Simulating the Transverse Ising Model on a Quantum Computer: Error Correction with the Surface Code

TL;DR

This paper estimates the resource requirements for simulating the ground state energy of the 1D transverse Ising model on a fault-tolerant quantum computer using the surface code, highlighting its practicality and resource trade-offs.

Contribution

It provides a comparative analysis of surface code and concatenated Steane code for quantum simulation, emphasizing surface code's higher error threshold and practical feasibility.

Findings

Surface code requires 2-3 orders of magnitude more physical qubits than Steane code.

Simulation time is comparable between surface code and Steane code.

Surface code's higher error threshold makes it more promising for current hardware.

Abstract

We estimate the resource requirements for the quantum simulation of the ground state energy of the one dimensional quantum transverse Ising model (TIM), based on the surface code implementation of a fault tolerant quantum computer. The surface code approach has one of the highest known tolerable error rates (1%) which makes it currently one of the most practical quantum computing schemes. Compared to results of the same model using the concatenated Steane code, the current results indicate that the simulation time is comparable but the number of physical qubits for the surface code is 2-3 orders of magnitude larger than that of the concatenation code. Considering that the error threshold requirements of the surface code is four orders of magnitude higher than the concatenation code, building a quantum computer with a surface code implementation appears more promising given current physical hardware capabilities.