Robust analog quantum simulators by quantum error-detecting codes

TL;DR

This paper introduces a scalable method for designing noise-resilient quantum simulators using error-detecting codes with 2-local commuting Hamiltonians, enabling longer high-fidelity quantum simulations on current hardware.

Contribution

It provides a novel, scalable approach to quantum error suppression using excited subspace encoding with 2-local commuting Hamiltonians, overcoming previous limitations.

Findings

Error-resilient Hamiltonian simulation using excited subspaces.

Method scales polynomially with system size.

Potential to extend high-fidelity simulation durations significantly.

Abstract

Achieving noise resilience is an outstanding challenge in Hamiltonian-based quantum computation. To this end, energy-gap protection provides a promising approach, where the desired quantum dynamics are encoded into the ground space of a penalty Hamiltonian that suppresses unwanted noise processes. However, existing approaches either explicitly require high-weight penalty terms that are not directly accessible in current hardware, or utilize non-commuting $2$-local Hamiltonians, which typically leads to an exponentially small energy gap. In this work, we provide a general recipe for designing error-resilient Hamiltonian simulations, making use of an excited encoding subspace stabilized by solely $2$-local commuting Hamiltonians. Our results thus overcome a no-go theorem previously derived for ground-space encoding that prevents noise suppression schemes with such Hamiltonians. Importantly, our method is scalable as it only requires penalty terms that scale polynomially with system size. To illustrate the utility of our approach, we further apply this method to a variety of $1$- and $2$-dimensional many-body spin models, potentially extending the duration of high-fidelity simulation by orders of magnitude in current hardware.