Quantum circuits for strongly correlated quantum systems

TL;DR

This paper introduces explicit quantum circuits that efficiently simulate the dynamics of strongly correlated quantum many-body systems, enabling experimental realization of complex states and evolution with minimal gates.

Contribution

The authors develop a method to construct finite local gate quantum circuits for diagonalizing key many-body Hamiltonians, including models with topological order.

Findings

Quantum circuits for 1D Ising model with 6 gates

Exact circuits for models with topological order

Potential for experimental realization of correlated states

Abstract

In recent years, we have witnessed an explosion of experimental tools by which quantum systems can be manipulated in a controlled and coherent way. One of the most important goals now is to build quantum simulators, which would open up the possibility of exciting experiments probing various theories in regimes that are not achievable under normal lab circumstances. Here we present a novel approach to gain detailed control on the quantum simulation of strongly correlated quantum many-body systems by constructing the explicit quantum circuits that diagonalize their dynamics. We show that the exact quantum circuits underlying some of the most relevant many-body Hamiltonians only need a finite amount of local gates. As a particularly simple instance, the full dynamics of a one-dimensional Quantum Ising model in a transverse field with four spins is shown to be reproduced using a quantum circuit of only six local gates. This opens up the possibility of experimentally producing strongly correlated states, their time evolution at zero time and even thermal superpositions at zero temperature. Our method also allows to uncover the exact circuits corresponding to models that exhibit topological order and to stabilizer states.