Improving Quantum Recurrent Neural Networks with Amplitude Encoding

TL;DR

This work targets practical amplitudes-encoded QRNNs for time-series forecasting by introducing (i) a preprocessing step that preserves amplitude information via a pre-normalized amplitude feature, (ii) a comparison between exact amplitude encoding and EnQode approximate state preparation with substantial circuit-depth reductions, and (iii) a depth-reducing alternating $F$-register circuit that remains equivalent on ideal hardware. Empirical results on Yahoo Finance and Oxford-Man SPX datasets show that amplitude-encoded QRNNs can outperform angle-encoded variants in generalization, with MaxMin-scaled amplitude preprocessing and EnQode offering notable gains in both predictive accuracy and hardware feasibility. While EnQode introduces some fidelity loss, the depth and coherence benefits offset this in noisy simulations, underscoring its practicality for near-term devices. The paper provides actionable guidance for deploying amplitude-encoded QRNNs and suggests avenues for extending these ideas to broader quantum-time-series models such as Quantum Reservoir Computing.

Abstract

Quantum machine learning holds promise for advancing time series forecasting. The Quantum Recurrent Neural Network (QRNN), inspired by classical RNNs, encodes temporal data into quantum states that are periodically input into a quantum circuit. While prior QRNN work has predominantly used angle encoding, alternative encoding strategies like amplitude encoding remain underexplored due to their high computational complexity. In this paper, we evaluate and improve amplitude-based QRNNs using EnQode, a recently introduced method for approximate amplitude encoding. We propose a simple pre-processing technique that augments amplitude encoded inputs with their pre-normalized magnitudes, leading to improved generalization on two real world data sets. Additionally, we introduce a novel circuit architecture for the QRNN that is mathematically equivalent to the original model but achieves a substantial reduction in circuit depth. Together, these contributions demonstrate practical improvements to QRNN design in both model performance and quantum resource efficiency.

Figures (8)

• Figure 1: A diagram of an example efficient_su2 Ansatz for an IBM processor. The unitary is constructed with a combination of two qubit entangling gates and parameterized native single qubit gates.
• Figure 2: High level diagram of a canonical QRNN (left) and a classical RNN that inspired it (right). The $FM$ gates encode the input data for time step $i$ while the $A$ gate is a parameterized quantum circuit.
• Figure 3: High level diagram of the state preparation circuit Ansatz used by EnQode for 8 features, of 3 feature map qubits.
• Figure 4: High level diagram of two proposed QRNN circuit structures with alternating $F$ registers.
• Figure 5: Comparison between classical RNN, angle QRNN, and an Amplitude QRNN without any of the proposed modifications. Panel (a) features the average training curve over the five trials for each data set. In panel (b) we show the average validation MSE and number of trainable parameters with the Yahoo Finance/Oxford-Man data sets.