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arXiv:2405.20525 · npj Unconventional Computing

Comparing quantum annealing and spiking neuromorphic computing for sampling binary sparse coding QUBO problems

Kyle Henke, Elijah Pelofske, Garrett T. Kenyon, Georg Hahn

Published Jun 4, 2025• 2 citations
arXivHTMLPDF

Abstract

Abstract We consider the problem of computing a sparse binary representation of an image. 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 loss on the binary vector enforcing sparsity. First, we solve the sparse representation QUBOs by solving them both on a D-Wave quantum annealer with Pegasus chip connectivity, as well as on the Intel Loihi 2 spiking neuromorphic processor using a stochastic Non-equilibrium Boltzmann Machine (NEBM). Second, using Quantum Evolution Monte Carlo with Reverse Annealing and iterated warm starting on Loihi 2 to evolve the solution quality from the respective machines. We demonstrate that both quantum annealing and neuromorphic computing are suitable for solving binary sparse coding QUBOs.

DOI
10.1038/s44335-025-00028-2

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Abstract We consider the problem of computing a sparse binary representation of an image. 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 loss on the binary vector enforcing sparsity. First, we solve the sparse representation QUBOs by solving them both on a D-Wave quantum annealer with Pegasus chip connectivity, as well as on the Intel Loihi 2 spiking neuromorphic processor using a stochastic Non-equilibrium Boltzmann Machine (NEBM). Second, using Quantum Evolution Monte Carlo with Reverse Annealing and iterated warm starting on Loihi 2 to evolve the solution quality from the respective machines. We demonstrate that both quantum annealing and neuromorphic computing are suitable for solving binary sparse coding QUBOs.
Machine Learning has achieved immense progress by exploiting CPUs and GPUs on classical computing hardware. However, the inevitable end of Moore's Law on these devices requires the adaptation and exploration of novel computational platforms in order to continue these advancements. Biologically accurate, energy efficient neuromorphic systems and fully en-tangled quantum systems are particularly promising arenas for enabling future advances. In this work, we perform a detailed comparison on a level playing field between these two novel substrates by applying them to an identical challenge.We solve the sparse coding problem using the biologically inspired Locally Competitive Algorithm (LCA) on the D-Wave quantum annealer and Intel Loihi neuromorphic spiking processor. The Fashion-MNIST data set was chosen and dimensionally-reduced by sparse Principal Component Analysis (sPCA). A sign flipped second data set was created and appended to the original in order to give each class a mean zero distribution, effectively creating an environment where the data could not be linearly separated. An early in time normalization technique for Loihi is presented along with analysis of optimal parameter selection and unsupervised dictionary learning for all three variations. Studies are ongoing, but preliminary results suggest each computational substrate requires casting the NP-Hard optimization problem in a slightly different manner to best capture the individual strengths, and the new Loihi method allows for more realistic comparison between the two.
Although machine learning currently relies on conventional computer architectures, the looming end of Moore's Law necessitates exploration of novel computational platforms. Neuromorphic and quantum systems are a natural path to pursue; biological neurons are incredibly efficient, and quantum mechanics provides theoretical foundations for fast solutions to optimization problems. Here, we make the first comparison of emerging hardware (D-Wave quantum annealer and Intel Loihi spiking processor) on an identically-posed machine learning problem. We implement the bioinspired Locally Competitive Algorithm (LCA) for solving sparse coding on the different substrates. To make the comparison valid, our dataset of choice (Fashion MNIST) is dimensionally-reduced via sparse principal component analysis, under the constraint that both classification performance and a graph-based clustering metric remain unchanged. This enables the problem to be mapped identically to both devices. An analysis of several metrics, including power consumption, reconstruction, and classification accuracy are presented. When given the same specifically-constructed challenge, both substrates perform similarly. Our results suggest while neuromorphic and quantum systems are still in their infancy, they present a possible route to address certain types of classically challenging problems, such as sparse coding, in a way that leverages the unique aspects of the substrates.
In this article, we describe an algorithm for solving Quadratic Unconstrained Binary Optimization problems on the Intel Loihi 2 neuromorphic processor. The solver is based on a hardware-aware fine-grained parallel simulated annealing algorithm developed for Intel's neuromorphic research chip Loihi 2. Preliminary results show that our approach can generate feasible solutions in as little as 1 ms and up to 37x more energy efficient compared to two baseline solvers running on a CPU. These advantages could be especially relevant for size-, weight-, and power-constrained edge computing applications.
Abstract The ultimate goal of any sparse coding method is to accurately recover from a few noisy linear measurements, an unknown sparse vector. Unfortunately, this estimation problem is NP-hard in general, and it is therefore always approached with an approximation method, such as lasso or orthogonal matching pursuit, thus trading off accuracy for less computational complexity. In this paper, we develop a quantum-inspired algorithm for sparse coding, with the premise that the emergence of quantum computers and Ising machines can potentially lead to more accurate estimations compared to classical approximation methods. To this end, we formulate the most general sparse coding problem as a quadratic unconstrained binary optimization (QUBO) task, which can be efficiently minimized using quantum technology. To derive at a QUBO model that is also efficient in terms of the number of spins (space complexity), we separate our analysis into three different scenarios. These are defined by the number of bits required to express the underlying sparse vector: binary, 2-bit, and a general fixed-point representation. We finally conduct numerical experiments with simulated data on LightSolver's quantum-inspired digital platform to verify the correctness of our QUBO formulation and to demonstrate that we obtain more accurate solutions in regimes where the baseline methods fail.
Abstract Many engineering problems involve solving large linear systems of equations. Conjugate gradient (CG) is one of the most popular iterative methods for solving such systems. However, CG typically requires a good preconditioner to speed up convergence. One such preconditioner is the sparse approximate inverse (SPAI). In this paper, we explore the computation of an SPAI on quantum annealing machines by solving a series of quadratic unconstrained binary optimization (QUBO) problems. Numerical experiments are conducted using both well-conditioned and poorly-conditioned linear systems arising from a 2D finite difference formulation of the Poisson problem.
Many engineering problems involve solving large linear systems of equations. Conjugate gradient (CG) is one of the most popular iterative methods for solving such systems. However, CG typically requires a good preconditioner to speed up convergence. One such preconditioner is the sparse approximate inverse (SPAI). In this paper, we explore the computation of an SPAI on quantum annealing machines by solving a series of quadratic unconstrained binary optimization (QUBO) problems. Numerical experiments are conducted using both well-conditioned and poorly-conditioned linear systems arising from a 2D finite difference formulation of the Poisson problem.