The original version of this story appeared in Quanta Magazine.

For computer scientists, tackling complex problems is akin to mountaineering; they must first select a problem to solve, similar to identifying a peak to conquer, and then devise a strategic approach to address it. Within this landscape, classical and quantum researchers engage in a spirited competition, each employing distinct strategies to advance their respective domains. Recently, quantum researchers unveiled a method that purportedly expedites the resolution of a specific problemoften by boldly exploring peaks that others deemed unworthy of interest. In turn, classical teams scramble to discover improved methodologies that might outperform their quantum counterparts.

This ongoing contest frequently culminates in a virtual stalemate: whenever researchers announce a quantum algorithm that seemingly performs better than all prior solutions, classical researchers typically step up with an alternative that matches its performance. For instance, just last week, excitement surrounding a claimed quantum speedup, published in the journal Science, was quickly dampened by skepticism from two independent research groups who demonstrated that similar calculations could be accomplished using classical machines.

However, a recent publication on the scientific preprint platform arxiv.org detailed what appears to be a substantial quantum speedup that is both convincing and practically beneficial. In this paper, researchers introduced a novel quantum algorithm that significantly outperforms all existing classical solutions in solving a broad category of optimization problems, which focus on identifying the best possible solutions among a staggering array of choices.

So far, no classical algorithm has matched the effectiveness of the new algorithm, termed Decoded Quantum Interferometry (DQI). Gil Kalai, a mathematician at Reichman University and a noted skeptic in the realm of quantum computing, referred to it as a breakthrough in quantum algorithms. The excitement surrounding quantum algorithms stems partly from their potential to shed light on new avenues for addressing complex problems, and partly because, amid the growing interest in quantum technology, it's still unclear which specific challenges will benefit from quantum solutions. An algorithm that outshines all known classical alternatives in optimization tasks would signify a monumental advance in the quest to harness the capabilities of quantum computers.

Ronald de Wolf, a theoretical computer scientist at the Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands, expressed enthusiasm about the development. However, he also prudently warned that it remains highly possible for researchers to eventually discover a classical algorithm that performs equally well. Additionally, the current shortage of quantum hardware means it may take some time before empirical tests of the new algorithm can be conducted.

The implications of this algorithm could very well stimulate further advancements in classical algorithms. Ewin Tang, a computer scientist at the University of California, Berkeley, who gained recognition in her teenage years for creating classical algorithms that rival quantum ones, remarked that the new findings are intriguing enough to merit attention from classical algorithm specialists. She advised, Hey, you should look at this paper and work on this problem.

The Best Way Forward?

In the competitive arena of algorithm development, classical and quantum approaches often intersect in the field of optimization, which is dedicated to pinpointing the most effective solutions to challenging problems. Researchers typically concentrate on scenarios where the number of possible solutions increases exponentially as the problem scales up. For instance, consider a delivery truck tasked with visiting ten cities within three dayswhat is the most efficient route? How should the parcels be arranged in the vehicle? Traditional methods for resolving these issues, generally involving the exploration of potential solutions through innovative strategies, quickly become impractical as the complexity escalates.

The particular optimization problem addressed by the DQI algorithm can be summarized as follows: given a series of points plotted on a sheet of paper, the goal is to construct a mathematical function that intersects these points. Specifically, this function must adhere to the constraints of being a polynomiala mixture of variables raised to whole-number powers and multiplied by coefficients. However, it cannot be overly complicated, meaning that the powers must remain relatively low. Ultimately, this task leads to the creation of a curved line that meanders up and down across the page. The objective then becomes identifying the most accurate line that intersects the greatest number of points.

Variations of this optimization challenge manifest in numerous applications across computer science, particularly in the domains of error coding and cryptographyfields dedicated to the secure and accurate transmission of encoded data. The researchers behind DQI recognized that effectively plotting a superior line is analogous to refining a noisy encoded message, bringing it closer to its true and accurate interpretation.