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Quantum circuits for strongly correlated quantum systems
Frank Verstraete, J. Ignacio Cirac, Jose I. Latorre
TL;DR
The paper addresses how quantum simulators can access more than low-energy states of strongly correlated many-body systems. It constructs explicit circuits that transform certain Hamiltonians into non-interacting forms, enabling preparation and evolution across the spectrum, with exact circuits also extended to topological and stabilizer systems.
Problem
Quantum simulators have limited access to the full spectrum of strongly correlated many-body problems, motivating methods that reach excited, thermal, and dynamically evolving states.
Method
The paper constructs a unitary disentangling circuit that maps selected many-body Hamiltonians to non-interacting Hamiltonians using polynomially many local gates.
Results
Certain relevant strongly correlated Hamiltonians are exactly diagonalized by finite-depth circuits, including explicit four- and eight-qubit realizations and circuits for topological-order and stabilizer models.
Takeaways & Limitations
The circuits enable preparation of ground, excited, and thermal states and simulation of arbitrary-time dynamics with effort independent of time, temperature, or excitation degree.
Takeaways & Limitations
The method works exactly only for a small set of integrable problems, while approximate transformations are suggested for systems described by quasiparticles.
Abstract
from arXiv · showhide
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.