95,995 research outputs found
Efficient algorithm for multi-qudit twirling for ensemble quantum computation
We present an efficient algorithm for twirling a multi-qudit quantum state.
The algorithm can be used for approximating the twirling operation in an
ensemble of physical systems in which the systems cannot be individually
accessed. It can also be used for computing the twirled density matrix on a
classical computer. The method is based on a simple non-unitary operation
involving a random unitary. When applying this basic building block
iteratively, the mean squared error of the approximation decays exponentially.
In contrast, when averaging over random unitary matrices the error decreases
only algebraically. We present evidence that the unitaries in our algorithm can
come from a very imperfect random source or can even be chosen
deterministically from a set of cyclically alternating matrices. Based on these
ideas we present a quantum circuit realizing twirling efficiently.Comment: 11 pages including 6 figures, revtex4; v2: presentation improved,
sections VI and VII added; v3: small changes before publicatio
Perfect zero knowledge for quantum multiprover interactive proofs
In this work we consider the interplay between multiprover interactive
proofs, quantum entanglement, and zero knowledge proofs - notions that are
central pillars of complexity theory, quantum information and cryptography. In
particular, we study the relationship between the complexity class MIP, the
set of languages decidable by multiprover interactive proofs with quantumly
entangled provers, and the class PZKMIP, which is the set of languages
decidable by MIP protocols that furthermore possess the perfect zero
knowledge property.
Our main result is that the two classes are equal, i.e., MIP
PZKMIP. This result provides a quantum analogue of the celebrated result of
Ben-Or, Goldwasser, Kilian, and Wigderson (STOC 1988) who show that MIP
PZKMIP (in other words, all classical multiprover interactive protocols can be
made zero knowledge). We prove our result by showing that every MIP
protocol can be efficiently transformed into an equivalent zero knowledge
MIP protocol in a manner that preserves the completeness-soundness gap.
Combining our transformation with previous results by Slofstra (Forum of
Mathematics, Pi 2019) and Fitzsimons, Ji, Vidick and Yuen (STOC 2019), we
obtain the corollary that all co-recursively enumerable languages (which
include undecidable problems as well as all decidable problems) have zero
knowledge MIP protocols with vanishing promise gap
Recursive Estimation of Orientation Based on the Bingham Distribution
Directional estimation is a common problem in many tracking applications.
Traditional filters such as the Kalman filter perform poorly because they fail
to take the periodic nature of the problem into account. We present a recursive
filter for directional data based on the Bingham distribution in two
dimensions. The proposed filter can be applied to circular filtering problems
with 180 degree symmetry, i.e., rotations by 180 degrees cannot be
distinguished. It is easily implemented using standard numerical techniques and
suitable for real-time applications. The presented approach is extensible to
quaternions, which allow tracking arbitrary three-dimensional orientations. We
evaluate our filter in a challenging scenario and compare it to a traditional
Kalman filtering approach
ELSI: A Unified Software Interface for Kohn-Sham Electronic Structure Solvers
Solving the electronic structure from a generalized or standard eigenproblem
is often the bottleneck in large scale calculations based on Kohn-Sham
density-functional theory. This problem must be addressed by essentially all
current electronic structure codes, based on similar matrix expressions, and by
high-performance computation. We here present a unified software interface,
ELSI, to access different strategies that address the Kohn-Sham eigenvalue
problem. Currently supported algorithms include the dense generalized
eigensolver library ELPA, the orbital minimization method implemented in
libOMM, and the pole expansion and selected inversion (PEXSI) approach with
lower computational complexity for semilocal density functionals. The ELSI
interface aims to simplify the implementation and optimal use of the different
strategies, by offering (a) a unified software framework designed for the
electronic structure solvers in Kohn-Sham density-functional theory; (b)
reasonable default parameters for a chosen solver; (c) automatic conversion
between input and internal working matrix formats, and in the future (d)
recommendation of the optimal solver depending on the specific problem.
Comparative benchmarks are shown for system sizes up to 11,520 atoms (172,800
basis functions) on distributed memory supercomputing architectures.Comment: 55 pages, 14 figures, 2 table
Quantum Algorithms for Fermionic Simulations
We investigate the simulation of fermionic systems on a quantum computer. We
show in detail how quantum computers avoid the dynamical sign problem present
in classical simulations of these systems, therefore reducing a problem
believed to be of exponential complexity into one of polynomial complexity. The
key to our demonstration is the spin-particle connection (or generalized
Jordan-Wigner transformation) that allows exact algebraic invertible mappings
of operators with different statistical properties. We give an explicit
implementation of a simple problem using a quantum computer based on standard
qubits.Comment: 38 pages, 2 psfigur
A Sparse SCF algorithm and its parallel implementation: Application to DFTB
We present an algorithm and its parallel implementation for solving a self
consistent problem as encountered in Hartree Fock or Density Functional Theory.
The algorithm takes advantage of the sparsity of matrices through the use of
local molecular orbitals. The implementation allows to exploit efficiently
modern symmetric multiprocessing (SMP) computer architectures. As a first
application, the algorithm is used within the density functional based tight
binding method, for which most of the computational time is spent in the linear
algebra routines (diagonalization of the Fock/Kohn-Sham matrix). We show that
with this algorithm (i) single point calculations on very large systems
(millions of atoms) can be performed on large SMP machines (ii) calculations
involving intermediate size systems (1~000--100~000 atoms) are also strongly
accelerated and can run efficiently on standard servers (iii) the error on the
total energy due to the use of a cut-off in the molecular orbital coefficients
can be controlled such that it remains smaller than the SCF convergence
criterion.Comment: 13 pages, 11 figure
TVL<sub>1</sub> Planarity Regularization for 3D Shape Approximation
The modern emergence of automation in many industries has given impetus to extensive research into mobile robotics. Novel perception technologies now enable cars to drive autonomously, tractors to till a field automatically and underwater robots to construct pipelines. An essential requirement to facilitate both perception and autonomous navigation is the analysis of the 3D environment using sensors like laser scanners or stereo cameras. 3D sensors generate a very large number of 3D data points when sampling object shapes within an environment, but crucially do not provide any intrinsic information about the environment which the robots operate within.
This work focuses on the fundamental task of 3D shape reconstruction and modelling from 3D point clouds. The novelty lies in the representation of surfaces by algebraic functions having limited support, which enables the extraction of smooth consistent implicit shapes from noisy samples with a heterogeneous density. The minimization of total variation of second differential degree makes it possible to enforce planar surfaces which often occur in man-made environments. Applying the new technique means that less accurate, low-cost 3D sensors can be employed without sacrificing the 3D shape reconstruction accuracy
Robust control of decoherence in realistic one-qubit quantum gates
We present an open loop (bang-bang) scheme to control decoherence in a
generic one-qubit quantum gate and implement it in a realistic simulation. The
system is consistently described within the spin-boson model, with interactions
accounting for both adiabatic and thermal decoherence. The external control is
included from the beginning in the Hamiltonian as an independent interaction
term. After tracing out the environment modes, reduced equations are obtained
for the two-level system in which the effects of both decoherence and external
control appear explicitly. The controls are determined exactly from the
condition to eliminate decoherence, i.e. to restore unitarity. Numerical
simulations show excellent performance and robustness of the proposed control
scheme.Comment: 21 pages, 8 figures, VIth International Conference on Quantum
Communication, Measurement and Computing (Boston, 2002
- âŠ