10,201 research outputs found
Estimation and uncertainty of reversible Markov models
Reversibility is a key concept in Markov models and Master-equation models of
molecular kinetics. The analysis and interpretation of the transition matrix
encoding the kinetic properties of the model relies heavily on the
reversibility property. The estimation of a reversible transition matrix from
simulation data is therefore crucial to the successful application of the
previously developed theory. In this work we discuss methods for the maximum
likelihood estimation of transition matrices from finite simulation data and
present a new algorithm for the estimation if reversibility with respect to a
given stationary vector is desired. We also develop new methods for the
Bayesian posterior inference of reversible transition matrices with and without
given stationary vector taking into account the need for a suitable prior
distribution preserving the meta- stable features of the observed process
during posterior inference. All algorithms here are implemented in the PyEMMA
software - http://pyemma.org - as of version 2.0
Witnessing eigenstates for quantum simulation of Hamiltonian spectra
The efficient calculation of Hamiltonian spectra, a problem often intractable
on classical machines, can find application in many fields, from physics to
chemistry. Here, we introduce the concept of an "eigenstate witness" and
through it provide a new quantum approach which combines variational methods
and phase estimation to approximate eigenvalues for both ground and excited
states. This protocol is experimentally verified on a programmable silicon
quantum photonic chip, a mass-manufacturable platform, which embeds entangled
state generation, arbitrary controlled-unitary operations, and projective
measurements. Both ground and excited states are experimentally found with
fidelities >99%, and their eigenvalues are estimated with 32-bits of precision.
We also investigate and discuss the scalability of the approach and study its
performance through numerical simulations of more complex Hamiltonians. This
result shows promising progress towards quantum chemistry on quantum computers.Comment: 9 pages, 4 figures, plus Supplementary Material [New version with
minor typos corrected.
Experimental Bayesian Quantum Phase Estimation on a Silicon Photonic Chip
Quantum phase estimation is a fundamental subroutine in many quantum
algorithms, including Shor's factorization algorithm and quantum simulation.
However, so far results have cast doubt on its practicability for near-term,
non-fault tolerant, quantum devices. Here we report experimental results
demonstrating that this intuition need not be true. We implement a recently
proposed adaptive Bayesian approach to quantum phase estimation and use it to
simulate molecular energies on a Silicon quantum photonic device. The approach
is verified to be well suited for pre-threshold quantum processors by
investigating its superior robustness to noise and decoherence compared to the
iterative phase estimation algorithm. This shows a promising route to unlock
the power of quantum phase estimation much sooner than previously believed
Analyzing many-body localization with a quantum computer
Many-body localization, the persistence against electron-electron
interactions of the localization of states with non-zero excitation energy
density, poses a challenge to current methods of theoretical and numerical
analysis. Numerical simulations have so far been limited to a small number of
sites, making it difficult to obtain reliable statements about the
thermodynamic limit. In this paper, we explore the ways in which a relatively
small quantum computer could be leveraged to study many-body localization. We
show that, in addition to studying time-evolution, a quantum computer can, in
polynomial time, obtain eigenstates at arbitrary energies to sufficient
accuracy that localization can be observed. The limitations of quantum
measurement, which preclude the possibility of directly obtaining the
entanglement entropy, make it difficult to apply some of the definitions of
many-body localization used in the recent literature. We discuss alternative
tests of localization that can be implemented on a quantum computer.Comment: 11 pages, 8 figures; slightly revised, published versio
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