21 research outputs found
Qubit flip game on a Heisenberg spin chain
We study a quantum version of a penny flip game played using control
parameters of the Hamiltonian in the Heisenberg model. Moreover, we extend this
game by introducing auxiliary spins which can be used to alter the behaviour of
the system. We show that a player aware of the complex structure of the system
used to implement the game can use this knowledge to gain higher mean payoff.Comment: 13 pages, 3 figures, 3 table
Simulations of quantum systems evolution with quantum-octave package
Article presents package of functions for GNU Octave computer algebra system. Those functions were designed to perform simple but not necessary efficient simulations of quantum systems, especially quantum computers. The most important feature of this package is the ability to perform calculations with mixed states.We describe application of quantum-octave package for simulation of Grovers algorithm, which is one of the most important quantum algorithms. We also list other possible calculations, which can be performed with this package
Noise Effects in Quantum Magic Squares Game
In the article we analyse how noisiness of quantum channels can influence the
magic squares quantum pseudo-telepathy game. We show that the probability of
success can be used to determine characteristics of quantum channels. Therefore
the game deserves more careful study aiming at its implementation.Comment: 5 figure
Numerical shadow and geometry of quantum states
The totality of normalised density matrices of order N forms a convex set Q_N
in R^(N^2-1). Working with the flat geometry induced by the Hilbert-Schmidt
distance we consider images of orthogonal projections of Q_N onto a two-plane
and show that they are similar to the numerical ranges of matrices of order N.
For a matrix A of a order N one defines its numerical shadow as a probability
distribution supported on its numerical range W(A), induced by the unitarily
invariant Fubini-Study measure on the complex projective manifold CP^(N-1). We
define generalized, mixed-states shadows of A and demonstrate their usefulness
to analyse the structure of the set of quantum states and unitary dynamics
therein.Comment: 19 pages, 5 figure
Computer Vision based inspection on post-earthquake with UAV synthetic dataset
The area affected by the earthquake is vast and often difficult to entirely
cover, and the earthquake itself is a sudden event that causes multiple defects
simultaneously, that cannot be effectively traced using traditional, manual
methods. This article presents an innovative approach to the problem of
detecting damage after sudden events by using an interconnected set of deep
machine learning models organized in a single pipeline and allowing for easy
modification and swapping models seamlessly. Models in the pipeline were
trained with a synthetic dataset and were adapted to be further evaluated and
used with unmanned aerial vehicles (UAVs) in real-world conditions. Thanks to
the methods presented in the article, it is possible to obtain high accuracy in
detecting buildings defects, segmenting constructions into their components and
estimating their technical condition based on a single drone flight.Comment: 15 pages, 8 figures, published version, software available from
https://github.com/MatZar01/IC_SHM_P
Restricted numerical shadow and geometry of quantum entanglement
The restricted numerical range of an operator acting on a
-dimensional Hilbert space is defined as a set of all possible expectation
values of this operator among pure states which belong to a certain subset
of the of set of pure quantum states of dimension . One considers for
instance the set of real states, or in the case of composite spaces, the set of
product states and the set of maximally entangled states. Combining the
operator theory with a probabilistic approach we introduce the restricted
numerical shadow of -- a normalized probability distribution on the complex
plane supported in . Its value at point z \in {\mathbbm C} is equal
to the probability that the expectation value is equal to ,
where represents a random quantum state in subset distributed
according to the natural measure on this set, induced by the unitarily
invariant Fubini--Study measure. Studying restricted shadows of operators of a
fixed size we analyse the geometry of sets of separable and
maximally entangled states of the composite quantum system.
Investigating trajectories formed by evolving quantum states projected into the
plane of the shadow we study the dynamics of quantum entanglement. A similar
analysis extended for operators on dimensional Hilbert space allows us
to investigate the structure of the orbits of and quantum states of a
three--qubit system.Comment: 33 pages, 8 figures, IOP styl
Enhancing variational quantum state diagonalization using reinforcement learning techniques
The development of variational quantum algorithms is crucial for the
application of NISQ computers. Such algorithms require short quantum circuits,
which are more amenable to implementation on near-term hardware, and many such
methods have been developed. One of particular interest is the so-called the
variational diagonalization method, which constitutes an important algorithmic
subroutine, and it can be used directly for working with data encoded in
quantum states. In particular, it can be applied to discern the features of
quantum states, such as entanglement properties of a system, or in quantum
machine learning algorithms. In this work, we tackle the problem of designing a
very shallow quantum circuit, required in the quantum state diagonalization
task, by utilizing reinforcement learning. To achieve this, we utilize a novel
encoding method that can be used to tackle the problem of circuit depth
optimization using a reinforcement learning approach. We demonstrate that our
approach provides a solid approximation to the diagonalization task while using
a small number of gates. The circuits proposed by the reinforcement learning
methods are shallower than the standard variational quantum state
diagonalization algorithm, and thus can be used in situations where the depth
of quantum circuits is limited by the hardware capabilities.Comment: 17 pages with 13 figures, some minor, important improvements, code
available at https://github.com/iitis/RL_for_VQSD_ansatz_optimizatio
Singular value decomposition and matrix reorderings in quantum information theory
We review Schmidt and Kraus decompositions in the form of singular value
decomposition using operations of reshaping, vectorization and reshuffling. We
use the introduced notation to analyse the correspondence between quantum
states and operations with the help of Jamiolkowski isomorphism. The presented
matrix reorderings allow us to obtain simple formulae for the composition of
quantum channels and partial operations used in quantum information theory. To
provide examples of the discussed operations we utilize a package for the
Mathematica computing system implementing basic functions used in the
calculations related to quantum information theory.Comment: 11 pages, no figures, see
http://zksi.iitis.pl/wiki/projects:mathematica-qi for related softwar
Experimentally feasible measures of distance between quantum operations
We present two measures of distance between quantum processes based on the
superfidelity, introduced recently to provide an upper bound for quantum
fidelity. We show that the introduced measures partially fulfill the
requirements for distance measure between quantum processes. We also argue that
they can be especially useful as diagnostic measures to get preliminary
knowledge about imperfections in an experimental setup. In particular we
provide quantum circuit which can be used to measure the superfidelity between
quantum processes.
As the behavior of the superfidelity between quantum processes is crucial for
the properties of the introduced measures, we study its behavior for several
families of quantum channels. We calculate superfidelity between arbitrary
one-qubit channels using affine parametrization and superfidelity between
generalized Pauli channels in arbitrary dimensions. Statistical behavior of the
proposed quantities for the ensembles of quantum operations in low dimensions
indicates that the proposed measures can be indeed used to distinguish quantum
processes.Comment: 9 pages, 4 figure
Quantum state discrimination: a geometric approach
We analyse the problem of finding sets of quantum states that can be
deterministically discriminated. From a geometric point of view this problem is
equivalent to that of embedding a simplex of points whose distances are maximal
with respect to the Bures distance (or trace distance). We derive upper and
lower bounds for the trace distance and for the fidelity between two quantum
states, which imply bounds for the Bures distance between the unitary orbits of
both states. We thus show that when analysing minimal and maximal distances
between states of fixed spectra it is sufficient to consider diagonal states
only. Hence considering optimal discrimination, given freedom up to unitary
orbits, it is sufficient to consider diagonal states. This is illustrated
geometrically in terms of Weyl chambers.Comment: 12 pages, 2 figure