Classical Optimizers for Noisy Intermediate-Scale Quantum Devices

Abstract

We present a collection of optimizers tuned for usage on Noisy Intermediate-Scale Quantum (NISQ) devices. Optimizers have a range of applications in quantum computing, including the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization (QAOA) algorithms. They are also used for calibration tasks, hyperparameter tuning, in machine learning, etc. We analyze the efficiency and effectiveness of different optimizers in a VQE case study. VQE is a hybrid algorithm, with a classical minimizer step driving the next evaluation on the quantum processor. While most results to date concentrated on tuning the quantum VQE circuit, we show that, in the presence of quantum noise, the classical minimizer step needs to be carefully chosen to obtain correct results. We explore state-of-the-art gradient-free optimizers capable of handling noisy, black-box, cost functions and stress-test them using a quantum circuit simulation environment with noise injection capabilities on individual gates. Our results indicate that specifically tuned optimizers are crucial to obtaining valid science results on NISQ hardware, and will likely remain necessary even for future fault tolerant circuits.

arXiv comment11 pages, 17 figures

References in corpus (14)

• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• The theory of variational hybrid quantum-classical algorithms
• A Quantum Approximate Optimization Algorithm
• Quantum computational chemistry
• Error mitigation for short-depth quantum circuits
• Efficient variational quantum simulator incorporating active error minimisation
• The CMA Evolution Strategy: A Tutorial
• Noise tailoring for scalable quantum computation via randomized compiling
• ProjectQ: An Open Source Software Framework for Quantum Computing
• Cloud Quantum Computing of an Atomic Nucleus
• Quantum Approximate Optimization Algorithm for MaxCut: A Fermionic View
• Decoding quantum errors with subspace expansions
• An Adaptive Optimizer for Measurement-Frugal Variational Algorithms
• Gradients of parameterized quantum gates using the parameter-shift rule and gate decomposition

Cited by in corpus (38)

• The Variational Quantum Eigensolver: a review of methods and best practices
• Equivalence of quantum barren plateaus to cost concentration and narrow gorges
• Qubit-excitation-based adaptive variational quantum eigensolver
• A Comparison of Various Classical Optimizers for a Variational Quantum Linear Solver
• A case study of variational quantum algorithms for a job shop scheduling problem
• Using models to improve optimizers for variational quantum algorithms
• Adaptive pruning-based optimization of parameterized quantum circuits
• Benchmarking quantum co-processors in an application-centric, hardware-agnostic and scalable way
• Chemistry on quantum computers with virtual quantum subspace expansion
• Qubit-efficient encoding schemes for binary optimisation problems
• Mitigating Barren Plateaus with Transfer-learning-inspired Parameter Initializations
• Analysis of The Vehicle Routing Problem Solved via Hybrid Quantum Algorithms in Presence of Noisy Channels
• Investigating the effect of circuit cutting in QAOA for the MaxCut problem on NISQ devices
• Non-trivial symmetries in quantum landscapes and their resilience to quantum noise
• Stochastic Gradient Line Bayesian Optimization for Efficient Noise-Robust Optimization of Parameterized Quantum Circuits
• Operator Sampling for Shot-frugal Optimization in Variational Algorithms
• Applying quantum approximate optimization to the heterogeneous vehicle routing problem
• Feature Selection for Classification with QAOA
• Improving the variational quantum eigensolver using variational adiabatic quantum computing
• A systematic variational approach to band theory in a quantum computer
• Security Aspects of Quantum Machine Learning: Opportunities, Threats and Defenses
• Data re-uploading with a single qudit
• Optimizing Variational Quantum Algorithms with qBang: Efficiently Interweaving Metric and Momentum to Navigate Flat Energy Landscapes
• QFactor: A Domain-Specific Optimizer for Quantum Circuit Instantiation
• Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Survey
• Amplitude amplification-inspired QAOA: Improving the success probability for solving 3SAT
• Adaptive shot allocation for fast convergence in variational quantum algorithms
• Scalability Challenges in Variational Quantum Optimization under Stochastic Noise
• Multireference error mitigation for quantum computation of chemistry
• Experimental semi-autonomous eigensolver using reinforcement learning
• Reducing measurement costs by recycling the Hessian in adaptive variational quantum algorithms
• Quantum implicit representation of vortex filaments in turbulence
• Global optimization in variational quantum algorithms via dynamic tunneling method
• Quantum natural gradient with thermal-state initialization
• Encoding strongly-correlated many-boson wavefunctions on a photonic quantum computer: application to the attractive Bose-Hubbard model
• Generative flow-based warm start of the variational quantum eigensolver
• A Noise-Aware Scalable Subspace Classical Optimizer for the Quantum Approximate Optimization Algorithm
• Towards a NISQ Algorithm to Simulate Hermitian Matrix Exponentiation