Halving the Cost of Controlled Time-Evolution

TL;DR

This paper introduces a compilation scheme that halves the number of arbitrary rotations needed for controlled Trotterized time evolution in quantum simulation, significantly reducing resource costs in fault-tolerant quantum computing.

Contribution

It presents a novel compilation method that avoids increasing the number of arbitrary rotations for symmetric Trotterizations, improving efficiency in quantum simulation.

Findings

Halves the number of arbitrary rotations for controlled Trotter evolution.

Reduces the T-cost of fault-tolerant quantum simulation.

Applicable to second-order and higher Suzuki-Trotter decompositions.

Abstract

Quantum simulation is a promising application for quantum computing. Quantum simulation algorithms may require the ability to control the time evolution unitary. Naive techniques to control a unitary can substantially increase the required computational resources. A standard approach to controlling Trotterized time evolution doubles the number of single-qubit arbitrary rotations. Here, we describe a compilation scheme that does not increase the number of arbitrary rotations for symmetric Trotterizations, which applies to second-order and higher Suzuki-Trotter decompositions. This halves the number of arbitrary rotations required to implement controlled, Trotterized time evolution compared to the standard approach. Arbitrary rotations contribute significantly to resource estimates in a fault-tolerant architecture due to the number of required magic states. Therefore, arbitrary rotations dominate the $T$-cost of fault-tolerant implementations of quantum simulation. This construction reduces the number of arbitrary rotations for controlled Trotter evolution to that of uncontrolled Trotter evolution, thereby reducing the cost of fault-tolerant quantum simulation.