402,940 research outputs found
Faster Coherent Quantum Algorithms for Phase, Energy, and Amplitude Estimation
We consider performing phase estimation under the following conditions: we
are given only one copy of the input state, the input state does not have to be
an eigenstate of the unitary, and the state must not be measured. Most quantum
estimation algorithms make assumptions that make them unsuitable for this
'coherent' setting, leaving only the textbook approach. We present novel
algorithms for phase, energy, and amplitude estimation that are both
conceptually and computationally simpler than the textbook method, featuring
both a smaller query complexity and ancilla footprint. They do not require a
quantum Fourier transform, and they do not require a quantum sorting network to
compute the median of several estimates. Instead, they use block-encoding
techniques to compute the estimate one bit at a time, performing all
amplification via singular value transformation. These improved subroutines
accelerate the performance of quantum Metropolis sampling and quantum Bayesian
inference.Comment: Accepted in Quantum. The algorithms were modified to work decently
well even without a rounding promis
PhasePack: A Phase Retrieval Library
Phase retrieval deals with the estimation of complex-valued signals solely
from the magnitudes of linear measurements. While there has been a recent
explosion in the development of phase retrieval algorithms, the lack of a
common interface has made it difficult to compare new methods against the
state-of-the-art. The purpose of PhasePack is to create a common software
interface for a wide range of phase retrieval algorithms and to provide a
common testbed using both synthetic data and empirical imaging datasets.
PhasePack is able to benchmark a large number of recent phase retrieval methods
against one another to generate comparisons using a range of different
performance metrics. The software package handles single method testing as well
as multiple method comparisons.
The algorithm implementations in PhasePack differ slightly from their
original descriptions in the literature in order to achieve faster speed and
improved robustness. In particular, PhasePack uses adaptive stepsizes,
line-search methods, and fast eigensolvers to speed up and automate
convergence
Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography
By 'atmospheric tomography' we mean the estimation of a layered atmospheric turbulence profile from measurements of the pupil-plane phase (or phase gradients) corresponding to several different guide star directions. We introduce what we believe to be a new Fourier domain preconditioned conjugate gradient (FD-PCG) algorithm for atmospheric tomography, and we compare its performance against an existing multigrid preconditioned conjugate gradient (MG-PCG) approach. Numerical results indicate that on conventional serial computers, FD-PCG is as accurate and robust as MG-PCG, but it is from one to two orders of magnitude faster for atmospheric tomography on 30 m class telescopes. Simulations are carried out for both natural guide stars and for a combination of finite-altitude laser guide stars and natural guide stars to resolve tip-tilt uncertainty
Calculating Unknown Eigenvalues with a Quantum Algorithm
Quantum algorithms are able to solve particular problems exponentially faster
than conventional algorithms, when implemented on a quantum computer. However,
all demonstrations to date have required already knowing the answer to
construct the algorithm. We have implemented the complete quantum phase
estimation algorithm for a single qubit unitary in which the answer is
calculated by the algorithm. We use a new approach to implementing the
controlled-unitary operations that lie at the heart of the majority of quantum
algorithms that is more efficient and does not require the eigenvalues of the
unitary to be known. These results point the way to efficient quantum
simulations and quantum metrology applications in the near term, and to
factoring large numbers in the longer term. This approach is architecture
independent and thus can be used in other physical implementations
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