Quantum computing technology is advancing rapidly. Yet, even accounting for these trends, a quantum leap would be needed for quantum computers to meaningfully impact deep learning over the coming decade or two. We arrive at this conclusion based on a first-of-its-kind survey of quantum algorithms and how they match potential deep learning applications. This survey reveals three important areas where quantum computing could potentially accelerate deep learning, each of which faces a challenging roadblock to realizing its potential. First, quantum algorithms for matrix multiplication and other algorithms central to deep learning offer small theoretical improvements in the number of operations needed, but this advantage is overwhelmed on practical problem sizes by how slowly quantum computers do each operation. Second, some promising quantum algorithms depend on practical Quantum Random Access Memory (QRAM), which is underdeveloped. Finally, there are quantum algorithms that offer large theoretical advantages, but which are only applicable to special cases, limiting their practical benefits. In each of these areas, we support our arguments using quantitative forecasts of quantum advantage that build on the work by Choi et al. [2023] as well as new research on limitations and quantum hardware trends. Our analysis outlines the current scope of quantum deep learning and points to research directions that could lead to greater practical advances in the field.

Algorithm research focuses primarily on how many operations processors need to do (time complexity). But for many problems, both the runtime and energy used are dominated by memory accesses. In this paper, we present the first broad survey of how algorithmic progress has improved memory usage (space complexity). We analyze 118 of the most important algorithm problems in computer science, reviewing the 800+ algorithms used to solve them. Our results show that space complexity has become much more important in recent years as worries have arisen about memory access bottle-necking performance (the ``memory wall''). In 20% of cases we find that space complexity improvements for large problems (n=1 billion) outpaced improvements in DRAM access speed, suggesting that for these problems algorithmic progress played a larger role than hardware progress in minimizing memory access delays. Increasingly, we also see the emergence of algorithmic Pareto frontiers, where getting better asymptotic time complexity for a problem requires getting worse asymptotic space complexity, and vice-versa. This tension implies that programmers will increasingly need to consider multiple algorithmic options to understand which is best for their particular problem. To help theorists and practitioners alike consider these trade-offs, we have created a reference for them at this https URL.

Language models have seen enormous progress on advanced benchmarks in recent years, but much of this progress has only been possible by using more costly models. Benchmarks may therefore present a warped picture of progress in practical capabilities per dollar. To remedy this, we use data from Artificial Analysis and Epoch AI to form the largest dataset of current and historical prices to run benchmarks to date. We find that the price for a given level of benchmark performance has decreased remarkably fast, around to per year, for frontier models on knowledge, reasoning, math, and software engineering benchmarks. These reductions in the cost of AI inference are due to economic forces, hardware efficiency improvements, and algorithmic efficiency improvements. Isolating out open models to control for competition effects and dividing by hardware price declines, we estimate that algorithmic efficiency progress is around per year. Finally, we recommend that evaluators both publicize and take into account the price of benchmarking as an essential part of measuring the real-world impact of AI.