57 research outputs found
Quantum Gaussian process regression
In this paper, a quantum algorithm based on gaussian process regression model
is proposed. The proposed quantum algorithm consists of three sub-algorithms.
One is the first quantum subalgorithm to efficiently generate mean predictor.
The improved HHL algorithm is proposed to obtain the sign of outcomes.
Therefore, the terrible situation that results is ambiguous in terms of
original HHL algorithm is avoided, which makes whole algorithm more clear and
exact. The other is to product covariance predictor with same method. Thirdly,
the squared exponential covariance matrices are prepared that annihilation
operator and generation operator are simulated by the unitary linear
decomposition Hamiltonian simulation and kernel function vectors is generated
with blocking coding techniques on covariance matrices. In addition, it is
shown that the proposed quantum gaussian process regression algorithm can
achieve quadratic faster over the classical counterpart
Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation
Based on the recently developed resummation-based quantum Monte Carlo method
for the SU() spin and loop-gas models, we develop a new algorithm, dubbed
ResumEE, to compute the entanglement entropy (EE) with greatly enhanced
efficiency. Our ResumEE converts the evaluation of the exponentially small
value of the , where is the 2nd order
R\'enyi EE, to an important sampling process with polynomial accuracy such that
the for a generic 2D quantum SU() spin models can be readily
computed without facing the exponential explosion of its variance. We benchmark
our algorithm with the previously proposed estimators of on 1D and 2D
SU() Heisenberg spin systems to reveal its superior performance and then use
it to detect the entanglement scaling data of the N\'eel-to-VBS transition on
2D SU() Heisenberg model with continuously varying . Our ResumEE
algorithm solves the critical problem of precisely evaluating the quantum
entanglement in many-body systems and will have a significant impact on
reliable access to the conformal field theory data for the highly entangled
quantum matter.Comment: 10 pages, 7 figure
Dynamical properties of quantum many-body systems with long range interactions
Employing large-scale quantum Monte Carlo simulations, we systematically
compute the energy spectra of the 2D spin-1/2 Heisenberg model with long-range
interactions. With the ferromagnetic and staggered
antiferromagnetic interactions, we find the explicit range in for
{\color{black} the short-range Goldstone-type (gapless), anomalous
Goldstone-type (gapless) and Higgs-type (gapped) spectra. Accompanied by the
spin wave analysis, our numerical results vividly reveal how the long-range
interactions alter the usual linear and quadratic magnon dispersions in 2D
quantum magnets and give rise to anomalous dynamical exponents. Moreover, we
find explicit case where the gapped excitation exists even when the Hamiltonian
is extensive. This work provides the first set of unbiased dynamical data} of
long-range quantum many-body systems and suggests that many universally
accepted low-energy customs for short-range systems need to be substantially
modified for long-range ones which are of immediate relevance to the ongoing
experimental efforts from quantum simulators to 2D quantum moir\'e materials.Comment: 5 pages,3 figure
Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model
The well-known Mermin-Wagner theorem prohibits the existence of
finite-temperature spontaneous continuous symmetry breaking phase in systems
with short-range interactions at spatial dimension [Phys. Rev. 158,
383; Phys. Rev. Lett. 17, 1133; Journal of Statistical Physics 175, 521-529].
For long-range interaction with monotonic power-law form (), the
theorem further forbids a ferro- or antiferromagnetic order at finite
temperature when [Phys. Rev. Lett. 87, 137203]. However, the
situation for at is beyond the predicting power of the
theorem and the situation is still unclear. Here we address this question by
large-scale quantum Monte Carlo simulations, accompanied with field theoretical
analysis. We find the spontaneous breaking of the symmetry for in ferromagnetic Heisenberg model with interaction at
, and obtain the accurate critical exponents by finite-size analysis for
where the system is above the upper critical dimension with Gaussian
fixed point and for where the system is below the upper critical
dimension with non-Gaussian fixed point. Our results reveal the novel critical
behaviors in 2D long-range Heisenberg models and will intrigue further
experimental studies of quantum materials with long-range interaction beyond
the realm of the Mermin-Wagner theorem
Quantum criticality and entanglement for 2d long-range Heisenberg bilayer
The study of quantum criticality and entanglement in systems with long-range
(LR) interactions is still in its early stages, with many open questions
remaining. In this work, we investigate critical exponents and scaling of
entanglement entropies (EE) in the LR bilayer Heisenberg model using
large-scale quantum Monte Carlo (QMC) simulations and the recently developed
nonequilibrium increment algorithm for measuring EE. By applying modified
(standard) finite-size scaling (FSS) above (below) the upper critical dimension
and field theory analysis, we obtain precise critical exponents in three
regimes: the LR Gaussian regime with a Gaussian fixed point, the short-range
(SR) regime with Wilson-Fisher (WF) exponents, and a LR non-Gaussian regime
where the critical exponents vary continuously from LR Gaussian to SR values.
We compute the R\'enyi EE both along the critical line and in the N\'eel phase
and observe that as the LR interaction is enhanced, the area-law contribution
in EE gradually vanishes both at quantum critical points (QCPs) and in the
N\'eel phase. The log-correction in EE arising from sharp corners at the QCPs
also decays to zero as LR interaction grows, whereas the log-correction for
N\'eel states, caused by the interplay of Goldstone modes and restoration of
the symmetry in a finite system, is enhanced as LR interaction becomes
stronger. We also discuss relevant experimental settings to detect these
nontrivial properties in critical behavior and entanglement information for
quantum many-body systems with LR interactions.Comment: 5pages, 4 figure
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