QASA Sequence: Hybrid Quantum Time-Series Model

• QASA Sequence is a hybrid quantum–classical model that integrates an LSTM sequence encoder with quantum self-attention mechanisms for financial time-series analysis.
• The method uses variational quantum circuits to generate query, key, and value embeddings, enhancing the capture of nonlinear features over raw 10-day price windows.
• Empirical studies demonstrate its superior risk-adjusted returns and stability compared to classical and pure quantum models in decentralized finance rebalancing.

QASA Sequence is a hybrid quantum–classical sequence model for financial time-series decision making in decentralized finance, defined in the AMM rebalancing literature as the sequence-oriented variant of Quantum Adaptive Self-Attention (QASA). In the comparative DeFi backtesting study, it is instantiated as an LSTM-based temporal encoder followed by quantum self-attention whose query, key, and value embeddings are generated by variational quantum circuits, and then a classical decoder producing a binary rebalancing decision for automated market makers (Chen et al., 14 Sep 2025). The underlying QASA mechanism originates in prior work on quantum-enhanced transformer models, where “Quantum Adaptive Self-Attention” was introduced as a hybrid classical–quantum attention framework (Chen et al., 5 Apr 2025).

1. Definition and nomenclature

“QASA” stands for Quantum Adaptive Self-Attention. In the financial rebalancing study, the term denotes a hybrid attention module in which the query, key, and value embeddings are produced by quantum circuits rather than by linear projections. The paper distinguishes two variants: QASA Hybrid, which takes engineered features as input, and QASA Sequence, which takes 10 time steps directly as input and is therefore explicitly a sequence model (Chen et al., 14 Sep 2025).

Conceptually, QASA Sequence is summarized as:

$$\text{LSTM (classical sequence encoder)} \rightarrow \text{quantum self-attention (QASA)} \rightarrow \text{classical feedforward decoder} \rightarrow y_t \in \{0,1\}.$$

The binary target is a rebalancing decision for AMM strategies in DeFi. The authors describe its superiority as arising from three components: LSTM temporal processing, because “Long Short-Term Memory networks capture sequential patterns in financial time series data, providing better context for decision making”; quantum enhancement, because “Quantum layers process the LSTM outputs to capture nonlinear relationships that classical methods might miss”; and hybrid architecture, because “The combination of classical sequence processing and quantum feature enhancement provides complementary advantages” (Chen et al., 14 Sep 2025).

A closely related single-asset study describes QASA-Sequence as operating directly on short raw price windows and using quantum circuits to generate Q/K/V for each time step before applying self-attention across the time dimension, confirming that the term refers to a sequence-centric QASA instantiation rather than to a generic QASA block (Chen et al., 21 Sep 2025).

2. Architecture and quantum attention mechanism

The core QASA mechanism is defined over an input sequence

$\mathbf{X} \in \mathbb{R}^{T \times d},$

with token vectors $\mathbf{x}_t \in \mathbb{R}^d$. For each token, QASA computes quantum query, key, and value embeddings through three variational quantum circuits:

$$\mathbf{Q}_t = \text{VQC}_q(\mathbf{x}_t),\quad \mathbf{K}_t = \text{VQC}_k(\mathbf{x}_t),\quad \mathbf{V}_t = \text{VQC}_v(\mathbf{x}_t).$$

Each $\text{VQC}(\cdot)$ consists of state preparation, a parameterized unitary, and measurement. The state-preparation step uses amplitude encoding:

$$\ket{\psi_t} = \frac{1}{\|\mathbf{x}_t\|} \sum_{i=1}^{d} x_{t,i} \ket{i},$$

with the number of qubits chosen as

$n = \lceil \log_2 d \rceil.$

The variational circuit is given as

$$U(\boldsymbol{\theta}) = \prod_{\ell=1}^{L} \left[ \bigotimes_{i=1}^{n} RY(\theta_{\ell,i}) \cdot CNOT_{i,i+1} \right].$$

Measurement returns expectation values of Pauli-$Z$ on each qubit:

$$\mathbf{z}_t = \left( \langle Z_1 \rangle, \dots, \langle Z_n \rangle \right),$$

and, more generally,

$\mathbf{X} \in \mathbb{R}^{T \times d},$0

These expectation vectors serve as the quantum-derived Q/K/V representations. Attention itself is then computed classically:

$\mathbf{X} \in \mathbb{R}^{T \times d},$1

For QASA Sequence specifically, the stated hyperparameters are: “LSTM with 64 units, 2 quantum layers, dropout = 0.2.” The model takes 10 time steps directly as input. A sliding window of $\mathbf{X} \in \mathbb{R}^{T \times d},$2 days is fed into the LSTM, which outputs hidden states that are then processed by the QASA quantum attention module; the resulting attention output is passed to a classical feedforward decoder that predicts the next-step decision $\mathbf{X} \in \mathbb{R}^{T \times d},$3 (Chen et al., 14 Sep 2025).

Formally, the overall mapping is summarized in the paper as

$\mathbf{X} \in \mathbb{R}^{T \times d},$4

where $\mathbf{X} \in \mathbb{R}^{T \times d},$5 bundles both classical parameters and quantum parameters $\mathbf{X} \in \mathbb{R}^{T \times d},$6.

3. Role in AMM rebalancing and DeFi workflow

In the DeFi setting, QASA Sequence solves a binary classification task

$\mathbf{X} \in \mathbb{R}^{T \times d},$7

where $\mathbf{X} \in \mathbb{R}^{T \times d},$8 answers “should we rebalance the AMM position at time $\mathbf{X} \in \mathbb{R}^{T \times d},$9?”. The model is trained on daily time-series data for BTCUSDC, ETHUSDC, and USDCUSDT, using a 10-day history per decision (Chen et al., 14 Sep 2025).

The study defines three labeling schemes. For the Rebalancing AMM Project,

$\mathbf{x}_t \in \mathbb{R}^d$0

with $\mathbf{x}_t \in \mathbb{R}^d$1. For the Concentrated Liquidity AMM Project,

$\mathbf{x}_t \in \mathbb{R}^d$2

For the Quantum-Enhanced AMM Project,

$\mathbf{x}_t \in \mathbb{R}^d$3

with $\mathbf{x}_t \in \mathbb{R}^d$4.

Within the backtest, QASA Sequence functions as a signal generator. If $\mathbf{x}_t \in \mathbb{R}^d$5, the strategy executes a rebalance trade; if $\mathbf{x}_t \in \mathbb{R}^d$6, it holds the current position. The paper does not provide an explicit position-sizing formula beyond this binary decision. Economic performance is evaluated through Total return

$\mathbf{x}_t \in \mathbb{R}^d$7

and Rebalancing count

$\mathbf{x}_t \in \mathbb{R}^d$8

The distinction between QASA Sequence and QASA Hybrid is central here. Classical models in the study use up to 122 engineered features, whereas quantum and hybrid models use compact feature sets (6–8 features) mapped to qubits. QASA Sequence differs from QASA Hybrid in that it operates on raw time steps rather than on extracted features; the LSTM ingests a temporal sequence $\mathbf{x}_t \in \mathbb{R}^d$9, making sequential dynamics an explicit part of the model design rather than a byproduct of feature engineering (Chen et al., 14 Sep 2025).

4. Training configuration and implementation characteristics

The principal implementation settings reported for QASA Sequence are a classical LSTM with 64 units, dropout 0.2, a classical feedforward decoder, and 2 quantum layers. The data split is 70% train, 15% validation, 15% test, preserving chronological order to avoid look-ahead bias (Chen et al., 14 Sep 2025).

The quantum component uses the VQC construction described above, with $$\mathbf{Q}_t = \text{VQC}_q(\mathbf{x}_t),\quad \mathbf{K}_t = \text{VQC}_k(\mathbf{x}_t),\quad \mathbf{V}_t = \text{VQC}_v(\mathbf{x}_t).$$0 rotations, CNOT entanglement, amplitude encoding, and Pauli-$$\mathbf{Q}_t = \text{VQC}_q(\mathbf{x}_t),\quad \mathbf{K}_t = \text{VQC}_k(\mathbf{x}_t),\quad \mathbf{V}_t = \text{VQC}_v(\mathbf{x}_t).$$1 readout. The qubit count follows

$$\mathbf{Q}_t = \text{VQC}_q(\mathbf{x}_t),\quad \mathbf{K}_t = \text{VQC}_k(\mathbf{x}_t),\quad \mathbf{V}_t = \text{VQC}_v(\mathbf{x}_t).$$2

where $$\mathbf{Q}_t = \text{VQC}_q(\mathbf{x}_t),\quad \mathbf{K}_t = \text{VQC}_k(\mathbf{x}_t),\quad \mathbf{V}_t = \text{VQC}_v(\mathbf{x}_t).$$3 is the dimension of the token vector after the LSTM or a projection thereof. The paper notes that an order of 6–7 qubits is typical for these hybrid models.

Evaluation combines classification and trading metrics. The classification metrics are

$$\mathbf{Q}_t = \text{VQC}_q(\mathbf{x}_t),\quad \mathbf{K}_t = \text{VQC}_k(\mathbf{x}_t),\quad \mathbf{V}_t = \text{VQC}_v(\mathbf{x}_t).$$4

$$\mathbf{Q}_t = \text{VQC}_q(\mathbf{x}_t),\quad \mathbf{K}_t = \text{VQC}_k(\mathbf{x}_t),\quad \mathbf{V}_t = \text{VQC}_v(\mathbf{x}_t).$$5

and AUC. Trading metrics include the Sharpe ratio

$$\mathbf{Q}_t = \text{VQC}_q(\mathbf{x}_t),\quad \mathbf{K}_t = \text{VQC}_k(\mathbf{x}_t),\quad \mathbf{V}_t = \text{VQC}_v(\mathbf{x}_t).$$6

and Maximum Drawdown

$$\mathbf{Q}_t = \text{VQC}_q(\mathbf{x}_t),\quad \mathbf{K}_t = \text{VQC}_k(\mathbf{x}_t),\quad \mathbf{V}_t = \text{VQC}_v(\mathbf{x}_t).$$7

The paper does not name specific quantum software frameworks or hardware for QASA Sequence, and no explicit noise models or error-mitigation techniques are described. This suggests simulator-based experimentation rather than deployment on physical quantum hardware. A related telecommunication forecasting benchmark explicitly reports implementation in PyTorch + PennyLane (quantum simulation) for a QASA model built from quantum-derived Q/K/V, which is consistent with this broader 2025 QASA literature (Chen et al., 6 Aug 2025).

5. Empirical performance and comparative standing

QASA Sequence is reported as the best-performing individual model in the comparative DeFi study. Its key metrics are: Return = 13.99%, Sharpe ratio = 1.76, Volatility = 8.35%, Maximum drawdown = -10.10%, and Calmar ratio = 6.51 (Chen et al., 14 Sep 2025).

Against classical baselines, the comparison is as follows. Random Forest achieves 13.16% return, Sharpe 1.68, volatility 14.88%, and Calmar 2.86. Gradient Boosting achieves 12.31% return, Sharpe 1.68, volatility 14.49%, and Calmar 2.41. Logistic Regression achieves 5.43% return and Sharpe 1.06. Against pure quantum baselines, QSVM records 4.77% return and Sharpe 0.87; QNN records 4.47% return, Sharpe 0.82, and volatility 19.76%; VQE Classifier records 3.00% return and Sharpe 0.79. Against other hybrid models, QASA Hybrid records 11.91% return, Sharpe 1.32, volatility 13.05%, and max drawdown -1.70%, while QuantumRWKV records 7.96% return and Sharpe 1.19. The Transformer records 11.73% return, Sharpe 1.23, volatility 15.39%, and max drawdown -8.21% (Chen et al., 14 Sep 2025).

At the family level, the study reports that hybrid quantum models achieve superior overall performance with 11.2% average return and 1.42 average Sharpe ratio, while classical ML models show 9.8% average return and 1.47 average Sharpe ratio. The paper nevertheless identifies QASA Sequence as the best individual model, with the highest return and highest Sharpe ratio among all ten compared models (Chen et al., 14 Sep 2025).

The multiple-run analysis reports 5 runs per model. For QASA Sequence, Return standard deviation = 2.04%, Sharpe standard deviation = 0.26, and Volatility standard deviation = 1.22%. It is ranked 1st in “stability rank.” The statistical testing states that “QASA Sequence shows significantly higher returns than all other models (p < 0.01)”, and that hybrid models significantly outperform pure quantum models in risk-adjusted returns (p < 0.01) (Chen et al., 14 Sep 2025).

A related BTCUSDC-focused study reaches the same headline conclusion, describing QASA-Sequence as attaining the best single-model risk-adjusted performance with 13.99% return and Sharpe 1.76, while placing hybrid QASA-family models in a broader performance–stability–cost trade-off (Chen et al., 21 Sep 2025).

6. Interpretation, misconceptions, and limitations

The authors interpret QASA Sequence’s results as evidence for the complementarity of temporal modeling and quantum feature transformation. Their explicit explanation is that the LSTM captures long- and short-term dependencies, the VQCs implement a high-dimensional, non-linear transformation via amplitude encoding and entangling rotations, and the combined architecture produces complementary advantages (Chen et al., 14 Sep 2025).

A recurrent misconception in the QASA literature is that the method replaces the entire attention mechanism with a quantum routine. The primary financial formulation of QASA Sequence does not do this: Q/K/V are quantum-derived, but attention is still computed with the standard classical softmax formula. In the earlier transformer-oriented QASA paper, the situation is even more nuanced: the final encoder layer retains classical multi-head self-attention, while a QuantumLayer performs a residual quantum projection before the FFN. That paper therefore treats QASA as a hybrid quantum refinement of contextual token representations rather than as a fully quantum attention computation (Chen et al., 5 Apr 2025).

The limits of QASA-style sequence modeling are also task-dependent. In the urban telecommunication forecasting benchmark, a QASA model using PQC-generated Q/K/V underperformed the baseline LSTM at every tested sequence length, and its error increased as $$\mathbf{Q}_t = \text{VQC}_q(\mathbf{x}_t),\quad \mathbf{K}_t = \text{VQC}_k(\mathbf{x}_t),\quad \mathbf{V}_t = \text{VQC}_v(\mathbf{x}_t).$$8 grew from 4 to 64. The authors conclude there that quantum enhancements are not universally advantageous and that effectiveness depends strongly on task and architectural design (Chen et al., 6 Aug 2025). This suggests that QASA Sequence’s strong DeFi performance should not be generalized indiscriminately to all sequential prediction domains.

The financial papers identify substantial practical constraints. QASA Sequence has complexity = 8, training time = 6.0 units, and efficiency score = 1.30. The authors state that “Quantum model training time is longer, potentially limiting real-time applications,” and recommend classical ML, particularly Random Forest and Gradient Boosting, for real-time trading, while recommending QASA Sequence for maximum return optimization when computational resources allow (Chen et al., 14 Sep 2025). They also note the absence of transaction-cost modeling, the longer training time of hybrid quantum models, and the uncertainty around how well the gains would persist once gas costs, slippage, and other DeFi deployment frictions are included.

Future directions mentioned for QASA-type models include further optimize quantum model architectures and training strategies, develop more efficient quantum models for real-time application feasibility, and deepen analysis of theoretical foundations for quantum model advantages. In the related AMM-rebalancing study, additional directions include multi-asset AMMs, higher-frequency data, improved quantum circuit architectures, and integration with full transformer stacks (Chen et al., 21 Sep 2025). A plausible implication is that “QASA Sequence” presently denotes an experimentally successful but still simulator-era research architecture, rather than a settled production design for on-chain DeFi systems.