Non-trivial symmetries in quantum landscapes and their resilience to quantum noise

Abstract

Very little is known about the cost landscape for parametrized Quantum Circuits (PQCs). Nevertheless, PQCs are employed in Quantum Neural Networks and Variational Quantum Algorithms, which may allow for near-term quantum advantage. Such applications require good optimizers to train PQCs. Recent works have focused on quantum-aware optimizers specifically tailored for PQCs. However, ignorance of the cost landscape could hinder progress towards such optimizers. In this work, we analytically prove two results for PQCs: (1) We find an exponentially large symmetry in PQCs, yielding an exponentially large degeneracy of the minima in the cost landscape. Alternatively, this can be cast as an exponential reduction in the volume of relevant hyperparameter space. (2) We study the resilience of the symmetries under noise, and show that while it is conserved under unital noise, non-unital channels can break these symmetries and lift the degeneracy of minima, leading to multiple new local minima. Based on these results, we introduce an optimization method called Symmetry-based Minima Hopping (SYMH), which exploits the underlying symmetries in PQCs. Our numerical simulations show that SYMH improves the overall optimizer performance in the presence of non-unital noise at a level comparable to current hardware. Overall, this work derives large-scale circuit symmetries from local gate transformations, and uses them to construct a noise-aware optimization method.

13 + 7 pages, 10 figures, updated title and article to published version

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• Barren Plateaus in Variational Quantum Computing
• Theory for Equivariant Quantum Neural Networks
• Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks
• Does provable absence of barren plateaus imply classical simulability?
• TETRIS-ADAPT-VQE: An adaptive algorithm that yields shallower, denser circuit ansätze
• Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?
• Quantum Architecture Search: A Survey
• Quantum Convolutional Neural Networks are Effectively Classically Simulable
• Quantum Energy Landscape and VQA Optimization
• Trainability Barriers in Low-Depth QAOA Landscapes
• Layering and subpool exploration for adaptive Variational Quantum Eigensolvers: Reducing circuit depth, runtime, and susceptibility to noise
• Quantum DeepONet: Neural operators accelerated by quantum computing
• Variational quantum computing for quantum simulation: principles, implementations, and challenges
• Analyzing the quantum approximate optimization algorithm: ansätze, symmetries, and Lie algebras
• Simulating quantum circuits with arbitrary local noise using Pauli Propagation
• Universal noise-precision relations in variational quantum algorithms
• Scalability Challenges in Variational Quantum Optimization under Stochastic Noise
• Characterization of overparametrization in the simulation of realistic quantum systems
• Efficient Estimation and Sequential Optimization of Cost Functions in Variational Quantum Algorithms
• Zero-Noise Extrapolation via Cyclic Permutations of Quantum Circuit Layouts
• Simplifying errors by symmetry and randomisation