1,606 research outputs found
The computational complexity of density functional theory
Density functional theory is a successful branch of numerical simulations of
quantum systems. While the foundations are rigorously defined, the universal
functional must be approximated resulting in a `semi'-ab initio approach. The
search for improved functionals has resulted in hundreds of functionals and
remains an active research area. This chapter is concerned with understanding
fundamental limitations of any algorithmic approach to approximating the
universal functional. The results based on Hamiltonian complexity presented
here are largely based on \cite{Schuch09}. In this chapter, we explain the
computational complexity of DFT and any other approach to solving electronic
structure Hamiltonians. The proof relies on perturbative gadgets widely used in
Hamiltonian complexity and we provide an introduction to these techniques using
the Schrieffer-Wolff method. Since the difficulty of this problem has been well
appreciated before this formalization, practitioners have turned to a host
approximate Hamiltonians. By extending the results of \cite{Schuch09}, we show
in DFT, although the introduction of an approximate potential leads to a
non-interacting Hamiltonian, it remains, in the worst case, an NP-complete
problem.Comment: Contributed chapter to "Many-Electron Approaches in Physics,
Chemistry and Mathematics: A Multidisciplinary View
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
Simulating chemistry using quantum computers
The difficulty of simulating quantum systems, well-known to quantum chemists,
prompted the idea of quantum computation. One can avoid the steep scaling
associated with the exact simulation of increasingly large quantum systems on
conventional computers, by mapping the quantum system to another, more
controllable one. In this review, we discuss to what extent the ideas in
quantum computation, now a well-established field, have been applied to
chemical problems. We describe algorithms that achieve significant advantages
for the electronic-structure problem, the simulation of chemical dynamics,
protein folding, and other tasks. Although theory is still ahead of experiment,
we outline recent advances that have led to the first chemical calculations on
small quantum information processors.Comment: 27 pages. Submitted to Ann. Rev. Phys. Che
The SLH framework for modeling quantum input-output networks
Many emerging quantum technologies demand precise engineering and control
over networks consisting of quantum mechanical degrees of freedom connected by
propagating electromagnetic fields, or quantum input-output networks. Here we
review recent progress in theory and experiment related to such quantum
input-output networks, with a focus on the SLH framework, a powerful modeling
framework for networked quantum systems that is naturally endowed with
properties such as modularity and hierarchy. We begin by explaining the
physical approximations required to represent any individual node of a network,
eg. atoms in cavity or a mechanical oscillator, and its coupling to quantum
fields by an operator triple . Then we explain how these nodes can be
composed into a network with arbitrary connectivity, including coherent
feedback channels, using algebraic rules, and how to derive the dynamics of
network components and output fields. The second part of the review discusses
several extensions to the basic SLH framework that expand its modeling
capabilities, and the prospects for modeling integrated implementations of
quantum input-output networks. In addition to summarizing major results and
recent literature, we discuss the potential applications and limitations of the
SLH framework and quantum input-output networks, with the intention of
providing context to a reader unfamiliar with the field.Comment: 60 pages, 14 figures. We are still interested in receiving
correction
Quantum computing modelling on field programmable gate array based on state vector and heisenberg models
As current trend of miniaturization in computing technology continues, modern computing devices would start to exhibit the behaviour of nanoscopic quantum objects. Quantum computing, which is based on the principles of quantum mechanics, becomes a promising candidate for future generation computing system. However, modelling quantum computing systems on existing classical computing platforms before the realization of viable large-scale quantum computer remains a major challenge. The exploration on the modelling of quantum computing systems on field programmable gate array (FPGA) platform, which offers the potential of massive parallelism and allows computational optimization at register-transfer level, is crucial. Due to the exponential growth of resource utilization with the increase in the number of quantum bits (qubit), existing works on modelling of quantum systems on FPGA platform are restricted to simple case studies using small qubit sizes. This work explores the modelling of quantum computing for emulation on FPGA platform based on two types of data structure: (a) state vector model and (b) Heisenberg model. For the conventional state vector modelling approach, an efficient datapath design that is based on serial-parallel hardware architecture, which allows resource sharing between unitary transformations, is proposed. Heisenberg model has been proven to be efficient in modelling stabilizer circuits, which are critical in error correction operations. In the effort to include the consideration of vital quantum error correction in practical quantum systems, a novel FPGA emulation framework that is based on the Heisenberg model is proposed. Effective algorithms for accurate global phase maintenance are proposed to facilitate the modelling of quantum systems based on the Heisenberg representation. The feasibility of the proposed state vector and Heisenberg emulation models are demonstrated based on a number of case studies with different characteristics, which include quantum Fourier transform, Grover’s search algorithm, and stabilizer circuits. Based on the state vector approach, this work has demonstrated the advantage of FPGA emulation over software simulation where hardware emulation of 7-qubit Grover’s search is about 3 × 104 times faster than the software simulation performed on Intel Core i7-4790 processor running at 3.6GHz clock rate. In contrast to the 8-qubit implementation based on the state vector model, the proposed FPGA emulation framework based on the Heisenberg model has successfully modelled 120-qubit stabilizer circuits on the Altera Stratix IV FPGA. In summary, the proposed work in this thesis contributes to the formulation of a proof-of-concept of efficient FPGA emulation framework based on the state vector and Heisenberg models
An Overview of Concepts and Applications of Fintech with Emphasis on Simulation and Artificial Intelligence
This paper discusses the Concepts and Applications of Fintech with emphasis on Simulation and Artificial intelligence for Optimization of the Financial outputs. The true amalgamation of the two topics (Finance and Technology) has taken place to give rise to Fintech, a topic which is evolving very fast in recent times. This paper is expected to be very useful for the researchers and managers engaged in this important field
Proposal for Quantum Simulation via All-Optically Generated Tensor Network States
We devise an all-optical scheme for the generation of entangled multimode
photonic states encoded in temporal modes of light. The scheme employs a
nonlinear down-conversion process in an optical loop to generate one- and
higher-dimensional tensor network states of light. We illustrate the principle
with the generation of two different classes of entangled tensor network states
and report on a variational algorithm to simulate the ground-state physics of
many-body systems. We demonstrate that state-of-the-art optical devices are
capable of determining the ground-state properties of the spin-1/2 Heisenberg
model. Finally, implementations of the scheme are demonstrated to be robust
against realistic losses and mode mismatch.Comment: 6 pages main text plus 6 pages Supplementary Material and many
figures. Updated to published version. Comments welcom
Quantum metrology and its application in biology
Quantum metrology provides a route to overcome practical limits in sensing
devices. It holds particular relevance to biology, where sensitivity and
resolution constraints restrict applications both in fundamental biophysics and
in medicine. Here, we review quantum metrology from this biological context,
focusing on optical techniques due to their particular relevance for biological
imaging, sensing, and stimulation. Our understanding of quantum mechanics has
already enabled important applications in biology, including positron emission
tomography (PET) with entangled photons, magnetic resonance imaging (MRI) using
nuclear magnetic resonance, and bio-magnetic imaging with superconducting
quantum interference devices (SQUIDs). In quantum metrology an even greater
range of applications arise from the ability to not just understand, but to
engineer, coherence and correlations at the quantum level. In the past few
years, quite dramatic progress has been seen in applying these ideas into
biological systems. Capabilities that have been demonstrated include enhanced
sensitivity and resolution, immunity to imaging artifacts and technical noise,
and characterization of the biological response to light at the single-photon
level. New quantum measurement techniques offer even greater promise, raising
the prospect for improved multi-photon microscopy and magnetic imaging, among
many other possible applications. Realization of this potential will require
cross-disciplinary input from researchers in both biology and quantum physics.
In this review we seek to communicate the developments of quantum metrology in
a way that is accessible to biologists and biophysicists, while providing
sufficient detail to allow the interested reader to obtain a solid
understanding of the field. We further seek to introduce quantum physicists to
some of the central challenges of optical measurements in biological science.Comment: Submitted review article, comments and suggestions welcom
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