High-expressibility Quantum Neural Networks using only classical resources

Abstract

Quantum neural networks (QNNs), as currently formulated, are near-term quantum machine learning architectures that leverage parameterized quantum circuits with the aim of improving upon the performance of their classical counterparts. In this work, we show that some desired properties attributed to these models can be efficiently reproduced without necessarily resorting to quantum hardware. We indeed study the expressibility of parametrized quantum circuit commonly used in QNN applications and contrast it to those of two classes of states that can be efficiently simulated classically: matrix-product states (MPS), and Clifford-enhanced MPS (CMPS), obtained by applying a set of Clifford gates to MPS. In addition to expressibility, we assess the level of primary quantum resources, entanglement and non-stabilizerness (a.k.a. "magic"), in random ensembles of such quantum states, tracking their convergence towards the Haar distribution. While MPS require a large number of parameters to effectively reproduce an arbitrary quantum state, we find that CMPS approach the Haar distribution more rapidly, in terms of both entanglement and magic. Our results on states with up to 20 qubits indicate that high expressibility in QNNs is attainable with purely classical resources.

6 figures

References in corpus (54)

• Quantum Machine Learning
• The density-matrix renormalization group in the age of matrix product states
• Area laws for the entanglement entropy - a review
• Quantum machine learning in feature Hilbert spaces
• Improved Simulation of Stabilizer Circuits
• Parameterized quantum circuits as machine learning models
• Circuit-centric quantum classifiers
• Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms
• Matrix product states represent ground states faithfully
• The effect of data encoding on the expressive power of variational quantum machine learning models
• Challenges and Opportunities in Quantum Machine Learning
• The quest for a Quantum Neural Network
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Quantum machine learning: a classical perspective
• The Resource Theory of Stabilizer Computation
• Stim: a fast stabilizer circuit simulator
• Random Quantum Circuits are Approximate 2-designs
• The Expressive Power of Parameterized Quantum Circuits
• Stabilizer Rényi entropy
• Multiqubit Clifford groups are unitary 3-designs
• Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates
• Stabilizer states and Clifford operations for systems of arbitrary dimensions, and modular arithmetic
• Introduction to Haar Measure Tools in Quantum Information: A Beginner's Tutorial
• Stabilizer entropies and nonstabilizerness monotones
• Scalable measures of magic resource for quantum computers
• Expressibility of the alternating layered ansatz for quantum computation
• Hadamard-free circuits expose the structure of the Clifford group
• Preparation of matrix product states with log-depth quantum circuits
• Stabilizer entropies are monotones for magic-state resource theory
• Measuring nonstabilizerness via multifractal flatness
• Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
• Constant-depth preparation of matrix product states with adaptive quantum circuits
• Augmenting Density Matrix Renormalization Group with Clifford Circuits
• Transitions in Entanglement Complexity in Random Circuits
• Stabilizer Tensor Networks: universal quantum simulator on a basis of stabilizer states
• Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding
• Efficient Quantum Tensor Product Expanders and k-designs
• Entanglement entropy production in Quantum Neural Networks
• Correlation length in random MPS and PEPS
• Evaluation of Parameterized Quantum Circuits with Cross-Resonance Pulse-Driven Entanglers
• Quantifying non-stabilizerness via information scrambling
• Hybrid Stabilizer Matrix Product Operator
• Clifford Dressed Time-Dependent Variational Principle
• Reducing the amount of single-qubit rotations in VQE and related algorithms
• Stabilizer disentangling of conformal field theories
• Entanglement and Stabilizer entropies of random bipartite pure quantum states
• Independent stabilizer Rényi entropy and entanglement fluctuations in random unitary circuits
• Magic of Random Matrix Product States
• Disentangling critical quantum spin chains with Clifford circuits
• Tensor Network Techniques for Quantum Computation
• Learning the expressibility of quantum circuit ansatz using transformer
• Universal Approximation Theorem and error bounds for quantum neural networks and quantum reservoirs
• Predicting Expressibility of Parameterized Quantum Circuits using Graph Neural Network
• Parent Hamiltonian for Fully-augmented Matrix Product States