An Adaptive Optimizer for Measurement-Frugal Variational Algorithms

Abstract

Variational hybrid quantum-classical algorithms (VHQCAs) have the potential to be useful in the era of near-term quantum computing. However, recently there has been concern regarding the number of measurements needed for convergence of VHQCAs. Here, we address this concern by investigating the classical optimizer in VHQCAs. We introduce a novel optimizer called individual Coupled Adaptive Number of Shots (iCANS). This adaptive optimizer frugally selects the number of measurements (i.e., number of shots) both for a given iteration and for a given partial derivative in a stochastic gradient descent. We numerically simulate the performance of iCANS for the variational quantum eigensolver and for variational quantum compiling, with and without noise. In all cases, and especially in the noisy case, iCANS tends to out-perform state-of-the-art optimizers for VHQCAs. We therefore believe this adaptive optimizer will be useful for realistic VHQCA implementations, where the number of measurements is limited.

11 pages, 3 figures, 4 tables. Figures and tables updated to include more optimizers in the comparison

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• Variational Quantum Algorithms
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• The Variational Quantum Eigensolver: a review of methods and best practices
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• Challenges and Opportunities in Quantum Machine Learning
• Generalization in quantum machine learning from few training data
• Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
• Effect of barren plateaus on gradient-free optimization
• Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
• Is quantum advantage the right goal for quantum machine learning?
• Stochastic gradient descent for hybrid quantum-classical optimization
• Variational Quantum Linear Solver
• Solving nonlinear differential equations with differentiable quantum circuits
• Noise Resilience of Variational Quantum Compiling
• Strategies for solving the Fermi-Hubbard model on near-term quantum computers
• Emerging quantum computing algorithms for quantum chemistry
• Efficient quantum measurement of Pauli operators in the presence of finite sampling error
• Trainability of Dissipative Perceptron-Based Quantum Neural Networks
• Fermionic partial tomography via classical shadows
• Estimating the gradient and higher-order derivatives on quantum hardware
• Large gradients via correlation in random parameterized quantum circuits
• Equivalence of quantum barren plateaus to cost concentration and narrow gorges
• Variational Quantum State Eigensolver
• Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithms
• Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware
• Classical Optimizers for Noisy Intermediate-Scale Quantum Devices
• Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information
• Variational-State Quantum Metrology
• Biology and medicine in the landscape of quantum advantages
• Universal discriminative quantum neural networks
• Minimizing estimation runtime on noisy quantum computers
• 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
• Quantum Singular Value Decomposer
• Using models to improve optimizers for variational quantum algorithms
• Adaptive pruning-based optimization of parameterized quantum circuits
• Robust quantum compilation and circuit optimisation via energy minimisation
• Quantum Analytic Descent
• Graph neural network initialisation of quantum approximate optimisation
• Solving hadron structures using the basis light-front quantization approach on quantum computers
• Detecting and quantifying entanglement on near-term quantum devices
• Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?
• Microcanonical and finite temperature ab initio molecular dynamics simulations on quantum computers
• Comparative study of variations in quantum approximate optimization algorithms for the Traveling Salesman Problem
• Optimal quantum control with poor statistics
• A semi-agnostic ansatz with variable structure for quantum machine learning
• 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
• Quantum Mixed State Compiling
• Applying quantum approximate optimization to the heterogeneous vehicle routing problem
• Hamiltonian operator approximation for energy measurement and ground state preparation
• Surrogate-based optimization for variational quantum algorithms
• Towards Cosmological Simulations of Dark Matter on Quantum Computers
• Latency considerations for stochastic optimizers in variational quantum algorithms
• Efficient quantum imaginary time evolution by drifting real time evolution: an approach with low gate and measurement complexity
• Accelerated variational quantum eigensolver with joint Bell measurement
• Quantum Generative Learning for High-Resolution Medical Image Generation
• Post-Hartree-Fock method in Quantum Chemistry for Quantum Computer
• Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping
• Optimizing Variational Quantum Algorithms with qBang: Efficiently Interweaving Metric and Momentum to Navigate Flat Energy Landscapes
• QAOA-MC: Markov chain Monte Carlo enhanced by Quantum Alternating Operator Ansatz
• Resource frugal optimizer for quantum machine learning
• Multi-variable integration with a variational quantum circuit
• Universal noise-precision relations in variational quantum algorithms
• Resource-efficient utilization of quantum computers
• Backpropagation scaling in parameterised quantum circuits
• Computing Electronic Correlation Energies using Linear Depth Quantum Circuits
• Parent Hamiltonian as a benchmark problem for variational quantum eigensolvers
• A Novel Noise-Aware Classical Optimizer for Variational Quantum Algorithms
• A Monte Carlo Tree Search approach to QAOA: finding a needle in the haystack
• VQE-generated quantum circuit dataset for machine learning
• End-to-End Protocol for High-Quality QAOA Parameters with Few Shots
• Variational quantum algorithm based on Lagrange polynomial encoding to solve differential equations
• A Noise-Aware Scalable Subspace Classical Optimizer for the Quantum Approximate Optimization Algorithm
• How Many Shots Are Enough for a Quantum Circuit?
• Topological and geometric patterns in optimal bang-bang protocols for variational quantum algorithms: application to the $XXZ$ model on the square lattice
• Clustering and enhanced classification using a hybrid quantum autoencoder
• Shot-Efficient ADAPT-VQE via Reused Pauli Measurements and Variance-Based Shot Allocation