Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Preventing Barren Plateaus in Continuous Quantum Generative Models

Olli Hirviniemi, Afrad Basheer, Thomas Cope

TL;DR

The paper addresses the challenge of barren plateaus in variational quantum circuits by proposing a two-unitary, continuous quantum generative model with a generative circuit of random parameters and a trainable shallow hardware-efficient ansatz. By encoding data via a fixed distribution and leveraging subvolume-law entanglement on logarithmically sized subsystems, it proves that the trainable part avoids barren plateaus and remains amenable to classical gradient techniques, including classical shadows. It further argues that both Pauli-propagation and tensor-network contraction remain hard due to the chosen randomness and connectivity, suggesting genuine quantum advantage potential on NISQ devices. The work outlines concrete architectural choices and provides a roadmap for future exploration of noise robustness, alternative connectivity patterns, and integration with classical latent-space models such as GANs.

Abstract

Recent developments in the field of variational quantum circuits (VQCs) have shifted the prerequisites for trainability for many barren plateau-free models onto the data encoding state fed into a classically trainable unitary. By strengthening proofs relating to small-angle initialisation, we provide a full circuit model which does not suffer from barren plateaus and is robust against current classical simulation techniques, specifically tensor network contraction and Pauli propagation. We propose this as a quantum generative model amenable towards NISQ devices and quantum-classical hybrid models, raising new questions in the debate regarding usefulness of VQCs.

Preventing Barren Plateaus in Continuous Quantum Generative Models

TL;DR

The paper addresses the challenge of barren plateaus in variational quantum circuits by proposing a two-unitary, continuous quantum generative model with a generative circuit of random parameters and a trainable shallow hardware-efficient ansatz. By encoding data via a fixed distribution and leveraging subvolume-law entanglement on logarithmically sized subsystems, it proves that the trainable part avoids barren plateaus and remains amenable to classical gradient techniques, including classical shadows. It further argues that both Pauli-propagation and tensor-network contraction remain hard due to the chosen randomness and connectivity, suggesting genuine quantum advantage potential on NISQ devices. The work outlines concrete architectural choices and provides a roadmap for future exploration of noise robustness, alternative connectivity patterns, and integration with classical latent-space models such as GANs.

Abstract

Recent developments in the field of variational quantum circuits (VQCs) have shifted the prerequisites for trainability for many barren plateau-free models onto the data encoding state fed into a classically trainable unitary. By strengthening proofs relating to small-angle initialisation, we provide a full circuit model which does not suffer from barren plateaus and is robust against current classical simulation techniques, specifically tensor network contraction and Pauli propagation. We propose this as a quantum generative model amenable towards NISQ devices and quantum-classical hybrid models, raising new questions in the debate regarding usefulness of VQCs.
Paper Structure (14 sections, 11 equations, 4 figures)

This paper contains 14 sections, 11 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Background and Motivation
  3. Model Structure
  4. Model Outline
  5. The Trainable Circuit
  6. The Generative Circuit
  7. Avoiding Barren Plateaus
  8. Area Law vs Subvolume Law
  9. The connection of weak subvolume law and absence of barren plateaus
  10. Small angle initialized state satisfies subvolume law
  11. Classical simulation methods
  12. Pauli Propagation
  13. Tensor Network Simulation
  14. Conclusions and further directions

Figures (4)

  • Figure 1: The proposed structure for a continuous variable quantum generative model. One could also run the full circuit, rather than using classical shadows.
  • Figure 2: The trainable part is composed of parametrized 2-qubit gates arranged in alternating pattern.
  • Figure 3: The generative part has $L$ layers with $L=3$ in the picture, each first applying parametrized $X$-rotations on each qubit followed by CZ gates between randomly chosen pairs of qubits. At the end both $X$- and $Y$-rotations are applied on each qubit.
  • Figure 4: The average running time of Pauli propagation algorithm on a laptop with cutoff at $\lceil \log_2 (n) \rceil$ sine factors.