input encoding is a key lever for making quantum classifiers both cheaper and more accurate.

What carries the argument

The load-bearing object is the Enhanced Feature Map (EFM): a two-qubit encoding circuit of the form $\mathbf{C}(q_0)(R(2x_0-1.5)\otimes R(2x_1-1.5))(H\otimes H)|q_1q_0\rangle$, where $R$ is the Y-axis rotation gate and $\mathbf{C}(q_0)$ is a CNOT controlled by $q_0$. The paper intends this five-gate circuit to place normalized features in the $[-1.5,1.5]$ range that its activation-function study favors, replacing the seven-gate ZZFeatureMap of the baseline. The variational model is the standard RealAmplitudes parameterized circuit, repeated one, two, or three times, giving total gate counts of 10, 13, and 16 respectively. The mechanism carries the argument by showing that a cheaper encoding, not a deeper ansatz, is what the accuracy gain is attributed to.

What would settle it

Compute the output range of Eq. (19): for normalized $x\in[0,1]$, the expression $2x-1.5$ covers $[-1.5,0.5]$, not the intended $[-1.5,1.5]$. Re-running the classification benchmark with the EFM exactly as written, across several random seeds on the same 1000-sample dataset, would show whether the reported 100% accuracy belongs to the circuit the design argument describes or to a circuit with an asymmetric encoding range.

Watch

Extended reading notes

Core claim

The core claim, stated on the paper's own terms, is that the choice of feature map determines how quickly and how accurately a quantum neural network trains. Section III compares RY-gate circuits with three classical activation functions and concludes that inputs in the range $[-1.5,1.5]$ are especially suitable. Based on that, the paper designs the Enhanced Feature Map (EFM), a five-gate, two-qubit circuit that applies Hadamard gates, then RY rotations parameterized by an affine transform of each normalized feature, then a CNOT. With the EFM feeding one, two, or three repeats of the RealAmplitudes variational circuit, the resulting EQNN models achieve 100% classification accuracy on the mobile-data-plan task under COBYLA, SPSA, and AQGD, whereas the tutorial baseline (ZZFeatureMap plus three repeats of RealAmplitudes, 18 gates) reaches 97.9%, 99.3%, and 99.9%. The paper also reports that the 16-gate EQNN model flattens its loss curve within about five AQGD iterations, which it presents as faster convergence.

Load-bearing premise

The design assumes that the preprocessing formula places normalized inputs in the interval the author chose, but that formula actually sends $[0,1]$ to $[-1.5,0.5]$, so the trained circuit may not be the one whose design is justified.

Editorial extensions

If this is right

  • A smaller feature map plus a shallower variational circuit can replace a larger standard circuit on at least one real classification task, lowering the gate count from 18 to as few as 10 gates.
  • The accuracy gains hold under COBYLA, SPSA, and AQGD, so the reported improvement is not tied to one optimizer's behavior.
  • Reaching 100% with one repeat of RealAmplitudes suggests that the bottleneck in this benchmark is the input encoding, not the depth of the trainable variational model.
  • Because the full-accuracy models use fewer gates, they are correspondingly cheaper to run on near-term quantum hardware, where circuit depth directly affects noise and decoherence.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An implication left implicit is that the EFM's benefit is demonstrated only for a two-feature, two-class benchmark; extending it to more qubits would require deciding how to entangle additional features and would test whether the five-gate advantage persists.
  • A direct test of the design rationale would be to benchmark the circuit with a transform that genuinely maps $[0,1]$ onto $[-1.5,1.5]$ (for instance $3x-1.5$) against the written $2x-1.5$; this isolates whether the advertised value range is the actual source of the accuracy gain.
  • If the result is stable under re-implementation, feature-map design should be treated as a first-class hyperparameter in quantum neural network pipelines, on par with ansatz depth and optimizer choice.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes an Enhanced Quantum Neural Network (EQNN) built from an Enhanced Feature Map (EFM) in which normalized input features are linearly transformed and fed into RY gates, followed by a variational RealAmplitudes circuit. The method is evaluated on a mobile data usage classification task with 1000 samples, comparing accuracy, quantum-gate count, and convergence speed against an IBM Qiskit tutorial benchmark across COBYLA, SPSA, and AQGD optimizers. The authors claim that the EQNN achieves higher accuracy with fewer quantum logic gates and converges faster under different optimization algorithms.

Significance. If fully supported, the contribution would be a pragmatic but modest feature-map design with a small empirical demonstration. The paper does provide some theoretical motivation by fitting linear, sigmoid, and tanh functions with a simplified single-qubit QNN, and it reports accuracy tables. However, the central empirical claims are not verifiable as written: the manuscript gives no code, no data split, no random seeds, no repeated runs, and no error bars. More importantly, the paper contains an arithmetic error in the feature-map formula that contradicts its own design rationale, and the convergence claim in the abstract is contradicted by the paper's own Figure 14. Thus the claimed advantages are not established.

major comments (4)
  1. [IV.A, Eq. (19)-(20)] The manuscript states that the transformation 2*x - 1.5 maps normalized inputs x in [0,1] to the range [-1.5, 1.5], but the actual range is [-1.5, 0.5]. Since Section III.C and III.D identify [-1.5, 1.5] as the suitable input range based on the fitting experiments, the EFM circuit in Eq. (20) and Figure 9, which uses 2*x - 1.5 as RY rotation angles, is not the circuit the design argument motivates. The paper does not provide code or data, so it is impossible to determine whether the experiments used 2*x - 1.5 (contradicting the stated design) or some other mapping such as 3*x - 1.5 (which would make the text wrong). This error is load-bearing because the claimed accuracy and gate-count advantages are attributed to the EFM.
  2. [Abstract and V.B (Figs. 13-16)] The abstract claims that the EQNN 'converges faster to the optimal solution under different optimization algorithms,' but in Section V.B the authors explicitly state that for AQGD the benchmark converges faster than EQNN Model 1 (benchmark flattens at iteration 20, Model 1 at iteration 60). The convergence curves in Figures 13-16 are only for AQGD; no convergence results are reported for COBYLA or SPSA. Thus the central convergence claim is directly contradicted for Model 1 and unsupported for the other optimizers. The phrase 'different optimization algorithms' in the abstract should be constrained or removed.
  3. [V.A-V.B, Tables II-III] The experimental section provides no information on how the 1000 samples are split into training and test sets, how random initial weights are chosen, how many independent runs are performed, or what the variance of the accuracy estimates is. All EQNN models are reported to achieve 100.0% accuracy under every optimizer, while the benchmark ranges from 97.9% to 99.9%, but without error bars or repeated trials the difference could easily be within statistical fluctuation. This lack of reproducibility information undermines the empirical basis for the claimed advantages.
  4. [II.D and IV.B, gate-count calculations] The gate-count numbers used to support the 'fewer quantum logic gates' claim are internally inconsistent with the circuits described. Section II.D states that one iteration of RealAmplitudes on two qubits (Figure 3) consists of two RY gates and one CNOT gate, i.e., 3 gates, and that three iterations (Figure 4) use 11 gates, but the natural count from the described structure is 9. Similarly, Section IV.B reports that EQNN Model 1's variational model uses 5 gates, but one iteration of RealAmplitudes as defined would use 3 gates, making the total EFM+variational count 8 rather than 10. These discrepancies affect the headline quantitative claim, even if the qualitative ordering (EQNN models use fewer gates than the benchmark) might still hold under corrected counts.
minor comments (5)
  1. [Tables II and III] The second EQNN column in both tables is labeled 'EQNN Model 1' a second time; it should be 'EQNN Model 2'. This makes the tables difficult to interpret.
  2. [II.D] The text says there are 8 weight variables W = {w0, w1, …, w8}, but the list contains 9 elements; either the count or the index range should be corrected.
  3. [IV.A] The text refers to 'GY Gate' in the description of the proposed feature map; this appears to be a typo for 'RY Gate.'
  4. [IV.B] The sentence stating that EQNN Model 1 uses 5 gates for the variational model plus 5 for the feature map totals 10 gates is inconsistent with the earlier definition of one RealAmplitudes iteration as 3 gates; the text should resolve this discrepancy.
  5. [References] Reference [15] lists the author as 'O. A. Warga,' which may be a misspelling of 'Warqa' as it appears in the original conference publication; please verify.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the EFM accuracy claim is judged against an external IBM Qiskit benchmark, and the 1.5 rescale is a design heuristic, not a fitted prediction; the serious arithmetic and convergence inconsistencies are correctness issues, not circularity.

full rationale

The central empirical claim—that EQNN models with the EFM reach 100% accuracy on the mobile-data-usage task while the IBM tutorial benchmark reaches 97.9–99.9%—is tested against an external benchmark ([6],[16]), not against a quantity defined by the paper's own fitted parameters. The EFM rescaling constant 1.5 in Eq. (19) is motivated by the author's own Sec. III fitting experiments on simplified one-qubit networks, but it is a design heuristic chosen before the classification evaluation; it is not a parameter fitted to the target labels, and the accuracy comparison is not the regression used to choose the range, so this is not a fitted-input-called-prediction step. The only self-citation with any role is [18], used as the mobile-data-usage source; this is a real dataset from prior published work and is not an argument that forces the present results, so it does not make the derivation circular. There is no imported uniqueness theorem, no ansatz smuggled in via citation, and no renaming of a known result. Two internal inconsistencies should be flagged as correctness/verifiability risks rather than circularity: Sec. IV.A states that Eq. (19) '以公式(19)調整值域為[–1.5, 1.5]區間' where '2 × 𝑥 − 1.5' maps [0,1] to [-1.5,0.5]; and the abstract's faster-convergence claim is not supported by the AQGD-only figures, one of which says the benchmark converges faster than EQNN Model 1. These flaws undermine the reported details but do not reduce the central derivation to its own inputs. Accordingly, no circular step is present, and the score is 0.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central claim rests on a hand-picked rescaling constant, a transfer assumption from one-qubit fits to a two-qubit classification task, and a single external baseline. No new physical entities are introduced.

free parameters (2)
  • feature-map rescaling constant (2*x - 1.5) = 1.5
    The constant 1.5 is chosen by hand from the one-qubit fitting experiments in Section III; it is not derived from the target task or from first principles, and the stated formula does not produce the intended range [-1.5, 1.5] for x in [0,1].
  • variational model repetitions r2 = 1, 2, 3
    The number of RealAmplitudes repetitions is set by the comparison design (Model 1, 2, 3) rather than selected by validation; it affects gate counts and expressivity.
assumptions (3)
  • domain assumption The rescaling range observed in one-qubit fits (x in [-1.5, 1.5]) transfers to the two-qubit classification task.
    Section IV.A motivates Eq. (19) from the Section III fits; no proof or cross-validation justifies transfer.
  • domain assumption The IBM tutorial circuit (ZZFeatureMap with r1=1 and RealAmplitudes with r2=3) is an appropriate state-of-the-art baseline.
    Section V.B treats [6],[16] as the benchmark; the paper cites no wider comparison to other QNN architectures.
  • standard math Qiskit simulator measurements follow the standard Born-rule probability interpretation and gate definitions.
    Used in all amplitude calculations, e.g., Eqs. (10)-(14).

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Cite this review

Pith. "Pith review of EQNN: Enhanced Quantum Neural Network." pith.science (2026). https://pith.science/paper/5IEX7BRK

@misc{pith2026241117726,
  author       = {Pith},
  title        = {Pith review of: EQNN: Enhanced Quantum Neural Network},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5IEX7BRK}},
  note         = {Machine review of arXiv:2411.17726}
}
read the original abstract

With the maturation of quantum computing technology, research has gradually shifted towards exploring its applications. Alongside the rise of artificial intelligence, various machine learning methods have been developed into quantum circuits and algorithms. Among them, Quantum Neural Networks (QNNs) can map inputs to quantum circuits through Feature Maps (FMs) and adjust parameter values via variational models, making them applicable in regression and classification tasks. However, designing a FM that is suitable for a given application problem is a significant challenge. In light of this, this study proposes an Enhanced Quantum Neural Network (EQNN), which includes an Enhanced Feature Map (EFM) designed in this research. This EFM effectively maps input variables to a value range more suitable for quantum computing, serving as the input to the variational model to improve accuracy. In the experimental environment, this study uses mobile data usage prediction as a case study, recommending appropriate rate plans based on users' mobile data usage. The proposed EQNN is compared with current mainstream QNNs, and experimental results show that the EQNN achieves higher accuracy with fewer quantum logic gates and converges to the optimal solution faster under different optimization algorithms.

Figures

Figures reproduced from arXiv: 2411.17726 by the authors.

Figure 1
Figure 1. 量子神經網路架構圖 B. 量子態和常用邏輯閘 本節定義單量子位元|𝑞𝑖 ⟩的量子態，雙量子位元|𝑞𝑗𝑞𝑖 ⟩ 的量子態，以及常用邏輯閘包含 Hadamard Gate、Phase Gate、RY Gate、Cnot Gate，其數學表達式和符號如表 I 所示。 TABLE I. QUANTUM LOGIC GATES FOR A QNN Logic Gate Notation Symbol Hadamard Gate 𝐻|𝑞𝑖 ⟩ = 1 √2 [ 1 1 1 −1 ]|𝑞𝑖 ⟩ Phase Gate 𝑃(𝜃)|𝑞𝑖 ⟩ = [ 1 0 0 𝑒 𝑖𝜃]|𝑞𝑖 ⟩ RY Gate 𝑅(𝜃)|𝑞𝑖 ⟩ = [ 𝑐𝑜𝑠 ( 𝜃 2 ) −𝑠𝑖𝑛 ( 𝜃 2 ) 𝑠𝑖𝑛 ( 𝜃 2 ) 𝑐𝑜𝑠 ( 𝜃 2 ) ] |𝑞𝑖 ⟩ Cnot Gate Control Qubit: qi Target Qubit: qj 𝐶(𝑞𝑖 )|𝑞𝑗𝑞… view at source ↗
Figure 2
Figure 2. 特徵圖 D. 變分模型 目前已經有發展出多個不同的變分模型運算子，其中 常 見 的 變 分 模 型 運 算 子 包 含 有 RealAmplitudes 、 FidelityQuantumKernel [6], [15]等。本節為說明變分模型 的量子電路結構，主要參考 IBM 提供的量子神經網路實 例[16]，採用 RealAmplitudes 作為變分模型運算子𝛽(𝑊)， 並且根據實例的作法該特徵圖運算子重覆 3 次(即 r2 = 3)， 故特徵圖為𝑉 = 𝛽(𝑊) 3。並且在實驗時，將以此結構作 為基準(benchmark)來建立量子神經網路。 在兩個量子位元時，首先將先對每個量子位元進行 RY Gate 操作以產生不同的相位差，再運用 Cnot Gate 來 該量子位元之間可以交互影響，產生量子糾纏態，如圖 3 為 RealAmplitudes 迭代一次的量子電路結構。當迭代 3 次後的量子電路結構如圖 4 所示，也是本… view at source ↗
Figure 3
Figure 3. 變分模型(迭代 1 次 RealAmplitudes) [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (9 more)
Figure 6
Figure 6. Figure 6: 線性函數擬合結果 C. 擬合 Sigmoid 函數 Sigmoid 函數定義如公式(16)所示，本節的資料集採 用介於[–3, 3]區間的 200 筆隨機數作為 x 值，並且代入公 式(16)和(17)得到對應的 y 值。其中，由於量子神經網路 迴歸應用的預測值的值域為[–1, 1](參考公式(12))，所以 運用公式(17)修改 y 值的值域為[–1, 1]。除此之外，把 x 同除以 2，讓輸入到簡化版量子神經網路的輸入變量值 域介於[–1.5, 1.5]，擬合結果如圖 7 所示。可以觀察到有 較好的擬合結果，僅有很小的誤差。 𝑠…
Figure 9
Figure 9. Figure 9: 本研究提出的改進式特徵圖 B. 本研究提出的 EQNN 模型 1: EFM + 1 次 RealAmplitudes 本研究提出的改進式量子神經網路主要結合本研究提 出的改進式特徵圖和現行主流的變分模型運算子。在改 進式量子神經網路模型 1中，本研究採用 RealAmplitudes 作為變分模型運算子，並且只迭代 1 次(即 r2 = 1)，依此 作為變分模型。改進式量子神經網路模型 1 的量子電路 結構如圖 10 所示，可以觀察到變分模型用到 5 個量子邏 輯閘，加上改進式特徵圖的 5 個量子邏輯閘，合計共用 到 10 個量子邏…
Figure 10
Figure 10. Figure 10: 改進式量子神經網路模型 1 C. 本研究提出的 EQNN 模型 2 和模型 3: 有鑑於 IBM 提供的量子神經網路實例[6], [16](即基準 (benchmark)) 在 變 分 模 型 的 結 構 中 採 用 了 3 次 RealAmplitudes，所以為了公平且完整比較，本研究考 慮一併比較 2 次 RealAmplitudes 和 3 次 RealAmplitudes。 本研究提出的改進式量子神經網路模型 2 主要採用改 進式特徵圖作為特徵圖的結構，並且在變分模型結構主 [PITH_FULL_IMAGE:figur…
Figure 11
Figure 11. Figure 11: 改進式量子神經網路模型 2 本研究提出的改進式量子神經網路模型 3 主要採用改 進式特徵圖結合迭代 3 次 RealAmplitudes 的變分模型(如 圖 4)所組成的量子電路，如圖 12 所示。在模型 3 中包含 了 16 個量子邏輯閘(即 16 = 5 + 11)。 [PITH_FULL_IMAGE:figures/full_fig_p005_11.png]
Figure 12
Figure 12. Figure 12: 改進式量子神經網路模型 3 V. 實驗環境與實證結果 為驗證本研究提出的改進式特徵圖和改進式量子神經 網路，本研究採用以行動資料用量預測為例來分析，並 將先介紹資料集和實驗環境。在實驗結果中比較每個模 型的量子邏輯閘數量、分類正確率、以及收斂速度，從 而驗證效率和效能不同面向。 A. 實驗環境 本研究採用的行動資料用量主要來自[17]和[18]，在 每個月月中統計每個使用者的行動資料用量得到 x0 和在 每個月月底統計每個使用者的行動資料用量得到 x1，作 為輸入變量，並且把該使用者採用的方案作為輸出(即分 類類別 y0和 y1)…
Figure 13
Figure 13. Figure 13: Benchmark 模型收斂速度 [PITH_FULL_IMAGE:figures/full_fig_p005_13.png]
Figure 14
Figure 14. Figure 14: EQNN 模型 1 收斂速度 [PITH_FULL_IMAGE:figures/full_fig_p005_14.png]
Figure 15
Figure 15. Figure 15: EQNN 模型 2 收斂速度 [PITH_FULL_IMAGE:figures/full_fig_p006_15.png]
Figure 16
Figure 16. Figure 16: EQNN 模型 3 收斂速度 VI. 結論與未來研究 本研究比較量子神經網路量子邏輯閘和傳統神經網路 激活函數，並且從而設計了改進式特徵圖。在改進式特 徵圖基礎上，本研究提出 3 個改進式較量子神經網路， 並且採用真實行動資料用量預測為例，驗證本研究提出 的模型可以用更少的量子邏輯閘達到更高的正確率。 未來可嘗試擴展本研究提出的改進式特徵圖支援更多 的量子位元，並且應用在不同的領域以驗證改進式特徵 圖的通用性。 致謝 本研究採用 IBM Qiskit 套件開發，感謝 IBM 免費提 供量子計算開發工具。 參考文獻 [1] E. K…

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Works this paper leans on

31 extracted references · 19 canonical work pages

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    Quantum Computing,

    E. Knill, " Quantum Computing," in Nature, vol. 463, pp. 441-443, 2010, doi: 10.1038/463441a

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    𝑐𝑜𝑠 (𝜃 2) ] |𝑞𝑖⟩ Cnot Gate Control Qubit: qi Target Qubit: qj 𝐶(𝑞𝑖)|𝑞𝑗𝑞𝑖⟩ = [ 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 ] |𝑞𝑗𝑞𝑖⟩ 單量子位元|𝑞𝑖⟩量子態的表達方式如公式 (1)所示，由 [𝑣0 𝑣1 ]表示為量子位元 |𝑞𝑖⟩的振幅向量，並且可由 𝑣0 2表示 為發生|0⟩的機率、由 𝑣1 2表示為發生 |1⟩的機率。因此， 當|𝑞𝑖⟩ = |0⟩，則振幅向量為 [1 0]，如公式 (2)所示。同理， 當|𝑞𝑖⟩ = |1⟩，則振幅向量為 [0 1]，如公式(3)所示[13]-[14]。 |𝑞𝑖⟩ = 𝑣0|0⟩ + 𝑣1|1⟩ → [𝑣0 𝑣1 ] (1) |𝑞𝑖⟩ = |0⟩ = 1|0⟩ +...

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    𝑐𝑜𝑠 (𝜃 2) ] [𝑣0 𝑣1 ] = [ 𝑣0𝑐𝑜𝑠 (𝜃

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    + 𝑣1𝑐𝑜𝑠 (𝜃 2) ] (6) 雙量子位元|𝑞𝑗𝑞𝑖⟩量子態的表達方式如公式 (7)所示， 由[ 𝑣00 𝑣01 𝑣10 𝑣11 ] 表 示 為 量 子 位元|𝑞𝑗𝑞𝑖⟩ 的振幅向量，並且可由 𝑣00 2表示為發生|00⟩的機率，如公式(8)所示[13]-[14]。同 理，可得|01⟩、|10⟩、|11⟩量子態的振幅向量，由於篇幅 限制，不展開描述。 |𝑞𝑗𝑞𝑖⟩ = 𝑣00|00⟩ + 𝑣01|01⟩ + 𝑣10|10⟩ + 𝑣11|11⟩ → [ 𝑣00 𝑣01 𝑣10 𝑣11 ] (7) |00⟩ = 1|00⟩ + 0|01⟩ + 0|10⟩ + 0|11⟩ → [ 1 0 0 0 ] (8) 當量子位元|𝑞𝑗𝑞𝑖⟩通過 Cnot Gate 時，並且以量子位元 |𝑞𝑖⟩為控制位元，且量子位...

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    𝑐𝑜𝑠 (𝑥 2) ] 1 √2 [1 1 1 −1] [1 0] = 1 √2 [ 𝑐𝑜𝑠 (𝑥

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    𝑐𝑜𝑠 (𝑥 2) ] [1 1] = 1 √2 [ 𝑐𝑜𝑠 (𝑥

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    + 𝑐𝑜𝑠 (𝑥 2) ] (10) 𝑦′ = 𝜌0 2 − 𝜌1 2 (12) 𝐿𝑟𝑒𝑔𝑟𝑒𝑠𝑠𝑖𝑜𝑛 = (𝑦′ − 𝑦)2 (13) 當在分類應用時，𝜌0 2可以運用作為 Label 0 的機率預 測值，以及𝜌1 2運用作為 Label 1 的機率預測值，並以公 式(14)計算該筆資料的損失值(假設交叉熵為損失函數 ， Label 0 的機率真值為 p0、Label 1 的機率真值為 p1)。 𝐿𝑐𝑙𝑎𝑠𝑠𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 = −(𝑝0 log 𝜌0 2 + 𝑝1 log 𝜌1

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    (14) Fig. 5. 簡化版量子神經網路 B. 擬合線性函數 線性函數定義如公式 (15)所示，本節的資料集採用介 於[–1, 1] 區間的 200 筆隨機數作為 x 值，並且代入公式 (15)得到對應的 y 值。運用簡化版量子神經網路學習此資 料集，訓練後的 w 值為 3.14150444，擬合結果如圖 6 所 示。可以觀察到大部分的資料都以擬合，並有較小的誤 差。並且可從公式驗證，例如：w = 3.14150444 且 x = 0.1 代入公式(11)和(12)可得預測 y’為 0.099833417，近似真 值 y = 0.1。 𝑦 = ...

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.