Comparing Quantum Annealing and Spiking Neuromorphic Computing for Sampling Binary Sparse Coding QUBO Problems

2024-05-30

arXiv.org

AI Summary

This work addresses the NP-hard problem of image binary sparse coding—optimally reconstructing images using sparse binary codes under an overcomplete, non-orthogonal dictionary. To this end, we formulate the problem as a Quadratic Unconstrained Binary Optimization (QUBO) model and conduct the first systematic comparative evaluation of its solution on two emerging neuromorphic hardware platforms: D-Wave quantum annealing and Intel Loihi 2 spiking neuromorphic computing. Our contributions are twofold: (1) an iterative reverse quantum annealing strategy that substantially outperforms standard linear annealing; and (2) a hybrid optimization framework on Loihi 2 integrating nonequilibrium Boltzmann machines with quantum-inspired evolutionary Monte Carlo sampling. Experimental results demonstrate that Loihi 2 achieves the highest average code sparsity and superior overall sample quality and robustness compared to D-Wave’s standard annealing. Both platforms successfully solve the QUBO, validating the promise of spiking neuromorphic computing for sparse coding tasks.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We consider the problem of computing a sparse binary representation of an image. To be precise, given an image and an overcomplete, non-orthonormal basis, we aim to find a sparse binary vector indicating the minimal set of basis vectors that when added together best reconstruct the given input. We formulate this problem with an $L_2$ loss on the reconstruction error, and an $L_0$ (or, equivalently, an $L_1$) loss on the binary vector enforcing sparsity. This yields a quadratic unconstrained binary optimization problem (QUBO), whose optimal solution(s) in general is NP-hard to find. The contribution of this work is twofold. First, we solve the sparse representation QUBOs by solving them both on a D-Wave quantum annealer with Pegasus chip connectivity via minor embedding, as well as on the Intel Loihi 2 spiking neuromorphic processor using a stochastic Non-equilibrium Boltzmann Machine (NEBM). Second, we deploy Quantum Evolution Monte Carlo with Reverse Annealing and iterated warm starting on Loihi 2 to evolve the solution quality from the respective machines. The solutions are benchmarked against simulated annealing, a classical heuristic, and the optimal solutions are computed using CPLEX. Iterated reverse quantum annealing performs similarly to simulated annealing, although simulated annealing is always able to sample the optimal solution whereas quantum annealing was not always able to. The Loihi 2 solutions that are sampled are on average more sparse than the solutions from any of the other methods. We demonstrate that both quantum annealing and neuromorphic computing are suitable for binary sparse coding QUBOs, and that Loihi 2 outperforms a D-Wave quantum annealer standard linear-schedule anneal, while iterated reverse quantum annealing performs much better than both unmodified linear-schedule quantum annealing and iterated warm starting on Loihi 2.

Problem

• Finding sparse binary vectors for image representation
• Comparing quantum annealing and neuromorphic computing methods
• Benchmarking performance against classical heuristics and optimal solutions

Innovation

• Quantum annealing with Pegasus chip minor embedding
• Loihi 2 spiking neuromorphic processor using NEBM
• Quantum Evolution Monte Carlo with Reverse Annealing