Cost function embedding and dataset encoding for machine learning with parameterized quantum circuits

Abstract

Machine learning is seen as a promising application of quantum computation. For near-term noisy intermediate-scale quantum (NISQ) devices, parametrized quantum circuits (PQCs) have been proposed as machine learning models due to their robustness and ease of implementation. However, the cost function is normally calculated classically from repeated measurement outcomes, such that it is no longer encoded in a quantum state. This prevents the value from being directly manipulated by a quantum computer. To solve this problem, we give a routine to embed the cost function for machine learning into a quantum circuit, which accepts a training dataset encoded in superposition or an easily preparable mixed state. We also demonstrate the ability to evaluate the gradient of the encoded cost function in a quantum state.

References in corpus (32)

• Adam: A Method for Stochastic Optimization
• Quantum Machine Learning
• Quantum algorithm for solving linear systems of equations
• Quantum-enhanced measurements: beating the standard quantum limit
• Supervised learning with quantum enhanced feature spaces
• Quantum support vector machine for big data classification
• Quantum machine learning in feature Hilbert spaces
• Quantum Circuit Learning
• Quantum fingerprinting
• Two-Bit Gates are Universal for Quantum Computation
• Evaluating analytic gradients on quantum hardware
• Circuit-centric quantum classifiers
• Practical Quantum Error Mitigation for Near-Future Applications
• Experimental Comparison of Two Quantum Computing Architectures
• Quantum machine learning: a classical perspective
• Optimal Quantum Circuits for General Two-Qubit Gates
• A generative modeling approach for benchmarking and training shallow quantum circuits
• Fluctuations of Energy-Relaxation Times in Superconducting Qubits
• Hierarchical quantum classifiers
• The Expressive Power of Parameterized Quantum Circuits
• Towards Quantum Machine Learning with Tensor Networks
• Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers
• Accelerated Variational Quantum Eigensolver
• A quantum linear system algorithm for dense matrices
• A quantum Fredkin gate
• Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithms
• Black-box quantum state preparation without arithmetic
• Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure
• Supervised Learning with Quantum-Inspired Tensor Networks
• Supervised learning with a quantum classifier using a multi-level system
• One-step implementation of a hybrid Fredkin gate with quantum memories and single superconducting qubit in circuit QED and its applications
• Bayesian Quantum Circuit

Cited by in corpus (16)

• The Variational Quantum Eigensolver: a review of methods and best practices
• Robust data encodings for quantum classifiers
• Robust in Practice: Adversarial Attacks on Quantum Machine Learning
• AutoQML: Automatic Generation and Training of Robust Quantum-Inspired Classifiers by Using Genetic Algorithms on Grayscale Images
• Harnessing Quantum Extreme Learning Machines for image classification
• Quantum Generative Adversarial Networks For Anomaly Detection In High Energy Physics
• The Unified Effect of Data Encoding, Ansatz Expressibility and Entanglement on the Trainability of HQNNs
• Entanglement assisted training algorithm for supervised quantum classifiers
• Ancilla-Error-Transparent Controlled Beam Splitter Gate
• The SWITCH test for discriminating quantum evolutions
• Non-parametric Semi-Supervised Learning in Many-body Hilbert Space with Rescaled Logarithmic Fidelity
• Quantum Neural Networks in Practice: A Comparative Study with Classical Models from Standard Data Sets to Industrial Images
• Learning Equivariant Maps with Variational Quantum Circuits
• A Unified Framework for Quantum Supervised Learning
• Quantum Machine Learning For Classical Data
• Finding eigenvectors with a quantum variational algorithm