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Quantum RNNs and LSTMs Through Entangling and Disentangling Power of Unitary Transformations

Ammar Daskin

TL;DR

The paper introduces a hybrid quantum-classical framework for quantum RNNs/LSTMs that encodes temporal memory in an ancilla quantum register and uses the entangling/disentangling power of unitary transformations to govern memory retention and forgetting. It formalizes this intuition by linking entanglement changes to memory via E^↑(U) and E^↓(U) bounds, and demonstrates how CPTP maps and fidelity considerations arise from measurement updates. The authors validate the approach with numerical simulations on synthetic noisy sine data and real-world Ontario weather data, comparing reduced-density-matrix and collapsed-state formalisms. The work offers a principled method to design parameterized quantum circuits that exploit entanglement as a controllable memory resource, potentially guiding quantum circuit design for time-series tasks.

Abstract

In this paper, we present a framework for modeling quantum recurrent neural networks (RNNs) and their enhanced version, long short-term memory (LSTM) networks using the core ideas presented by Linden et al. (2009), where the entangling and disentangling power of unitary transformations is investigated. In particular, we interpret entangling and disentangling power as information retention and forgetting mechanisms in LSTMs. Thus, entanglement emerges as a key component of the optimization (training) process. We believe that, by leveraging prior knowledge of the entangling power of unitaries, the proposed quantum-classical framework can guide the design of better-parameterized quantum circuits for various real-world applications.

Quantum RNNs and LSTMs Through Entangling and Disentangling Power of Unitary Transformations

TL;DR

The paper introduces a hybrid quantum-classical framework for quantum RNNs/LSTMs that encodes temporal memory in an ancilla quantum register and uses the entangling/disentangling power of unitary transformations to govern memory retention and forgetting. It formalizes this intuition by linking entanglement changes to memory via E^↑(U) and E^↓(U) bounds, and demonstrates how CPTP maps and fidelity considerations arise from measurement updates. The authors validate the approach with numerical simulations on synthetic noisy sine data and real-world Ontario weather data, comparing reduced-density-matrix and collapsed-state formalisms. The work offers a principled method to design parameterized quantum circuits that exploit entanglement as a controllable memory resource, potentially guiding quantum circuit design for time-series tasks.

Abstract

In this paper, we present a framework for modeling quantum recurrent neural networks (RNNs) and their enhanced version, long short-term memory (LSTM) networks using the core ideas presented by Linden et al. (2009), where the entangling and disentangling power of unitary transformations is investigated. In particular, we interpret entangling and disentangling power as information retention and forgetting mechanisms in LSTMs. Thus, entanglement emerges as a key component of the optimization (training) process. We believe that, by leveraging prior knowledge of the entangling power of unitaries, the proposed quantum-classical framework can guide the design of better-parameterized quantum circuits for various real-world applications.
Paper Structure (8 sections, 12 equations, 5 figures)

This paper contains 8 sections, 12 equations, 5 figures.

Table of Contents

  1. INTRODUCTION
  2. THE HYBRID GENERAL FRAMEWORK
  3. ANALYSIS OF THE MODEL TO SHOW WHY IT WORKS
  4. NUMERICAL SIMULATIONS
  5. CONCLUSION
  6. DATA AVAILABILITY
  7. FUNDING
  8. ACKNOWLEDGMENT

Figures (5)

  • Figure 1: Generic Structure of Quantum LSTM.
  • Figure 2: A Single Quantum LSTM Cell.
  • Figure 3: Numerical Steps Used to Simulate Quantum LSTM.
  • Figure 4: The loss and the predictions vs true values in the test cases of the noisy sine function for the values in range $[0, 8\pi]$.
  • Figure 5: The loss and the predictions vs true values in the test cases of the weather data for Ontario, Canada.