Quantum Advantage in Resource Estimation

TL;DR

This paper presents a quantum algorithm that significantly reduces the runtime for estimating resources of large quantum algorithms, potentially demonstrating practical quantum advantage in resource estimation tasks.

Contribution

The authors introduce a quantum algorithm for measuring simulation errors that drastically reduces runtimes, enabling feasible resource estimation for large quantum systems.

Findings

Reduces quantum algorithm runtimes by ~1000x for 100-qubit systems

Method requires few qubits and operations, suitable for near-term quantum computers

Potential to demonstrate practical quantum advantage in resource estimation

Abstract

Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a classical computer. Demonstrating quantum advantage requires a powerful quantum computer with low error rates and an efficient quantum algorithm that has a useful application. Despite rapid progress in hardware development, we still lack useful applications that are feasible for the next generation of quantum computers. Here we argue that an exponential quantum advantage exists in producing numerical resource estimates of larger quantum algorithms by accurately measuring simulation errors. We provide a quantum algorithm for measuring simulation errors of Trotter-based algorithms. Our results indicate that this method will reduce runtimes of quantum algorithms by approximately three orders of magnitude for one-hundred qubit systems. We also predict that these reductions will increase with system size. The methods we propose require relatively few qubits and operations, meaning the next generation of quantum computers could compute simulation errors for classically intractable systems. Since the underlying computations that lead to reduced resource estimates are infeasible for classical computers, this task is a candidate for demonstrating practical quantum advantage.