Compilation of a simple chemistry application to quantum error correction primitives

TL;DR

This paper estimates the quantum resources needed for fault-tolerant quantum phase estimation on a simple chemical system, highlighting the significant qubit and error correction requirements for practical quantum chemistry applications.

Contribution

It provides a detailed compilation and optimization of a quantum chemistry algorithm within the surface code framework, bridging experimental demonstrations and resource estimation.

Findings

Requires 1,000 qubits for minimal chemistry circuit

Needs 2,300 error correction rounds for fault tolerance

Highlights the challenge of early fault-tolerant quantum chemistry

Abstract

A number of exciting recent results have been seen in the field of quantum error correction. These include initial demonstrations of error correction on current quantum hardware, and resource estimates which improve understanding of the requirements to run large-scale quantum algorithms for real-world applications. In this work, we bridge the gap between these two developments by performing careful estimation of the resources required to fault-tolerantly perform quantum phase estimation (QPE) on a minimal chemical example. Specifically, we describe a detailed compilation of the QPE circuit to lattice surgery operations for the rotated surface code, for a hydrogen molecule in a minimal basis set. We describe a number of optimisations at both the algorithmic and error correction levels. We find that implementing even a simple chemistry circuit requires 1,000 qubits and 2,300 quantum error correction rounds, emphasising the need for improved error correction techniques specifically targeting the early fault-tolerant regime.