Data is often loadable in short depth: Quantum circuits from tensor networks for finance, images, fluids, and proteins

TL;DR

This paper introduces a tensor network-based method called AMLET for efficiently loading classical data into quantum circuits, significantly reducing circuit depth compared to traditional methods, with broad applications across various fields.

Contribution

The paper presents a novel tensor network compilation technique for quantum data loading, demonstrating its effectiveness on real-world datasets from multiple domains.

Findings

Circuit depths are often orders of magnitude lower than exponential estimates.

Many classical datasets can be loaded in surprisingly shallow quantum circuits.

The method broadens the practical feasibility of quantum data loading for classical datasets.

Abstract

Though there has been substantial progress in developing quantum algorithms to study classical datasets, the cost of simply \textit{loading} classical data is an obstacle to quantum advantage. When the amplitude encoding is used, loading an arbitrary classical vector requires up to exponential circuit depths with respect to the number of qubits. Here, we address this ``input problem'' with two contributions. First, we introduce a circuit compilation method based on tensor network (TN) theory. Our method -- AMLET (Automatic Multi-layer Loader Exploiting TNs) -- proceeds via careful construction of a specific TN topology and can be tailored to arbitrary circuit depths. Second, we perform numerical experiments on real-world classical data from four distinct areas: finance, images, fluid mechanics, and proteins. To the best of our knowledge, this is the broadest numerical analysis to date of loading classical data into a quantum computer. The required circuit depths are often several orders of magnitude lower than the exponentially-scaling general loading algorithm would require. Besides introducing a more efficient loading algorithm, this work demonstrates that many classical datasets are loadable in depths that are much shorter than previously expected, which has positive implications for speeding up classical workloads on quantum computers.