Magic State Distillation and Gate Compilation in Quantum Algorithms for Quantum Chemistry

TL;DR

This paper reviews recent advances in quantum gate compilation and magic state distillation, crucial for implementing fault-tolerant quantum algorithms in quantum chemistry, significantly improving efficiency.

Contribution

It summarizes recent progress that has enhanced the efficiency of gate compilation and magic state distillation for quantum chemistry applications.

Findings

Order-of-magnitude improvements in efficiency

Enhanced fault-tolerant gate synthesis methods

Optimized magic state distillation protocols

Abstract

Quantum algorithms for quantum chemistry map the dynamics of electrons in a molecule to the dynamics of a coupled spin system. To reach chemical accuracy for interesting molecules, a large number of quantum gates must be applied which implies the need for quantum error correction and fault-tolerant quantum computation. Arbitrary fault-tolerant operations can be constructed from a small, universal set of fault-tolerant operations by gate compilation. Quantum chemistry algorithms are compiled by decomposing the dynamics of the coupled spin-system using a Trotter formula, synthesizing the decomposed dynamics using Clifford operations and single-qubit rotations, and finally approximating the single-qubit rotations by a sequence of fault-tolerant single-qubit gates. Certain fault-tolerant gates rely on the preparation of specific single-qubit states referred to as magic states. As a result, gate compilation and magic state distillation are critical for solving quantum chemistry problems on a quantum computer. We review recent progress that has improved the efficiency of gate compilation and magic state distillation by orders of magnitude.