Titans-QFWP: A Regime-Aware Hybrid Quantum Fast Weight Programmer for Portfolio Optimization

Ming-Kai Hung; Jun-Hao Chen; Yun-Cheng Tsai; Samuel Yen-Chi Chen

cs.LGAug 29, 2026

Titans-QFWP: A Regime-Aware Hybrid Quantum Fast Weight Programmer for Portfolio Optimization

Authors: Ming-Kai Hung, Jun-Hao Chen, Yun-Cheng Tsai, Samuel Yen-Chi Chen

Organizations: Dept. of Technology Application and Human Resource Development, National Taiwan Normal University, Taipei, Taiwan · Dept. of Bioenvironmental Systems Engineering, National Taiwan University, Taipei, Taiwan · PecuLab LLC, Seattle, WA, USA · Wells Fargo, USA

Abstract

We propose Titans-QFWP, a hybrid reinforcement learning architecture integrating a Quantum Fast Weight Programmer with Titans-style memory (Persistence, Surprise, and Forgetting) for adaptive portfolio optimization. To address high-dimensional market features, we introduce an enhanced A3C^2 framework with Hungarian-aligned K-means clustering and scaled log-return rewards. Evaluated on 468 S&P 500 stocks under an Equal-Parameter-Count (EPC) benchmark with approximately 3,000 trainable parameters, Titans-QFWP achieves strong performance (median ARR 0.4260, Calmar 8.5504, IR 0.8427). Ablation results reveal that quantum gating fundamentally reshapes memory component roles, with Persistence supporting drawdown control, Surprise contributing to return generation, and Forgetting providing additional stabilization. By stabilizing these quantum representations, the model enables defensive allocation during market drawdowns while preserving upside potential.

Figures & tables

Fig. 1: System architecture of the hybrid Titans-QFWP agent integrated with the Enhanced A3C 2 continuous-reward portfolio simulation environment.

Architecture	Total	Quantum	Classical
Classical Architectures
Titans (Memory-as-Context)	2,997	0	2,997
FWP	3,000	0	3,000
Titans-FWP (Full)	2,999	0	2,999
Titans-FWP ( $-$ Forgetting)	2,990	0	2,990
Titans-FWP ( $-$ Persistence)	2,931	0	2,931

TABLE I: Parameter configuration for the EPC benchmark.

Architecture	ARR	MDD	Sortino	Calmar	IR
Market Benchmark
S&P 500 (Buy & Hold)	$0.2528$	$-0.0353$	$8.5405$	$7.1638$	N/A
Baseline & Classical Architectures
Titans (Memory-as-Context)	$0.2557\;\;[0.2649]$	$\mathbf{-0.0512}\;\;[\mathbf{0.0355}]$	$3.3645\;\;[4.4568]$	$3.9077\;\;[7.2651]$	$0.1374\;\;[1.8125]$
FWP	$\mathbf{0.3423}\;\;[\mathbf{0.1904}]$	$-0.0918\;\;[0.1046]$	$3.3498\;\;[6.1209]$	$3.9429\;\;[7.7964]$	$\mathbf{0.4447}\;\;[\mathbf{1.3117}]$
Titans-FWP (Full)	$0.3175\;\;[0.2013]$	$-0.0606\;\;[0.0648]$	$\mathbf{4.9382}\;\;[\mathbf{3.6665}]$	$\mathbf{6.2776}\;\;[\mathbf{5.6673}]$	$0.3891\;\;[0.9531]$

TABLE II: S&P 500 out-of-sample performance across asset allocation baselines (median [IQR], seeds 1–10).

Architecture	ARR	MDD	Sortino	Calmar	IR
Classical Ablation Study: Titans-FWP
FWP (Baseline)	$\mathbf{0.3423}\;\;[\mathbf{0.1904}]$	$-0.0918\;\;[0.1046]$	$3.3498\;\;[6.1209]$	$3.9429\;\;[7.7964]$	$\mathbf{0.4447}\;\;[\mathbf{1.3117}]$
Titans-FWP (Full)	$0.3175\;\;[0.2013]$	$\mathbf{-0.0606}\;\;[\mathbf{0.0648}]$	$\mathbf{4.9382}\;\;[\mathbf{3.6665}]$	$\mathbf{6.2776}\;\;[\mathbf{5.6673}]$	$0.3891\;\;[0.9531]$
Titans-FWP ( $-$ Forgetting)	$0.2752\;\;[0.1713]$	$-0.0790\;\;[0.0453]$	$3.5281\;\;[3.4122]$	$3.4519\;\;[4.0856]$	$0.1993\;\;[1.0045]$
Titans-FWP ( $-$ Persistence)	$0.2841\;\;[0.2500]$	$-0.0702\;\;[0.0540]$	$4.1309\;\;[2.8475]$	$4.5385\;\;[3.4245]$	$0.1927\;\;[1.2757]$
Titans-FWP ( $-$ Surprise)	$0.1907\;\;[0.1834]$	$-0.0774\;\;[0.0731]$	$2.8587\;\;[3.8253]$	$2.5238\;\;[6.5771]$	$-0.4547\;\;[1.1375]$

TABLE III: Performance metrics for Titans-FWP ablation variants (median [IQR], seeds 1–10).

Architecture	ARR	MDD	Sortino	Calmar	IR
Quantum Ablation Study: Titans-QFWP
QFWP (Baseline)	$0.1806\;\;[0.1437]$	$-0.1017\;\;[0.0887]$	$1.8849\;\;[1.1011]$	$1.5299\;\;[2.2969]$	$-0.4002\;\;[0.8815]$
Titans-QFWP (Full)	$\mathbf{0.4260}\;\;[\mathbf{0.4197}]$	$\mathbf{-0.0500}\;\;[\mathbf{0.0212}]$	$\mathbf{6.9018}\;\;[\mathbf{6.5930}]$	$\mathbf{8.5504}\;\;[\mathbf{6.0697}]$	$\mathbf{0.8427}\;\;[\mathbf{1.3992}]$
Titans-QFWP ( $-$ Forgetting)	$0.1965\;\;[0.1276]$	$-0.0520\;\;[0.0415]$	$3.0186\;\;[1.3646]$	$3.3316\;\;[2.0293]$	$-0.3887\;\;[0.9337]$
Titans-QFWP ( $-$ Persistence)	$0.1929\;\;[0.1297]$	$-0.1010\;\;[0.0400]$	$2.0905\;\;[1.1939]$	$2.1663\;\;[1.7055]$	$-0.3136\;\;[0.6757]$
Titans-QFWP ( $-$ Surprise)	$0.1586\;\;[0.1749]$	$-0.0782\;\;[0.0318]$	$2.6949\;\;[1.5092]$	$2.3728\;\;[1.3064]$	$-0.5138\;\;[1.1810]$

TABLE IV: Performance metrics for Titans-QFWP ablation variants (median [IQR], seeds 1–10).

Fig. 2: Dynamic cluster selection of Titans-QFWP vs. the S&P 500 index.

Fig. 3: Top-20 selected stocks of Titans-QFWP vs. the S&P 500 index.

Portfolio Optimization

Portfolio optimization selects asset weights to balance expected return, risk, diversification, and trading constraints.

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Quantum-Assisted Optimal Rebalancing with Uncorrelated Asset Selection for Algorithmic Trading Walk-Forward QUBO Scheduling via QAOA

Abraham Itzhak Weinberg

AI-WEINBERG, AI Experts, Tel Aviv, Israel

Algorithmic Trading Portfolio Optimization Quadratic Unconstrained Binary Optimization Quantum Approximate Optimization Algorithm

Open paper AskPDF arXiv

We present a hybrid classical-quantum framework for portfolio construction and rebalancing. Asset selection is performed using Ledoit-Wolf shrinkage covariance estimation combined with hierarchical correlation clustering to extract n = 10 decorrelated stocks from the S&P 500 universe without survivorship bias. Portfolio weights are optimised via an entropy-regularised Genetic Algorithm (GA) accelerated on GPU, alongside closed-form minimum-variance and equal-weight benchmarks. Our primary contribution is the formulation of the portfolio rebalancing schedule as a Quadratic Unconstrained Binary Optimisation (QUBO) problem. The resulting combinatorial optimisation task is solved using the Quantum Approximate Optimisation Algorithm (QAOA) within a walk-forward framework designed to eliminate lookahead bias. This approach recasts dynamic rebalancing as a structured binary scheduling problem amenable to variational quantum methods. Backtests on S&P 500 data (training: 2010-2024; out-of-sample test: 2025, n = 249 trading days) show that the GA + QAOA strategy attains a Sharpe ratio of 0.588 and total return of 10.1%, modestly outperforming the strongest classical baseline (GA with 10-day periodic rebalancing, Sharpe 0.575) while executing 8 rebalances versus 24, corresponding to a 44.5% reduction in transaction costs. Multi-restart QAOA (4096 measurement shots per run) exhibits concentrated probability mass on high-quality schedules, indicating stable convergence of the variational procedure. These findings suggest that hybrid classical-quantum architectures can reduce turnover in portfolio rebalancing while preserving competitive risk-adjusted performance, providing a structured testbed for near-term quantum optimisation in financial applications.

Abstract

Portfolio Optimization

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