36,570 research outputs found
Resource Evaluation of Quantum Linear Systems Algorithm for Application to Electromagnetic Scattering Problems
Current limitations in quantum computing technology does not allow for very large applications of quantum algorithms, and it is the nature of quantum algorithms not only to be able to solve problems of interest much more quickly than classical means but also to do so with less resources which makes them so promising! One such problem of interest is the application of the Quantum Linear Systems Algorithm, along with a few other subroutines, to the calculation of an electromagnetic scattering cross-section via finite element methods. This work composes a resource analysis of the algorithm as well as required subroutines and details the primary contributors to the resources involved as well as methods to decrease these resource requirements
Quantum Resources in Harrow-Hassidim-Lloyd Algorithm
Quantum algorithms have the ability to reduce runtime for executing tasks
beyond the capabilities of classical algorithms. Therefore, identifying the
resources responsible for quantum advantages is an interesting endeavour. We
prove that nonvanishing quantum correlations, both bipartite and genuine
multipartite entanglement, are required for solving nontrivial linear systems
of equations in the Harrow-Hassidim-Lloyd (HHL) algorithm. Moreover, we find a
nonvanishing l1-norm quantum coherence of the entire system and the register
qubit which turns out to be related to the success probability of the
algorithm. Quantitative analysis of the quantum resources reveals that while a
significant amount of bipartite entanglement is generated in each step and
required for this algorithm, multipartite entanglement content is inversely
proportional to the performance indicator. In addition, we report that when
imperfections chosen from Gaussian distribution are incorporated in controlled
rotations, multipartite entanglement increases with the strength of the
disorder, albeit error also increases while bipartite entanglement and
coherence decreases, confirming the beneficial role of bipartite entanglement
and coherence in this algorithm.Comment: 11 pages, 8 figure
Quantum machine learning: a classical perspective
Recently, increased computational power and data availability, as well as
algorithmic advances, have led machine learning techniques to impressive
results in regression, classification, data-generation and reinforcement
learning tasks. Despite these successes, the proximity to the physical limits
of chip fabrication alongside the increasing size of datasets are motivating a
growing number of researchers to explore the possibility of harnessing the
power of quantum computation to speed-up classical machine learning algorithms.
Here we review the literature in quantum machine learning and discuss
perspectives for a mixed readership of classical machine learning and quantum
computation experts. Particular emphasis will be placed on clarifying the
limitations of quantum algorithms, how they compare with their best classical
counterparts and why quantum resources are expected to provide advantages for
learning problems. Learning in the presence of noise and certain
computationally hard problems in machine learning are identified as promising
directions for the field. Practical questions, like how to upload classical
data into quantum form, will also be addressed.Comment: v3 33 pages; typos corrected and references adde
Climbing Mount Scalable: Physical-Resource Requirements for a Scalable Quantum Computer
The primary resource for quantum computation is Hilbert-space dimension.
Whereas Hilbert space itself is an abstract construction, the number of
dimensions available to a system is a physical quantity that requires physical
resources. Avoiding a demand for an exponential amount of these resources
places a fundamental constraint on the systems that are suitable for scalable
quantum computation. To be scalable, the effective number of degrees of freedom
in the computer must grow nearly linearly with the number of qubits in an
equivalent qubit-based quantum computer.Comment: LATEX, 24 pages, 1 color .eps figure. This new version has been
accepted for publication in Foundations of Physic
Efficient Quantum Algorithms for State Measurement and Linear Algebra Applications
We present an algorithm for measurement of -local operators in a quantum
state, which scales logarithmically both in the system size and the output
accuracy. The key ingredients of the algorithm are a digital representation of
the quantum state, and a decomposition of the measurement operator in a basis
of operators with known discrete spectra. We then show how this algorithm can
be combined with (a) Hamiltonian evolution to make quantum simulations
efficient, (b) the Newton-Raphson method based solution of matrix inverse to
efficiently solve linear simultaneous equations, and (c) Chebyshev expansion of
matrix exponentials to efficiently evaluate thermal expectation values. The
general strategy may be useful in solving many other linear algebra problems
efficiently.Comment: 17 pages, 3 figures (v2) Sections reorganised, several clarifications
added, results unchange
Concrete resource analysis of the quantum linear system algorithm used to compute the electromagnetic scattering cross section of a 2D target
We provide a detailed estimate for the logical resource requirements of the
quantum linear system algorithm (QLSA) [Phys. Rev. Lett. 103, 150502 (2009)]
including the recently described elaborations [Phys. Rev. Lett. 110, 250504
(2013)]. Our resource estimates are based on the standard quantum-circuit model
of quantum computation; they comprise circuit width, circuit depth, the number
of qubits and ancilla qubits employed, and the overall number of elementary
quantum gate operations as well as more specific gate counts for each
elementary fault-tolerant gate from the standard set {X, Y, Z, H, S, T, CNOT}.
To perform these estimates, we used an approach that combines manual analysis
with automated estimates generated via the Quipper quantum programming language
and compiler. Our estimates pertain to the example problem size N=332,020,680
beyond which, according to a crude big-O complexity comparison, QLSA is
expected to run faster than the best known classical linear-system solving
algorithm. For this problem size, a desired calculation accuracy 0.01 requires
an approximate circuit width 340 and circuit depth of order if oracle
costs are excluded, and a circuit width and depth of order and
, respectively, if oracle costs are included, indicating that the
commonly ignored oracle resources are considerable. In addition to providing
detailed logical resource estimates, it is also the purpose of this paper to
demonstrate explicitly how these impressively large numbers arise with an
actual circuit implementation of a quantum algorithm. While our estimates may
prove to be conservative as more efficient advanced quantum-computation
techniques are developed, they nevertheless provide a valid baseline for
research targeting a reduction of the resource requirements, implying that a
reduction by many orders of magnitude is necessary for the algorithm to become
practical.Comment: 37 pages, 40 figure
Introduction to Quantum Information Processing
As a result of the capabilities of quantum information, the science of
quantum information processing is now a prospering, interdisciplinary field
focused on better understanding the possibilities and limitations of the
underlying theory, on developing new applications of quantum information and on
physically realizing controllable quantum devices. The purpose of this primer
is to provide an elementary introduction to quantum information processing, and
then to briefly explain how we hope to exploit the advantages of quantum
information. These two sections can be read independently. For reference, we
have included a glossary of the main terms of quantum information.Comment: 48 pages, to appear in LA Science. Hyperlinked PDF at
http://www.c3.lanl.gov/~knill/qip/prhtml/prpdf.pdf, HTML at
http://www.c3.lanl.gov/~knill/qip/prhtm
Simple digital quantum algorithm for symmetric first order linear hyperbolic systems
This paper is devoted to the derivation of a digital quantum algorithm for
the Cauchy problem for symmetric first order linear hyperbolic systems, thanks
to the reservoir technique. The reservoir technique is a method designed to
avoid artificial diffusion generated by first order finite volume methods
approximating hyperbolic systems of conservation laws. For some class of
hyperbolic systems, namely those with constant matrices in several dimensions,
we show that the combination of i) the reservoir method and ii) the alternate
direction iteration operator splitting approximation, allows for the derivation
of algorithms only based on simple unitary transformations, thus perfectly
suitable for an implementation on a quantum computer. The same approach can
also be adapted to scalar one-dimensional systems with non-constant velocity by
combining with a non-uniform mesh. The asymptotic computational complexity for
the time evolution is determined and it is demonstrated that the quantum
algorithm is more efficient than the classical version. However, in the quantum
case, the solution is encoded in probability amplitudes of the quantum
register. As a consequence, as with other similar quantum algorithms, a
post-processing mechanism has to be used to obtain general properties of the
solution because a direct reading cannot be performed as efficiently as the
time evolution.Comment: 28 pages, 12 figures, major rewriting of the section describing the
numerical method, simplified the presentation and notation, reorganized the
sections, comments are welcome
- …