Taylor L. Patti

Freya Shah, Taylor L. Patti, Julius Berner et al.

Fourier Neural Operators (FNOs) excel on tasks using functional data, such as those originating from partial differential equations. Such characteristics render them an effective approach for simulating the time evolution of quantum wavefunctions, which is a computationally challenging, yet coveted task for studying quantum systems. In this manuscript, we use FNOs to model the evolution of quantum spin systems, so chosen due to their representative quantum dynamics. We explore two distinct FNO architectures, examining their performance for learning and predicting time evolution on both random and low-energy input states. We find that standard neural networks in fixed dimensions, such as U-Net, exhibit limited ability to extrapolate beyond the training time interval, whereas FNOs reliably capture the underlying time-evolution operator, generalizing effectively to unseen times. Additionally, we apply FNOs to a compact set of Hamiltonian observables ($\sim\text{poly}(n)$) instead of the entire $2^n$ quantum wavefunction, which greatly reduces the size of our FNO inputs, outputs and model dimensions. Moreover, this Hamiltonian observable-based method demonstrates that FNOs can effectively distill information from high-dimensional spaces into lower-dimensional spaces. Using this approach, we perform numerical experiments on a 20-qubit system and extrapolate Hamiltonian observables to twice the training time with a relative error of $5.8\%$. Relative to numerical time-evolution methods, FNO achieves an inference speedup of approximately $10^{4}\times$ for 20-qubit systems. The extrapolation of Hamiltonian observables to times later than those used in training is of particular interest, as this stands to fundamentally increase the simulatability of quantum systems past both the coherence times of contemporary quantum architectures and the circuit-depths of tractable tensor networks.

Rahul Marchand, Lucas Schorling, Cornelius Carlsson et al.

Transformer models and end-to-end learning frameworks are rapidly revolutionizing the field of artificial intelligence. In this work, we apply object detection transformers to analyze charge stability diagrams in semiconductor quantum dot arrays, a key task for achieving scalability with spin-based quantum computing. Specifically, our model identifies triple points and their connectivity, which is crucial for virtual gate calibration, charge state initialization, drift correction, and pulse sequencing. We show that it surpasses convolutional neural networks in performance on three different spin qubit architectures, all without the need for retraining. In contrast to existing approaches, our method significantly reduces complexity and runtime, while enhancing generalizability. The results highlight the potential of transformer-based end-to-end learning frameworks as a foundation for a scalable, device- and architecture-agnostic tool for control and tuning of quantum dot devices.

Iddo Drori, Sarah Zhang, Reece Shuttleworth et al.

We demonstrate that a neural network pre-trained on text and fine-tuned on code solves mathematics course problems, explains solutions, and generates new questions at a human level. We automatically synthesize programs using few-shot learning and OpenAI's Codex transformer and execute them to solve course problems at 81% automatic accuracy. We curate a new dataset of questions from MIT's largest mathematics courses (Single Variable and Multivariable Calculus, Differential Equations, Introduction to Probability and Statistics, Linear Algebra, and Mathematics for Computer Science) and Columbia University's Computational Linear Algebra. We solve questions from a MATH dataset (on Prealgebra, Algebra, Counting and Probability, Intermediate Algebra, Number Theory, and Precalculus), the latest benchmark of advanced mathematics problems designed to assess mathematical reasoning. We randomly sample questions and generate solutions with multiple modalities, including numbers, equations, and plots. The latest GPT-3 language model pre-trained on text automatically solves only 18.8% of these university questions using zero-shot learning and 30.8% using few-shot learning and the most recent chain of thought prompting. In contrast, program synthesis with few-shot learning using Codex fine-tuned on code generates programs that automatically solve 81% of these questions. Our approach improves the previous state-of-the-art automatic solution accuracy on the benchmark topics from 8.8% to 81.1%. We perform a survey to evaluate the quality and difficulty of generated questions. This work is the first to automatically solve university-level mathematics course questions at a human level and the first work to explain and generate university-level mathematics course questions at scale, a milestone for higher education.