Mitigated barren plateaus in the time-nonlocal optimization of analog quantum-algorithm protocols

Abstract

Quantum machine learning has emerged as a promising utilization of near-term quantum computation devices. However, algorithmic classes such as variational quantum algorithms have been shown to suffer from barren plateaus due to vanishing gradients in their parameters spaces. We present an approach to quantum algorithm optimization that is based on trainable Fourier coefficients of Hamiltonian system parameters. Our ansatz is exclusive to the extension of discrete quantum variational algorithms to analog quantum optimal control schemes and is non-local in time. We demonstrate the viability of our ansatz on the objectives of compiling the quantum Fourier transform and preparing ground states of random problem Hamiltonians. In comparison to the temporally local discretization ansätze in quantum optimal control and parameterized circuits, our ansatz exhibits faster and more consistent convergence. We uniformly sample objective gradients across the parameter space and find that in our ansatz the variance decays at a non-exponential rate with the number of qubits, while it decays at an exponential rate in the temporally local benchmark ansatz. This indicates the mitigation of barren plateaus in our ansatz. We propose our ansatz as a viable candidate for near-term quantum machine learning.

References in corpus (23)

• Variational Quantum Algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• The power of quantum neural networks
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• Challenges and Opportunities in Quantum Machine Learning
• Efficient quantum state tomography
• The quest for a Quantum Neural Network
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Absence of Barren Plateaus in Quantum Convolutional Neural Networks
• Permutationally invariant quantum tomography
• Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
• Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
• Equivalence of quantum barren plateaus to cost concentration and narrow gorges
• Entanglement Devised Barren Plateau Mitigation
• Higher Order Derivatives of Quantum Neural Networks with Barren Plateaus
• On barren plateaus and cost function locality in variational quantum algorithms
• Performance comparison of optimization methods on variational quantum algorithms
• From pulses to circuits and back again: A quantum optimal control perspective on variational quantum algorithms
• Quantum-optimal-control-inspired ansatz for variational quantum algorithms
• Neural network quantum state tomography in a two-qubit experiment
• Out-of-distribution generalization for learning quantum dynamics
• Quantum optimal control using phase-modulated driving fields
• Optimizing quantum control pulses with complex constraints and few variables through Tensorflow

Cited by in corpus (5)

• Barren Plateaus in Variational Quantum Computing
• Beyond Quantum Annealing: Optimal control solutions to MaxCut problems
• SHARC-VQE: Simplified Hamiltonian Approach with Refinement and Correction enabled Variational Quantum Eigensolver for Molecular Simulation
• Consensus-based qubit configuration optimization for variational algorithms on neutral atom quantum systems
• Pulse engineering via projection of response functions