A semi-agnostic ansatz with variable structure for quantum machine learning

Abstract

Quantum machine learning -- and specifically Variational Quantum Algorithms (VQAs) -- offers a powerful, flexible paradigm for programming near-term quantum computers, with applications in chemistry, metrology, materials science, data science, and mathematics. Here, one trains an ansatz, in the form of a parameterized quantum circuit, to accomplish a task of interest. However, challenges have recently emerged suggesting that deep ansatzes are difficult to train, due to flat training landscapes caused by randomness or by hardware noise. This motivates our work, where we present a variable structure approach to build ansatzes for VQAs. Our approach, called VAns (Variable Ansatz), applies a set of rules to both grow and (crucially) remove quantum gates in an informed manner during the optimization. Consequently, VAns is ideally suited to mitigate trainability and noise-related issues by keeping the ansatz shallow. We employ VAns in the variational quantum eigensolver for condensed matter and quantum chemistry applications, in the quantum autoencoder for data compression and in unitary compilation problems showing successful results in all cases.

arXiv comment20 pages, 14 figures, 1 table, updated to published version

References in corpus (68)

• Quantum Computing in the NISQ era and beyond
• Quantum Machine Learning
• A variational eigenvalue solver on a quantum processor
• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Barren plateaus in quantum neural network training landscapes
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum computational chemistry
• Quantum Chemistry in the Age of Quantum Computing
• Simulated Quantum Computation of Molecular Energies
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• The power of quantum neural networks
• Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
• Hartree-Fock on a superconducting qubit quantum computer
• Exact and Approximate Unitary 2-Designs: Constructions and Applications
• The quest for a Quantum Neural Network
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Quantum autoencoders for efficient compression of quantum data
• Quantum process tomography of a controlled-NOT gate
• Generalization in quantum machine learning from few training data
• Quantum Approximate Optimization of Non-Planar Graph Problems on a Planar Superconducting Processor
• Quantum Natural Gradient
• Theory of variational quantum simulation
• qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor
• An initialization strategy for addressing barren plateaus in parametrized quantum circuits
• Quantum-assisted quantum compiling
• Absence of Barren Plateaus in Quantum Convolutional Neural Networks
• Layerwise learning for quantum neural networks
• Random Quantum Circuits are Approximate 2-designs
• Local random quantum circuits are approximate polynomial-designs
• Quantum Circuit Simplification and Level Compaction
• Software Mitigation of Crosstalk on Noisy Intermediate-Scale Quantum Computers
• Learning the quantum algorithm for state overlap
• Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
• Efficient Symmetry-Preserving State Preparation Circuits for the Variational Quantum Eigensolver Algorithm
• Effect of barren plateaus on gradient-free optimization
• Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
• Structure optimization for parameterized quantum circuits
• Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor
• Variational Quantum State Diagonalization
• Noise Resilience of Variational Quantum Compiling
• Sequential minimal optimization for quantum-classical hybrid algorithms
• Variational algorithms for linear algebra
• Trainability of Dissipative Perceptron-Based Quantum Neural Networks
• Variational Quantum State Eigensolver
• Entanglement Devised Barren Plateau Mitigation
• Barren plateaus preclude learning scramblers
• Higher Order Derivatives of Quantum Neural Networks with Barren Plateaus
• Modelling and Simulating the Noisy Behaviour of Near-term Quantum Computers
• Avoiding barren plateaus using classical shadows
• An Adaptive Optimizer for Measurement-Frugal Variational Algorithms
• Machine learning of noise-resilient quantum circuits
• Variational-State Quantum Metrology
• Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers
• Random quantum circuits are approximate unitary $t$-designs in depth $O\left(n{t}^{5+o(1)}\right)$
• Variational Quantum Algorithm for Estimating the Quantum Fisher Information
• Quantum Assisted Simulator
• The Meta-Variational Quantum Eigensolver (Meta-VQE): Learning energy profiles of parameterized Hamiltonians for quantum simulation
• Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus
• Correlation-Informed Permutation of Qubits for Reducing Ansatz Depth in VQE
• Adaptive pruning-based optimization of parameterized quantum circuits
• Mutual information-assisted Adaptive Variational Quantum Eigensolver
• Benchmarking adaptive variational quantum eigensolvers
• Factorization and criticality in finite XXZ systems of arbitrary spin

Cited by in corpus (17)

• Barren Plateaus in Variational Quantum Computing
• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
• A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance
• On the practical usefulness of the Hardware Efficient Ansatz
• Quantum Architecture Search: A Survey
• Distributed quantum architecture search
• Variational quantum computing for quantum simulation: principles, implementations, and challenges
• Application of ZX-calculus to Quantum Architecture Search
• Mitigating Quantum Gate Errors for Variational Eigensolvers Using Hardware-Inspired Zero-Noise Extrapolation
• Deep Circuit Compression for Quantum Dynamics via Tensor Networks
• Cascaded variational quantum eigensolver algorithm
• Advantage of discrete variable representation in variational quantum eigensolvers for vibrational energy calculations
• Expressivity of deterministic quantum computation with one qubit
• Multi-channel convolutional neural quantum embedding
• Sub-universal variational circuits for combinatorial optimization problems
• Generating Generalised Ground-State Ansatzes from Few-Body Examples
• Hamiltonian Expressibility for Ansatz Selection in Variational Quantum Algorithms