1,332 research outputs found
Sampling reduced density matrix to extract fine levels of entanglement spectrum
Low-lying entanglement spectrum provides the quintessential fingerprint to
identify the highly entangled quantum matter with topological and conformal
field-theoretical properties. However, when the entangling region acquires long
boundary with the environment, such as that between long coupled chains or in
two or higher dimensions, there unfortunately exists no universal yet practical
method to compute the entanglement spectra with affordable computational cost.
Here we propose a new scheme to overcome such difficulty and successfully
extract the low-lying fine entanglement spectrum (ES). We trace out the
environment via quantum Monte Carlo simulation and diagonalize the reduced
density matrix to gain the ES. We demonstrate the strength and reliability of
our method through long coupled spin chains and answer its long-standing
controversy. Our simulation results, with unprecedentedly large system sizes,
establish the practical computation scheme of the entanglement spectrum with a
huge freedom degree of environment
Quantum imaginary time evolution and quantum annealing meet topological sector optimization
Optimization problems are the core challenge in many fields of science and
engineering, yet general and effective methods are scarce for searching optimal
solutions. Quantum computing has been envisioned to help solve such problems,
for example, the quantum annealing (QA) method based on adiabatic evolution has
been extensively explored and successfully implemented on quantum simulators
such as D-wave's annealers and some Rydberg arrays. In this work, we
investigate topological sector optimization (TSO) problem, which attracts
particular interests in the quantum many-body physics community. We reveal that
the topology induced by frustration in the spin model is an intrinsic
obstruction for QA and other traditional methods to approach the ground state.
We demonstrate that the optimization difficulties of TSO problem are not
restricted to the gaplessness, but are also due to the topological nature which
are often ignored for the analysis of optimization problems before. To solve
TSO problems, we utilize quantum imaginary time evolution (QITE) with a
possible realization on quantum computers, which exploits the property of
quantum superposition to explore the full Hilbert space and can thus address
optimization problems of topological nature. We report the performance of
different quantum optimization algorithms on TSO problems and demonstrate that
their capability to address optimization problems are distinct even when
considering the quantum computational resources required for practical QITE
implementations
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