Fast suppression of classification error in variational quantum circuits

Abstract

Variational quantum circuits (VQCs) have shown great potential in near-term applications. However, the discriminative power of a VQC, in connection to its circuit architecture and depth, is not understood. To unleash the genuine discriminative power of a VQC, we propose a VQC system with the optimal classical post-processing -- maximum-likelihood estimation on measuring all VQC output qubits. Via extensive numerical simulations, we find that the error of VQC quantum data classification typically decay exponentially with the circuit depth, when the VQC architecture is extensive -- the number of gates does not shrink with the circuit depth. This fast error suppression ends at the saturation towards the ultimate Helstrom limit of quantum state discrimination. On the other hand, non-extensive VQCs such as quantum convolutional neural networks are sub-optimal and fail to achieve the Helstrom limit. To achieve the best performance for a given VQC, the optimal classical post-processing is crucial even for a binary classification problem. To simplify VQCs for near-term implementations, we find that utilizing the symmetry of the input properly can improve the performance, while oversimplification can lead to degradation.

arXiv comment15 pages, 19 figures

References in corpus (42)

• Quantum Computing in the NISQ era and beyond
• Quantum Machine Learning
• Entanglement Entropy and Quantum Field Theory
• Supervised learning with quantum enhanced feature spaces
• Barren plateaus in quantum neural network training landscapes
• A Quantum Approximate Optimization Algorithm
• Quantum machine learning in feature Hilbert spaces
• Geometric and Renormalized Entropy in Conformal Field Theory
• Quantum Circuit Learning
• Quantum Convolutional Neural Networks
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• Operator Spreading in Random Unitary Circuits
• Towards Practical Quantum Variational Algorithms
• Quantum Illumination with Gaussian States
• Variational ansatz-based quantum simulation of imaginary time evolution
• Robust determination of molecular spectra on a quantum processor
• Optimal Quantum Circuits for General Two-Qubit Gates
• Cloud Quantum Computing of an Atomic Nucleus
• Evenly distributed unitaries: on the structure of unitary designs
• Variational quantum algorithms for nonlinear problems
• One-Shot Classical-Quantum Capacity and Hypothesis Testing
• Distributed Quantum Sensing Using Continuous-Variable Multipartite Entanglement
• Distributed Quantum Metrology and the Entangling Power of Linear Networks
• Quantum Reading of a Classical Digital Memory
• Quantum Hopfield neural network
• Linear growth of quantum circuit complexity
• Equivalence of quantum barren plateaus to cost concentration and narrow gorges
• Barren plateaus preclude learning scramblers
• Higher Order Derivatives of Quantum Neural Networks with Barren Plateaus
• The power of deeper networks for expressing natural functions
• One shot entanglement assisted classical and quantum communication over noisy quantum channels: A hypothesis testing and convex split approach
• Universal discriminative quantum neural networks
• Quantum message compression with applications
• Adversarial quantum circuit learning for pure state approximation
• Scrambling and Complexity in Phase Space
• Quantum ranging with Gaussian entanglement
• Entangling power and quantum circuit complexity
• A smooth entropy approach to quantum hypothesis testing and the classical capacity of quantum channels
• Entanglement-Assisted Absorption Spectroscopy
• Scrambling Ability of Quantum Neural Networks Architectures
• Provable superior accuracy in machine learned quantum models