Quantum-Enhanced LSTM Architectures

• Quantum-enhanced LSTM is a hybrid model that replaces classical gate computations with quantum components like variational quantum circuits and kernel expansions.
• These architectures retain the classical LSTM cell structure while integrating quantum modules for gate pre-activations, parameter generation, and feature encoding.
• Empirical studies demonstrate improvements in convergence, error reduction, and efficiency across applications such as solar forecasting, stock prediction, and generative modeling.

Searching arXiv for papers on quantum-enhanced LSTM and related variants. Searching arXiv for "quantum long short-term memory". Quantum-Enhanced Long Short-Term Memory (LSTM) denotes a family of hybrid recurrent architectures in which the classical LSTM recurrence is retained, but selected components of the gate computation, feature mapping, or parameterization are replaced or augmented by quantum computational primitives. In the published literature, these primitives include variational quantum circuits (VQCs), quantum-kernel expansions, quantum modules that generate classical LSTM parameters, and quantum-inspired single-qubit activations. The resulting models span sequence forecasting, generative modeling, spatial prediction, and federated learning, and are usually framed for the Noisy Intermediate-Scale Quantum (NISQ) regime rather than for fault-tolerant quantum computing (Chen et al., 2020, Hsu et al., 2024, Liu et al., 20 Mar 2025, Zhang et al., 6 Jan 2026).

1. Classical recurrence and the quantum substitution

The classical LSTM cell remains the reference template for essentially all quantum-enhanced variants. Given input $x_t$ and previous hidden state $h_{t-1}$, a standard cell computes

$$f_t = \sigma\bigl(W_f [h_{t-1};x_t] + b_f \bigr),\quad i_t = \sigma\bigl(W_i [h_{t-1};x_t] + b_i \bigr),$$

$$\tilde C_t = \tanh\bigl(W_C [h_{t-1};x_t] + b_C \bigr),\quad o_t = \sigma\bigl(W_o [h_{t-1};x_t] + b_o \bigr),$$

followed by

$$C_t = f_t \odot C_{t-1} + i_t \odot \tilde C_t,\qquad h_t = o_t \odot \tanh(C_t).$$

This gate-and-memory recursion is reproduced verbatim in later QK-LSTM and QLSTM papers, with the quantum component usually confined to the computation of the gate pre-activations (Hsu et al., 2024, Mahmood et al., 2024).

A common QLSTM formulation defines the concatenated vector $v_t=[h_{t-1};x_t]$ and replaces the classical affine maps by gate-specific quantum functions. In that form,

$$f_t = \sigma\bigl(\mathrm{VQC}_f(v_t)\bigr),\quad i_t = \sigma\bigl(\mathrm{VQC}_i(v_t)\bigr),\quad \tilde c_t = \tanh\bigl(\mathrm{VQC}_C(v_t)\bigr),\quad o_t = \sigma\bigl(\mathrm{VQC}_o(v_t)\bigr),$$

while the cell-state and hidden-state recursions remain classical. This pattern appears in stock forecasting, distributed QLSTM, and battery state-of-health prediction, although the precise encoding map, ansatz, and readout vary across papers (Mahmood et al., 2024, Chen et al., 18 Mar 2025, Xu et al., 22 Apr 2026).

The original hybrid QLSTM of Chen et al. is broader than the later gate-only pattern. It uses six VQC blocks in a single cell: four for the forget, input, candidate-state, and output gates, and two additional VQCs to map $o_t\cdot\tanh(c_t)$ to the hidden state $h_t$ and to the output $y_t$ (Chen et al., 2020). That design makes explicit that early quantum-enhanced LSTMs were not restricted to gate replacement alone.

2. Architectural families

The literature has diversified into several distinct model classes rather than a single canonical “quantum LSTM.” The main families can be organized as follows.

Family	Defining mechanism	Representative papers
VQC-gated QLSTM	Gate pre-activations computed by measured VQCs	(Chen et al., 2020, Mahmood et al., 2024, Xu et al., 22 Apr 2026)
QK-LSTM	Each gate uses a quantum-kernel expansion instead of $h_{t-1}$0	(Hsu et al., 2024, Hsu et al., 2024)
Post-LSTM quantum hybrid	Classical LSTM hidden state is reduced, encoded into a VQC, then read out classically	(Ubale et al., 30 Apr 2025)
Quantum-train parameterization	A QNN generates the classical LSTM weights during training	(Liu et al., 20 Mar 2025)
Federated or modular variants	QLSTM/QK-LSTM trained across clients or split across QPUs	(Hsu et al., 8 Aug 2025, Chen et al., 18 Mar 2025, Sawaika et al., 17 Apr 2026)
Quantum-inspired recurrent variants	Quantum-style nonlinearities or stochasticity on classical hardware	(Hsu et al., 4 Dec 2025, Lindsay et al., 2023)

Within the VQC-gated family, gate sharing versus gate independence is itself an architectural axis. The permeability-prediction QLSTMA introduces QLSTMA-SG, in which one VQC is shared across all four gates, and QLSTMA-IG, in which the forget, input, output, and candidate gates each receive an independent VQC (Zhang et al., 6 Jan 2026). This distinction is operationally important because it trades circuit-call count against per-gate specialization.

Kernel-based models form a separate lineage. Instead of measuring a VQC directly as the gate output, QK-LSTM replaces each classical weight matrix multiplication by a weighted expansion over quantum kernel values. In this design, the recurrent structure remains classical, but the gate nonlinearities are driven by similarities in a quantum feature space rather than by dense affine maps (Hsu et al., 2024, Hsu et al., 2024).

A further distinction concerns where the quantum computation resides. Some models embed quantum computation inside the recurrent cell, while others place it after a classical LSTM or use it only during training. Fed-QT-LSTM is especially distinctive: the QT module and a classical mapping network generate the full set of classical LSTM weights during training, but the quantum device is no longer required at inference time (Liu et al., 20 Mar 2025).

3. Encoding schemes, circuit ansätze, and readout

Two encoding strategies dominate: angle encoding and amplitude encoding. Angle encoding maps real-valued inputs to rotation angles. In stock forecasting, the classical input $h_{t-1}$1 and hidden state $h_{t-1}$2 are concatenated, encoded by a layer of $h_{t-1}$3 rotations, processed by a small entangling block such as a ring of CNOTs with parameterized $h_{t-1}$4 and $h_{t-1}$5 rotations, and then measured in the $h_{t-1}$6 basis to obtain $h_{t-1}$7 values that are classically post-processed into $h_{t-1}$8 (Mahmood et al., 2024).

Amplitude encoding is used in the QLSTM generator of LSTM-QGAN. There, each patch $h_{t-1}$9 is normalized and prepared as

$$f_t = \sigma\bigl(W_f [h_{t-1};x_t] + b_f \bigr),\quad i_t = \sigma\bigl(W_i [h_{t-1};x_t] + b_i \bigr),$$0

The previous hidden and cell states are likewise encoded into quantum states $$f_t = \sigma\bigl(W_f [h_{t-1};x_t] + b_f \bigr),\quad i_t = \sigma\bigl(W_i [h_{t-1};x_t] + b_i \bigr),$$1 and $$f_t = \sigma\bigl(W_f [h_{t-1};x_t] + b_f \bigr),\quad i_t = \sigma\bigl(W_i [h_{t-1};x_t] + b_i \bigr),$$2. For MNIST, each $$f_t = \sigma\bigl(W_f [h_{t-1};x_t] + b_f \bigr),\quad i_t = \sigma\bigl(W_i [h_{t-1};x_t] + b_i \bigr),$$3 image is divided into $$f_t = \sigma\bigl(W_f [h_{t-1};x_t] + b_f \bigr),\quad i_t = \sigma\bigl(W_i [h_{t-1};x_t] + b_i \bigr),$$4 patches of size $$f_t = \sigma\bigl(W_f [h_{t-1};x_t] + b_f \bigr),\quad i_t = \sigma\bigl(W_i [h_{t-1};x_t] + b_i \bigr),$$5; with $$f_t = \sigma\bigl(W_f [h_{t-1};x_t] + b_f \bigr),\quad i_t = \sigma\bigl(W_i [h_{t-1};x_t] + b_i \bigr),$$6, each patch has $$f_t = \sigma\bigl(W_f [h_{t-1};x_t] + b_f \bigr),\quad i_t = \sigma\bigl(W_i [h_{t-1};x_t] + b_i \bigr),$$7 pixels and $$f_t = \sigma\bigl(W_f [h_{t-1};x_t] + b_f \bigr),\quad i_t = \sigma\bigl(W_i [h_{t-1};x_t] + b_i \bigr),$$8, rounded to $$f_t = \sigma\bigl(W_f [h_{t-1};x_t] + b_f \bigr),\quad i_t = \sigma\bigl(W_i [h_{t-1};x_t] + b_i \bigr),$$9 time-steps in practice (Chu et al., 2024).

The kernel-based branch introduces a different abstraction. A classical vector $$\tilde C_t = \tanh\bigl(W_C [h_{t-1};x_t] + b_C \bigr),\quad o_t = \sigma\bigl(W_o [h_{t-1};x_t] + b_o \bigr),$$0 is embedded into an $$\tilde C_t = \tanh\bigl(W_C [h_{t-1};x_t] + b_C \bigr),\quad o_t = \sigma\bigl(W_o [h_{t-1};x_t] + b_o \bigr),$$1-qubit feature state

$$\tilde C_t = \tanh\bigl(W_C [h_{t-1};x_t] + b_C \bigr),\quad o_t = \sigma\bigl(W_o [h_{t-1};x_t] + b_o \bigr),$$2

and the kernel is the squared overlap

$$\tilde C_t = \tanh\bigl(W_C [h_{t-1};x_t] + b_C \bigr),\quad o_t = \sigma\bigl(W_o [h_{t-1};x_t] + b_o \bigr),$$3

QK-LSTM papers typically use shallow NISQ-friendly feature maps with $$\tilde C_t = \tanh\bigl(W_C [h_{t-1};x_t] + b_C \bigr),\quad o_t = \sigma\bigl(W_o [h_{t-1};x_t] + b_o \bigr),$$4, data rotations $$\tilde C_t = \tanh\bigl(W_C [h_{t-1};x_t] + b_C \bigr),\quad o_t = \sigma\bigl(W_o [h_{t-1};x_t] + b_o \bigr),$$5, and a linear CNOT chain; one reported configuration uses $$\tilde C_t = \tanh\bigl(W_C [h_{t-1};x_t] + b_C \bigr),\quad o_t = \sigma\bigl(W_o [h_{t-1};x_t] + b_o \bigr),$$6 qubits and depth approximately $$\tilde C_t = \tanh\bigl(W_C [h_{t-1};x_t] + b_C \bigr),\quad o_t = \sigma\bigl(W_o [h_{t-1};x_t] + b_o \bigr),$$7 layers (Hsu et al., 2024, Hsu et al., 2024).

Across VQC-gated models, the circuit ansatz is usually hardware-efficient. Examples include two repeat layers of $$\tilde C_t = \tanh\bigl(W_C [h_{t-1};x_t] + b_C \bigr),\quad o_t = \sigma\bigl(W_o [h_{t-1};x_t] + b_o \bigr),$$8 plus ring CX entanglers in LSTM-QGAN; Hadamard-plus-angle encoding followed by CNOT rings and trainable single-qubit rotations in Chen et al.; and shallow layers of $$\tilde C_t = \tanh\bigl(W_C [h_{t-1};x_t] + b_C \bigr),\quad o_t = \sigma\bigl(W_o [h_{t-1};x_t] + b_o \bigr),$$9, $$C_t = f_t \odot C_{t-1} + i_t \odot \tilde C_t,\qquad h_t = o_t \odot \tanh(C_t).$$0, $$C_t = f_t \odot C_{t-1} + i_t \odot \tilde C_t,\qquad h_t = o_t \odot \tanh(C_t).$$1 plus ring or ladder CNOTs in battery SOH estimation (Chu et al., 2024, Chen et al., 2020, Xu et al., 22 Apr 2026). Alternative kernel circuits include a Block-Product State ansatz in which qubits are partitioned into pairs, features are encoded by $$C_t = f_t \odot C_{t-1} + i_t \odot \tilde C_t,\qquad h_t = o_t \odot \tanh(C_t).$$2 rotations, entangled by CNOT, and followed by a parameterized $$C_t = f_t \odot C_{t-1} + i_t \odot \tilde C_t,\qquad h_t = o_t \odot \tanh(C_t).$$3 on one qubit (Hsu et al., 8 Aug 2025).

Regardless of encoding, the readout is typically classical. Measured $$C_t = f_t \odot C_{t-1} + i_t \odot \tilde C_t,\qquad h_t = o_t \odot \tanh(C_t).$$4-basis expectation values or probabilities are mapped through $$C_t = f_t \odot C_{t-1} + i_t \odot \tilde C_t,\qquad h_t = o_t \odot \tanh(C_t).$$5 or $$C_t = f_t \odot C_{t-1} + i_t \odot \tilde C_t,\qquad h_t = o_t \odot \tanh(C_t).$$6 and inserted into the ordinary LSTM recursions

$$C_t = f_t \odot C_{t-1} + i_t \odot \tilde C_t,\qquad h_t = o_t \odot \tanh(C_t).$$7

which remain the structural backbone of the model (Chu et al., 2024, Mahmood et al., 2024).

4. Optimization and training dynamics

Training is almost always hybrid: classical backpropagation through time (BPTT) through the recurrent graph, and quantum gradient estimation for circuit parameters. The standard quantum gradient primitive is the parameter-shift rule. In the LSTM-QGAN exposition, for a rotation gate $$C_t = f_t \odot C_{t-1} + i_t \odot \tilde C_t,\qquad h_t = o_t \odot \tanh(C_t).$$8,

$$C_t = f_t \odot C_{t-1} + i_t \odot \tilde C_t,\qquad h_t = o_t \odot \tanh(C_t).$$9

The same rule is used in stock forecasting, QK-LSTM, solar forecasting, fraud detection, distributed QLSTM, and battery SOH prediction (Chu et al., 2024, Hsu et al., 2024, Khan et al., 2023, Ubale et al., 30 Apr 2025, Chen et al., 18 Mar 2025, Xu et al., 22 Apr 2026).

Loss functions vary with the task. Mean-squared error is standard in forecasting and regression. Binary cross-entropy is used in fraud detection and SUSY classification. Cross-entropy appears in human activity recognition. Huber loss is used in permeability prediction. LSTM-QGAN instead uses the Wasserstein QGAN objective with gradient penalty,

$v_t=[h_{t-1};x_t]$0

(Chu et al., 2024, Hsu et al., 8 Aug 2025, Ubale et al., 30 Apr 2025, Zhang et al., 6 Jan 2026, Sawaika et al., 17 Apr 2026).

Reported optimizers include RMSProp with learning rate $v_t=[h_{t-1};x_t]$1, decay $v_t=[h_{t-1};x_t]$2, and $v_t=[h_{t-1};x_t]$3 in the 2020 QLSTM; Adam with learning rate $v_t=[h_{t-1};x_t]$4 in solar forecasting; Adam or SGD with $v_t=[h_{t-1};x_t]$5 in QK-LSTM; and Adam with learning rate $v_t=[h_{t-1};x_t]$6, weight decay $v_t=[h_{t-1};x_t]$7, and dropout $v_t=[h_{t-1};x_t]$8 in Fed-QK-LSTM (Chen et al., 2020, Khan et al., 2023, Hsu et al., 2024, Hsu et al., 8 Aug 2025).

Federated and modular models add a systems layer to the optimization. Fed-QK-LSTM and Fed-QT-LSTM use Federated Averaging, while distributed QLSTM partitions each gate circuit into subcircuits executed across multiple QPUs and concatenates their outputs classically. In Fed-QK-LSTM the server update is

$v_t=[h_{t-1};x_t]$9

where $$f_t = \sigma\bigl(\mathrm{VQC}_f(v_t)\bigr),\quad i_t = \sigma\bigl(\mathrm{VQC}_i(v_t)\bigr),\quad \tilde c_t = \tanh\bigl(\mathrm{VQC}_C(v_t)\bigr),\quad o_t = \sigma\bigl(\mathrm{VQC}_o(v_t)\bigr),$$0 and $$f_t = \sigma\bigl(\mathrm{VQC}_f(v_t)\bigr),\quad i_t = \sigma\bigl(\mathrm{VQC}_i(v_t)\bigr),\quad \tilde c_t = \tanh\bigl(\mathrm{VQC}_C(v_t)\bigr),\quad o_t = \sigma\bigl(\mathrm{VQC}_o(v_t)\bigr),$$1 denote the distributed model parameters (Hsu et al., 8 Aug 2025, Liu et al., 20 Mar 2025, Chen et al., 18 Mar 2025).

5. Empirical record across applications

The empirical literature is heterogeneous in task design and evaluation protocol, but several papers report concrete improvements relative to classical LSTM baselines.

Domain	Representative model	Reported outcome
Solar power forecasting	QLSTM (Khan et al., 2023)	up to 50% lower test loss; 2× faster convergence
KSE 100 forecasting	QLSTM (Mahmood et al., 2024)	train MSE $$f_t = \sigma\bigl(\mathrm{VQC}_f(v_t)\bigr),\quad i_t = \sigma\bigl(\mathrm{VQC}_i(v_t)\bigr),\quad \tilde c_t = \tanh\bigl(\mathrm{VQC}_C(v_t)\bigr),\quad o_t = \sigma\bigl(\mathrm{VQC}_o(v_t)\bigr),$$2 vs $$f_t = \sigma\bigl(\mathrm{VQC}_f(v_t)\bigr),\quad i_t = \sigma\bigl(\mathrm{VQC}_i(v_t)\bigr),\quad \tilde c_t = \tanh\bigl(\mathrm{VQC}_C(v_t)\bigr),\quad o_t = \sigma\bigl(\mathrm{VQC}_o(v_t)\bigr),$$3; test MSE $$f_t = \sigma\bigl(\mathrm{VQC}_f(v_t)\bigr),\quad i_t = \sigma\bigl(\mathrm{VQC}_i(v_t)\bigr),\quad \tilde c_t = \tanh\bigl(\mathrm{VQC}_C(v_t)\bigr),\quad o_t = \sigma\bigl(\mathrm{VQC}_o(v_t)\bigr),$$4 vs $$f_t = \sigma\bigl(\mathrm{VQC}_f(v_t)\bigr),\quad i_t = \sigma\bigl(\mathrm{VQC}_i(v_t)\bigr),\quad \tilde c_t = \tanh\bigl(\mathrm{VQC}_C(v_t)\bigr),\quad o_t = \sigma\bigl(\mathrm{VQC}_o(v_t)\bigr),$$5
AQI forecasting	QK-LSTM (Hsu et al., 2024)	RMSE 9.20 vs 15.94; MAE 7.15 vs 11.07; $$f_t = \sigma\bigl(\mathrm{VQC}_f(v_t)\bigr),\quad i_t = \sigma\bigl(\mathrm{VQC}_i(v_t)\bigr),\quad \tilde c_t = \tanh\bigl(\mathrm{VQC}_C(v_t)\bigr),\quad o_t = \sigma\bigl(\mathrm{VQC}_o(v_t)\bigr),$$6 0.84 vs 0.78
POS tagging benchmark	QK-LSTM (Hsu et al., 2024)	183 vs 477 parameters; final accuracy $$f_t = \sigma\bigl(\mathrm{VQC}_f(v_t)\bigr),\quad i_t = \sigma\bigl(\mathrm{VQC}_i(v_t)\bigr),\quad \tilde c_t = \tanh\bigl(\mathrm{VQC}_C(v_t)\bigr),\quad o_t = \sigma\bigl(\mathrm{VQC}_o(v_t)\bigr),$$7; loss $$f_t = \sigma\bigl(\mathrm{VQC}_f(v_t)\bigr),\quad i_t = \sigma\bigl(\mathrm{VQC}_i(v_t)\bigr),\quad \tilde c_t = \tanh\bigl(\mathrm{VQC}_C(v_t)\bigr),\quad o_t = \sigma\bigl(\mathrm{VQC}_o(v_t)\bigr),$$8
Human activity recognition	Fed-QK-LSTM (Hsu et al., 8 Aug 2025)	accuracy 0.95 vs 0.90; parameters 137,996 vs 202,696
SUSY classification	Federated QLSTM (Sawaika et al., 17 Apr 2026)	$$f_t = \sigma\bigl(\mathrm{VQC}_f(v_t)\bigr),\quad i_t = \sigma\bigl(\mathrm{VQC}_i(v_t)\bigr),\quad \tilde c_t = \tanh\bigl(\mathrm{VQC}_C(v_t)\bigr),\quad o_t = \sigma\bigl(\mathrm{VQC}_o(v_t)\bigr),$$9 parameters; 20K data points; performance within $o_t\cdot\tanh(c_t)$0
Battery SOH prediction	QLSTM (Xu et al., 22 Apr 2026)	CALCE MAE $o_t\cdot\tanh(c_t)$1 vs $o_t\cdot\tanh(c_t)$2
Reservoir permeability	QLSTMA-IG (Zhang et al., 6 Jan 2026)	8 qubits: MAE 108.0 mD vs 133.7 mD; RMSE 140.7 mD vs 175.9 mD
MNIST generative modeling	LSTM-QGAN (Chu et al., 2024)	FID 193.28 vs 318.02; 5× fewer total qubits; 12× fewer two-qubit gates

The reported gains are not confined to scalar forecasting. In LSTM-QGAN, replacing a patch-based generator with a QLSTM generator removes PCA preprocessing and reduces total qubits from $o_t\cdot\tanh(c_t)$3 to $o_t\cdot\tanh(c_t)$4, total 1-qubit gates from $o_t\cdot\tanh(c_t)$5 to $o_t\cdot\tanh(c_t)$6, and total 2-qubit gates from $o_t\cdot\tanh(c_t)$7 to $o_t\cdot\tanh(c_t)$8, while lowering average FID from $o_t\cdot\tanh(c_t)$9 to $h_t$0 (Chu et al., 2024).

Distributed QLSTM results also indicate that modular execution does not necessarily destroy trainability. On the damped harmonic oscillator benchmark, the distributed QLSTM reports $h_t$1 and convergence in $h_t$2 epochs; on NARMA, the distributed QLSTM reports $h_t$3 and convergence in $h_t$4 epochs (Chen et al., 18 Mar 2025).

Not all empirical gains are purely accuracy-oriented. Fed-QT-LSTM reports $h_t$5 classical plus $h_t$6 quantum trainable parameters, total $h_t$7, while generating a classical LSTM of size $h_t$8; the paper states that QT-LSTM uses only $h_t$9 of the classical LSTM’s trainable parameters (Liu et al., 20 Mar 2025). The fraud-detection hybrid reports accuracy $y_t$0 versus $y_t$1, recall $y_t$2 versus $y_t$3, and F1 score $y_t$4 versus $y_t$5, but also average time per epoch $y_t$6 s versus $y_t$7 s and inference time $y_t$8 s versus $y_t$9 s (Ubale et al., 30 Apr 2025).

6. Limitations, controversies, and common misconceptions

A recurring limitation is that many studies are simulation-based. Mahmood et al. state that their QLSTM stock experiments are conducted with noise-free circuits and acknowledge that real hardware would degrade performance. The implementation-guidelines paper is explicitly theoretical and states that the actual architecture and its practical effectiveness remain to be developed and demonstrated in future work (Mahmood et al., 2024, Zhou et al., 2024). This makes hardware transfer a central unresolved issue.

Noise, depth, and trainability are persistent concerns. Several papers explicitly mention circuit depth and noise accumulation on NISQ devices, barren plateaus as qubit count or layer count grows, and the cost of encoding high-dimensional time series into limited qubit registers (Mahmood et al., 2024, Xu et al., 22 Apr 2026). In the battery SOH study, qubit scaling produces a non-monotonic MAE curve: performance improves from $h_{t-1}$00, dips around $h_{t-1}$01, and plateaus at $h_{t-1}$02, which the authors interpret as a balance between expressive capacity and trainability (Xu et al., 22 Apr 2026). Kernel models additionally face sampling overhead because every kernel estimate requires repeated circuit evaluation (Hsu et al., 2024).

Scalability is therefore not a single notion. LSTM-QGAN emphasizes constant NISQ footprint as input size grows because only the number of time steps $h_{t-1}$03 increases (Chu et al., 2024). Distributed QLSTM instead emphasizes partitioning large gate circuits into smaller subcircuits, but it also notes an $h_{t-1}$04 communication latency and classical memory overhead for aggregating outputs across $h_{t-1}$05 subcircuits (Chen et al., 18 Mar 2025). Federated formulations shift the problem again, treating privacy, communication, and small local quantum models as the primary design constraints (Hsu et al., 8 Aug 2025, Sawaika et al., 17 Apr 2026).

A common misconception is that “quantum-enhanced LSTM” names one uniform architecture deployed on quantum hardware end to end. The literature shows otherwise. Fed-QT-LSTM uses a QNN only to generate classical LSTM weights during training and eliminates reliance on quantum devices during inference (Liu et al., 20 Mar 2025). QKAN-LSTM is quantum-inspired rather than quantum-executed and is described as preserving quantum-level expressivity while remaining fully executable on classical hardware (Hsu et al., 4 Dec 2025). The stochastic LSTM of 2023 goes further by replacing quantum measurement stochasticity with classical stochastic rounding, explicitly asking whether some reported benefits can be approached without quantum hardware at all (Lindsay et al., 2023).

7. Research directions

Several research trajectories recur across the literature. One is direct hardware validation with error mitigation. Proposed directions include real NISQ implementation with error mitigation, zero-noise extrapolation, probabilistic error cancellation, noise-aware circuit design, and embedding small error-correcting codes into VQCs (Mahmood et al., 2024, Khan et al., 2023). These proposals reflect a shared recognition that noiseless simulator gains do not by themselves establish deployable advantage.

A second trajectory is architectural co-design. Papers propose advanced encodings such as amplitude encoding or hybrid classical/quantum feature maps, automated circuit architecture search over depth and entangling pattern, quantum-aware regularizers, and hybrid stacking with Transformer or attention blocks (Mahmood et al., 2024). QLSTMA already couples quantum gate augmentation with attention, and its authors suggest future extensions such as multi-head quantum attention and quantum reservoir computing (Zhang et al., 6 Jan 2026). This suggests that the field is moving from isolated recurrent cells toward composite sequence models.

A third direction is systems scaling. Distributed QLSTM frames modular quantum computers as a route to larger recurrent models, and identifies dynamic repartitioning, adaptive shot allocation, and tighter integration with Quantum High-performance computing ecosystems as open problems (Chen et al., 18 Mar 2025). Federated QK-LSTM and federated QLSTM papers place the same models in edge and privacy-sensitive environments, where communication efficiency and compact parameterization become first-order concerns (Hsu et al., 8 Aug 2025, Sawaika et al., 17 Apr 2026).

Finally, the domain range continues to broaden. Published applications now include stock forecasting, solar power, air quality, human activity recognition, gravitational-wave signals, battery state of health, fraud detection, SUSY classification, reservoir permeability, and generative modeling (Mahmood et al., 2024, Khan et al., 2023, Hsu et al., 2024, Hsu et al., 8 Aug 2025, Liu et al., 20 Mar 2025, Xu et al., 22 Apr 2026, Ubale et al., 30 Apr 2025, Sawaika et al., 17 Apr 2026, Zhang et al., 6 Jan 2026, Chu et al., 2024). A plausible implication is that “quantum-enhanced LSTM” is better understood as a design space for hybrid sequential models than as a single settled architecture.