19,380 research outputs found
Quantum computation of multifractal exponents through the quantum wavelet transform
We study the use of the quantum wavelet transform to extract efficiently
information about the multifractal exponents for multifractal quantum states.
We show that, combined with quantum simulation algorithms, it enables to build
quantum algorithms for multifractal exponents with a polynomial gain compared
to classical simulations. Numerical results indicate that a rough estimate of
fractality could be obtained exponentially fast. Our findings are relevant e.g.
for quantum simulations of multifractal quantum maps and of the Anderson model
at the metal-insulator transition.Comment: 9 pages, 9 figure
Quantum computation and analysis of Wigner and Husimi functions: toward a quantum image treatment
We study the efficiency of quantum algorithms which aim at obtaining phase
space distribution functions of quantum systems. Wigner and Husimi functions
are considered. Different quantum algorithms are envisioned to build these
functions, and compared with the classical computation. Different procedures to
extract more efficiently information from the final wave function of these
algorithms are studied, including coarse-grained measurements, amplitude
amplification and measure of wavelet-transformed wave function. The algorithms
are analyzed and numerically tested on a complex quantum system showing
different behavior depending on parameters, namely the kicked rotator. The
results for the Wigner function show in particular that the use of the quantum
wavelet transform gives a polynomial gain over classical computation. For the
Husimi distribution, the gain is much larger than for the Wigner function, and
is bigger with the help of amplitude amplification and wavelet transforms. We
also apply the same set of techniques to the analysis of real images. The
results show that the use of the quantum wavelet transform allows to lower
dramatically the number of measurements needed, but at the cost of a large loss
of information.Comment: Revtex, 13 pages, 16 figure
Simulating chemistry efficiently on fault-tolerant quantum computers
Quantum computers can in principle simulate quantum physics exponentially
faster than their classical counterparts, but some technical hurdles remain.
Here we consider methods to make proposed chemical simulation algorithms
computationally fast on fault-tolerant quantum computers in the circuit model.
Fault tolerance constrains the choice of available gates, so that arbitrary
gates required for a simulation algorithm must be constructed from sequences of
fundamental operations. We examine techniques for constructing arbitrary gates
which perform substantially faster than circuits based on the conventional
Solovay-Kitaev algorithm [C.M. Dawson and M.A. Nielsen, \emph{Quantum Inf.
Comput.}, \textbf{6}:81, 2006]. For a given approximation error ,
arbitrary single-qubit gates can be produced fault-tolerantly and using a
limited set of gates in time which is or ; with sufficient parallel preparation of ancillas, constant average
depth is possible using a method we call programmable ancilla rotations.
Moreover, we construct and analyze efficient implementations of first- and
second-quantized simulation algorithms using the fault-tolerant arbitrary gates
and other techniques, such as implementing various subroutines in constant
time. A specific example we analyze is the ground-state energy calculation for
Lithium hydride.Comment: 33 pages, 18 figure
Using Quantum Computers for Quantum Simulation
Numerical simulation of quantum systems is crucial to further our
understanding of natural phenomena. Many systems of key interest and
importance, in areas such as superconducting materials and quantum chemistry,
are thought to be described by models which we cannot solve with sufficient
accuracy, neither analytically nor numerically with classical computers. Using
a quantum computer to simulate such quantum systems has been viewed as a key
application of quantum computation from the very beginning of the field in the
1980s. Moreover, useful results beyond the reach of classical computation are
expected to be accessible with fewer than a hundred qubits, making quantum
simulation potentially one of the earliest practical applications of quantum
computers. In this paper we survey the theoretical and experimental development
of quantum simulation using quantum computers, from the first ideas to the
intense research efforts currently underway.Comment: 43 pages, 136 references, review article, v2 major revisions in
response to referee comments, v3 significant revisions, identical to
published version apart from format, ArXiv version has table of contents and
references in alphabetical orde
Introduction to Quantum Algorithms for Physics and Chemistry
In this introductory review, we focus on applications of quantum computation
to problems of interest in physics and chemistry. We describe quantum
simulation algorithms that have been developed for electronic-structure
problems, thermal-state preparation, simulation of time dynamics, adiabatic
quantum simulation, and density functional theory.Comment: 44 pages, 5 figures; comments or suggestions for improvement are
welcom
Simulating quantum field theory with a quantum computer
Forthcoming exascale digital computers will further advance our knowledge of
quantum chromodynamics, but formidable challenges will remain. In particular,
Euclidean Monte Carlo methods are not well suited for studying real-time
evolution in hadronic collisions, or the properties of hadronic matter at
nonzero temperature and chemical potential. Digital computers may never be able
to achieve accurate simulations of such phenomena in QCD and other
strongly-coupled field theories; quantum computers will do so eventually,
though I'm not sure when. Progress toward quantum simulation of quantum field
theory will require the collaborative efforts of quantumists and field
theorists, and though the physics payoff may still be far away, it's worthwhile
to get started now. Today's research can hasten the arrival of a new era in
which quantum simulation fuels rapid progress in fundamental physics.Comment: 22 pages, The 36th Annual International Symposium on Lattice Field
Theory - LATTICE201
- …