Resource Requirements for Fault-Tolerant Quantum Simulation: The Transverse Ising Model Ground State

TL;DR

This paper estimates the quantum resource requirements, including qubits and computational time, for fault-tolerant simulation of the Transverse Ising Model's ground state, highlighting the exponential scaling with precision and error correction needs.

Contribution

It provides a detailed analysis of resource scaling for fault-tolerant quantum simulation of the TIM ground state, comparing it to Shor's algorithm requirements.

Findings

Exponential increase in computational time with precision

Similar logical qubit reliability needed for TIM and factoring

Significant error correction is essential for accurate simulation

Abstract

We estimate the resource requirements, the total number of physical qubits and computational time, required to compute the ground state energy of a 1-D quantum Transverse Ising Model (TIM) of N spin-1/2 particles, as a function of the system size and the numerical precision. This estimate is based on analyzing the impact of fault-tolerant quantum error correction in the context of the Quantum Logic Array (QLA) architecture. Our results show that due to the exponential scaling of the computational time with the desired precision of the energy, significant amount of error correciton is required to implement the TIM problem. Comparison of our results to the resource requirements for a fault-tolerant implementation of Shor's quantum factoring algorithm reveals that the required logical qubit reliability is similar for both the TIM problem and the factoring problem.