# Toward convergence of effective field theory simulations on digital quantum computers

## TL;DR

This paper demonstrates the use of a hybrid quantum algorithm on a trapped-ion quantum computer to accurately compute the deuteron binding energy using effective field theory, introducing new error mitigation techniques and benchmarking quantum computational capabilities.

## Contribution

It presents the first application of Richardson extrapolation error mitigation on ion traps and benchmarks quantum computers' ability to simulate effective field theories with increasing complexity.

## Key findings

- Achieved binding energy within a few percent of the exact value.
- Implemented a record-deep quantum circuit on a trapped-ion quantum computer.
- Demonstrated scalable calculation of effective field theory terms.

## Abstract

We report results for simulating an effective field theory to compute the binding energy of the deuteron nucleus using a hybrid algorithm on a trapped-ion quantum computer. Two increasingly complex unitary coupled-cluster ansaetze have been used to compute the binding energy to within a few percent for successively more complex Hamiltonians. By increasing the complexity of the Hamiltonian, allowing more terms in the effective field theory expansion and calculating their expectation values, we present a benchmark for quantum computers based on their ability to scalably calculate the effective field theory with increasing accuracy. Our result of $E_4=-2.220 \pm 0.179$MeV may be compared with the exact Deuteron ground-state energy $-2.224$MeV. We also demonstrate an error mitigation technique using Richardson extrapolation on ion traps for the first time. The error mitigation circuit represents a record for deepest quantum circuit on a trapped-ion quantum computer.