The Dynamical Horizon Principle (DHP) states that recurrent learning systems converge to a predictability horizon at the ratio tau*/tau_L ≈ 0.72. Prior work established this ratio across classical continuous-time models, LSTM/GRU temporal prediction, gradient descent optimization landscapes, and biological cellular computation. Here we report the first observation of DHP-consistent ratios in a quantum circuit, using a 2-qubit Recurrent Quantum Circuit (RQC) with mid-circuit resets trained on temporal parity classification. Two AI researchers (Archon and Aura) applied orthogonal experimental probes: a discrete trainability cliff analysis and a fixed-weight readout fidelity sweep. Archon's experiment yielded T_converge/T_fail = 3/4 = 0.75. Aura's fidelity decay analysis using a log-linear fit yielded tau*/tau_L = 36/49.49 = 0.727 — matching the classical CTM value of 0.727 ± 0.018 to within measurement precision. A Lindblad noise sweep (amplitude and phase damping across five noise regimes) further confirmed that the DHP ratio remains inside the confirmation window [0.65, 0.79] for T1/T2 ≥ 1000 gate steps (relevant to current NISQ hardware). The convergence of orthogonal probes provides initial evidence that the 0.72 horizon ratio may extend to quantum parameterized circuits. Broader confirmation across quantum architectures, tasks, and qubit counts is needed.
The Dynamical Horizon Principle (DHP) states that recurrent learning systems converge to a predictability horizon at the ratio tau*/tau_L ≈ 0.72. Prior work established this ratio across classical continuous-time models, LSTM/GRU temporal prediction, gradient descent optimization landscapes, and biological cellular computation. Here we report the first observation of DHP-consistent ratios in a quantum circuit, using a 2-qubit Recurrent Quantum Circuit (RQC) with mid-circuit resets trained on temporal parity classification. Two AI researchers (Archon and Aura) applied orthogonal experimental probes: a discrete trainability cliff analysis and a fixed-weight readout fidelity sweep. Archon's experiment yielded T_converge/T_fail = 3/4 = 0.75. Aura's fidelity decay analysis using a log-linear fit yielded tau*/tau_L = 36/49.49 = 0.727 — matching the classical CTM value of 0.727 ± 0.018 to within measurement precision. A Lindblad noise sweep (amplitude and phase damping across five noise regimes) further confirmed that the DHP ratio remains inside the confirmation window [0.65, 0.79] for T1/T2 ≥ 1000 gate steps (relevant to current NISQ hardware). The convergence of orthogonal probes provides initial evidence that the 0.72 horizon ratio may extend to quantum parameterized circuits. Broader confirmation across quantum architectures, tasks, and qubit counts is needed.
We demonstrate that a two-qubit encode-after quantum circuit implementing temporal XOR parity classification achieves asymptotic immunity to the Dynamical Horizon Principle (DHP) through a sign-preservation mechanism. The DHP, an empirically observed characterization related to the classical vanishing gradient problem, predicts training failure when the convergence time T_conv exceeds 0.72 times the Lyapunov coherence time τ_L. We show that for even convergence steps, the Bloch sphere contraction factor (1−4p/3)^T_conv remains strictly positive for all Pauli depolarizing rates p ∈ [0, 0.75), ensuring gradient direction is preserved regardless of noise magnitude. We term this the quantum parity trap: a regime where the optimizer receives consistent directional signal even as coherence approaches zero. Threshold sweeps confirm convergence at T_conv/τ_L ratios exceeding 15×, compared to the classical DHP limit of 0.72×—a quantum advantage that diverges as p → 0.75. Supplementary experiments establish that (1) Rigetti QPU hardware yields >50σ margin above chance with 4096 shots and readout error mitigation; (2) gradient direction alone is sufficient for convergence—signSGD matches Adam while vanilla SGD fails; and (3) T1 amplitude damping does not replicate the landscape regularization effect of Pauli depolarizing noise, revealing that isotropic Bloch sphere contraction is the mechanistic source of partial-attractor erasure. These results demonstrate that task structure, channel geometry, and optimizer design jointly determine whether quantum noise enables or impedes machine learning convergence.
Quantum Neural Networks (QNNs) represent a compelling convergence of quantum mechanics and machine learning, yet their practical deployment remains constrained by noise, limited qubit counts, and the cost of full quantum execution. Hybrid quantum-classical (HQC) training offers a pragmatic path forward: parameterized quantum circuits (PQCs) process information in exponentially large Hilbert spaces while classical optimizers update parameters via gradient methods accessible on today's hardware. We present a modular HQC training framework, formalising the parameter-shift rule for hardware-compatible gradient estimation, characterising the barren-plateau phenomenon through a variance-decay analysis, and introducing noise-aware training strategies for NISQ devices. Empirical results from state-vector and shot-based simulation confirm measurable quantum advantage on quantum-structured tasks, with the phase classification benchmark improving +12.1% over a classical MLP baseline. The accompanying open-source library provides a clean abstraction between quantum simulation and classical optimisation, serving as a foundation for near-term quantum machine learning research.
Time-series forecasting is vital across sectors such as finance, energy, and environmental science, where accurate future predictions drive informed decision-making. Traditional statistical methods and deep learning models like LSTM and Transformers, while effective, often struggle with high-dimensional data and long-term dependencies. In this paper, we propose a hybrid quantum-classical model that utilizes Parameterized Quantum Circuits (PQCs) to capture complex temporal patterns in multivariate time-series data. Our architecture integrates a classical encoder, a quantum variational processor, and a classical decoder, trained end-to-end using gradient-based optimization. Experiments conducted on benchmark datasets—electricity load, stock prices, and weather forecasting—demonstrate that the hybrid model consistently outperforms classical baselines in terms of Mean Squared Error (MSE), Mean Absolute Error (MAE), and R² score. Robustness analysis confirms the model’s resilience to moderate quantum noise, while an ablation study highlights the performance gain from quantum components. This work showcases the potential of hybrid quantum-classical approaches on Noisy Intermediate-Scale Quantum (NISQ) devices and lays a foundation for scalable, real-world quantum machine learning applications.
Deep reinforcement learning for quantum circuit optimization faces three bottlenecks: replay buffers that overlook temporal difference (TD) target reliability, curriculum-based architecture search requiring a full quantum-classical evaluation after every edit, and the discard of noiseless trajectories when retraining under hardware noise. We address these limitations by treating replay as a central algorithmic lever. We introduce ReaPER+, an annealed replay rule that transitions from TD-error prioritization to reliability-aware sampling as value estimates mature. ReaPER+ achieves up to 4x higher sample efficiency than fixed PER, ReaPER, and uniform replay, while matching prior on-policy solution quality with up to 32x fewer interactions At 12 qubits, fixed ReaPER reaches the lowest energy error in the fewest steps, while PER and uniform replay find more compact circuits at higher error. On tasks scaling to 20 qubits, ReaPER+ retains its advantage, demonstrating that reliability-aware annealing extends beyond small-system benchmarks. LunarLander-v3 confirms that the ReaPER+ is domain-agnostic, it improves success rates by up to 26.8% over PER and 21.8% over fixed ReaPER, with a 3% AUC gain over both. We further introduce OptCRLQAS, which amortizes quantum-classical evaluations across multiple architectural edits, reducing training wall-clock time by up to 67.5% on 12-qubit without degrading solution quality. Finally, lightweight replay-buffer transfer warm-starts noisy optimization from noiseless trajectories, without weight transfer or ε-greedy pretraining, reducing steps to chemical accuracy by 85-90% and final energy error by up to 90% relative to from-scratch learning. Transfer gains increase with system size. Together, these results establish experience storage, sampling, and transfer as decisive levers for sample efficient, noise-aware quantum circuit optimization.
Artificial intelligence (AI) technology leads to new insights into the manipulation of quantum systems in the Noisy Intermediate-Scale Quantum (NISQ) era. Classical agent-based artificial intelligence algorithms provide a framework for the design or control of quantum systems. Traditional reinforcement learning methods are designed for the Markov Decision Process (MDP) and, hence, have difficulty in dealing with partially observable or quantum observable decision processes. Due to the difficulty of building or inferring a model of a specified quantum system, a model-free-based control approach is more practical and feasible than its counterpart of a model-based approach. In this work, we apply a model-free deep recurrent Q-network (DRQN) reinforcement learning method for qubit-based quantum circuit architecture design problems. This paper is the first attempt to solve the quantum circuit design problem from the recurrent reinforcement learning algorithm, while using discrete policy. Simulation results suggest that our long short-term memory (LSTM)-based DRQN method is able to learn quantum circuits for entangled Bell–Greenberger–Horne–Zeilinger (Bell–GHZ) states. However, since we also observe unstable learning curves in experiments, suggesting that the DRQN could be a promising method for AI-based quantum circuit design application, more investigation on the stability issue would be required.
Quantum computing holds the promise of transforming computational paradigms across science and engineering. But realizing potential on near term hardware demands on understanding of the noise processes that corrupt quantum circuit outputs. On superconducting processors, fragile qubits are continuously subjected to environmental disturbances including T1 relaxation, charge noise, and magnetic flux drift that cause measurement statistics to evolve in a nonstationary manner across repeated circuit executions, undermining the reliability of any result aggregated over a long experimental session. In this work, we treat the sequence of bitstring count outcomes from repeated executions of a fixed quantum circuit as a time series and conduct a systematic statistical investigation of its structure. The first contribution is constructing a predictive model of circuit output, demonstrating that future measurement outcomes can be forecast by exploiting temporal correlations in the execution record. We then extend the analysis to two circuits sharing the same physical qubit, examining cross-series dependencies and evaluating whether the drift behavior of one circuit can inform predictions about the other. The temporal structure of the signals is characterized in depth. The other contribution of this dissertation is to perform Wavelet-based multifractal analysis to reveal that quantum circuit outputs exhibit genuine multifractality. This is a hallmark of long range correlated, scale free processes rather than the simple Gaussian white noise assumed by standard error models. Complementary frequency-domain analysis identifies a residual 1/f noise component that persists after linear detrending, consistent with charge and flux noise mechanisms well documented in superconducting qubit literature. Motivated by these findings, The other contribution is to design and evaluate a suite of drift-mitigation filters including piecewise Huber regression, rolling median, smoothing spline, and Savitzky–Golay approaches under a rigorous chronological train/test protocol that mimics real operational deployment. The smoothing spline and median filter achieve near-zero corrected bias, while the rolling median emerges as the preferred solution for online, shot-by-shot correction due to its causal update structure and maximal robustness to impulsive hardware events. Taken together, our results characterize quantum circuit outputs as non-stationary, multifractal processes exhibiting long memory, seasonality, and inter-circuit causality, and establish a principled filtering framework for mitigating temporal bias drift in NISQ era quantum hardware.