74 research outputs found
Quantum Zeno Effect in the Decoherent Histories
The quantum Zeno effect arises due to frequent observation. That implies the
existence of some experimenter and its interaction with the system. In this
contribution, we examine what happens for a closed system if one considers a
quantum Zeno type of question, namely: "what is the probability of a system,
remaining always in a particular subspace". This has implications to the
arrival time problem that is also discussed. We employ the decoherent histories
approach to quantum theory, as this is the better developed formulation of
closed system quantum mechanics, and in particular, dealing with questions that
involve time in a non-trivial way. We get a very restrictive decoherence
condition, that implies that even if we do introduce an environment, there will
be very few cases that we can assign probabilities to these histories, but in
those cases, the quantum Zeno effect is still present.Comment: 7 pages, To appear in DICE 2006 (Decoherence Information Complexity
and Entropy) conference proceeding
Quantum Zeno Effect in the Decoherent Histories
The quantum Zeno effect arises due to frequent observation. That implies the
existence of some experimenter and its interaction with the system. In this
contribution, we examine what happens for a closed system if one considers a
quantum Zeno type of question, namely: "what is the probability of a system,
remaining always in a particular subspace". This has implications to the
arrival time problem that is also discussed. We employ the decoherent histories
approach to quantum theory, as this is the better developed formulation of
closed system quantum mechanics, and in particular, dealing with questions that
involve time in a non-trivial way. We get a very restrictive decoherence
condition, that implies that even if we do introduce an environment, there will
be very few cases that we can assign probabilities to these histories, but in
those cases, the quantum Zeno effect is still present.Comment: 7 pages, To appear in DICE 2006 (Decoherence Information Complexity
and Entropy) conference proceeding
Evolving objective function for improved variational quantum optimization
A promising approach to useful computational quantum advantage is to use
variational quantum algorithms for optimisation problems. Crucial for the
performance of these algorithms is to ensure that the algorithm converges with
high probability to a near-optimal solution in a small time. In Barkoutsos et
al (Quantum 2020) an alternative class of objective functions, called
Conditional Value-at-Risk (CVaR), was introduced and it was shown that they
perform better than standard objective functions. Here we extend that work by
introducing an evolving objective function, which we call Ascending-CVaR and
that can be used for any optimisation problem. We test our proposed objective
function, in an emulation environment, using as case-studies three different
optimisation problems: Max-Cut, Number Partitioning and Portfolio Optimisation.
We examine multiple instances of different sizes and analyse the performance
using the Variational Quantum Eigensolver (VQE) with hardware-efficient ansatz
and the Quantum Approximate Optimization Algorithm (QAOA). We show that
Ascending-CVaR in all cases performs better than standard objective functions
or the "constant" CVaR of Barkoutsos et al (Quantum 2020) and that it can be
used as a heuristic for avoiding sub-optimal minima. Our proposal achieves
higher overlap with the ideal state in all problems, whether we consider easy
or hard instances -- on average it gives up to ten times greater overlap at
Portfolio Optimisation and Number Partitioning, while it gives an 80%
improvement at Max-Cut. In the hard instances we consider, for the number
partitioning problem, standard objective functions fail to find the correct
solution in almost all cases, CVaR finds the correct solution at 60% of the
cases, while Ascending-CVaR finds the correct solution in 95% of the cases.Comment: 20 pages, 13 figures; v3 published versio
Quantum Zeno effect in the decoherent histories
The quantum Zeno effect arises due to frequent observation. That implies the
existence of some experimenter and its interaction with the system. In this
contribution, we examine what happens for a closed system if one considers a
quantum Zeno type of question, namely: "what is the probability of a system,
remaining always in a particular subspace". This has implications to the
arrival time problem that is also discussed. We employ the decoherent histories
approach to quantum theory, as this is the better developed formulation of
closed system quantum mechanics, and in particular, dealing with questions that
involve time in a non-trivial way. We get a very restrictive decoherence
condition, that implies that even if we do introduce an environment, there will
be very few cases that we can assign probabilities to these histories, but in
those cases, the quantum Zeno effect is still present.Comment: 7 pages, To appear in DICE 2006 (Decoherence Information Complexity
and Entropy) conference proceeding
Practical parallel self-testing of Bell states via magic rectangles
Self-testing is a method to verify that one has a particular quantum state
from purely classical statistics. For practical applications, such as
device-independent delegated verifiable quantum computation, it is crucial that
one self-tests multiple Bell states in parallel while keeping the quantum
capabilities required of one side to a minimum. In this work, we use the magic rectangle games (generalizations of the magic square game) to
obtain a self-test for Bell states where the one side needs only to measure
single-qubit Pauli observables. The protocol requires small input sizes
(constant for Alice and bits for Bob) and is robust with robustness
, where is the closeness of the
ideal (perfect) correlations to those observed. To achieve the desired
self-test we introduce a one-side-local quantum strategy for the magic square
game that wins with certainty, generalize this strategy to the family of magic rectangle games, and supplement these nonlocal games with extra
check rounds (of single and pairs of observables).Comment: 29 pages, 6 figures; v3 minor corrections and changes in response to
comment
Reasoning in Quantum Theory: Modus Ponens and the co-event interpretation
Classical logic does not apply in quantum theory. However one would like
to be able to reason according to some standard rules, for quantum
systems as well (whether they are an electron or the universe itself).
We examine what exactly is needed in order to be able to construct
deductive arguments, and in particular to maintain the “Modus
Ponens”, which is the basic deductive rule of inference. It turns out
that this requirement restricts the possible theories and in the context
of the coevent interpretation, it results uniquely to the
“multiplicative-scheme”
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