4,862 research outputs found
Relaxation due to random collisions with a many-qudit environment
We analyze the dynamics of a system qudit of dimension mu sequentially
interacting with the nu-dimensional qudits of a chain playing the ore of an
environment. Each pairwise collision has been modeled as a random unitary
transformation. The relaxation to equilibrium of the purity of the system
qudit, averaged over random collisions, is analytically computed by means of a
Markov chain approach. In particular, we show that the steady state is the one
corresponding to the steady state for random collisions with a single
environment qudit of effective dimension nu_e=nu*mu. Finally, we numerically
investigate aspects of the entanglement dynamics for qubits (mu=nu=2) and show
that random unitary collisions can create multipartite entanglement between the
system qudit and the qudits of the chain.Comment: 7 pages, 6 figure
Characterization of complex quantum dynamics with a scalable NMR information processor
We present experimental results on the measurement of fidelity decay under
contrasting system dynamics using a nuclear magnetic resonance quantum
information processor. The measurements were performed by implementing a
scalable circuit in the model of deterministic quantum computation with only
one quantum bit. The results show measurable differences between regular and
complex behaviour and for complex dynamics are faithful to the expected
theoretical decay rate. Moreover, we illustrate how the experimental method can
be seen as an efficient way for either extracting coarse-grained information
about the dynamics of a large system, or measuring the decoherence rate from
engineered environments.Comment: 4pages, 3 figures, revtex4, updated with version closer to that
publishe
Incoherent Noise and Quantum Information Processing
Incoherence in the controlled Hamiltonian is an important limitation on the
precision of coherent control in quantum information processing. Incoherence
can typically be modelled as a distribution of unitary processes arising from
slowly varying experimental parameters. We show how it introduces artifacts in
quantum process tomography and we explain how the resulting estimate of the
superoperator may not be completely positive. We then go on to attack the
inverse problem of extracting an effective distribution of unitaries that
characterizes the incoherence via a perturbation theory analysis of the
superoperator eigenvalue spectra.Comment: 15 pages, 5 figures, replaced with future JCP published versio
Efficient Symmetry Reduction and the Use of State Symmetries for Symbolic Model Checking
One technique to reduce the state-space explosion problem in temporal logic
model checking is symmetry reduction. The combination of symmetry reduction and
symbolic model checking by using BDDs suffered a long time from the
prohibitively large BDD for the orbit relation. Dynamic symmetry reduction
calculates representatives of equivalence classes of states dynamically and
thus avoids the construction of the orbit relation. In this paper, we present a
new efficient model checking algorithm based on dynamic symmetry reduction. Our
experiments show that the algorithm is very fast and allows the verification of
larger systems. We additionally implemented the use of state symmetries for
symbolic symmetry reduction. To our knowledge we are the first who investigated
state symmetries in combination with BDD based symbolic model checking
Information-theoretic equilibration: the appearance of irreversibility under complex quantum dynamics
The question of how irreversibility can emerge as a generic phenomena when
the underlying mechanical theory is reversible has been a long-standing
fundamental problem for both classical and quantum mechanics. We describe a
mechanism for the appearance of irreversibility that applies to coherent,
isolated systems in a pure quantum state. This equilibration mechanism requires
only an assumption of sufficiently complex internal dynamics and natural
information-theoretic constraints arising from the infeasibility of collecting
an astronomical amount of measurement data. Remarkably, we are able to prove
that irreversibility can be understood as typical without assuming decoherence
or restricting to coarse-grained observables, and hence occurs under distinct
conditions and time-scales than those implied by the usual decoherence point of
view. We illustrate the effect numerically in several model systems and prove
that the effect is typical under the standard random-matrix conjecture for
complex quantum systems.Comment: 15 pages, 7 figures. Discussion has been clarified and additional
numerical evidence for information theoretic equilibration is provided for a
variant of the Heisenberg model as well as one and two-dimensional random
local Hamiltonian
Four activities to promote student engagement with referencing skills
Teaching academic writing skills in a way that engages students in deep learning is difficult and there is a risk of encouraging surface learning approaches. Moreover, linking the experience of the research process to understanding the provenance of research studies is difficult for students as they tend to experience research, referencing, citing, and related areas in disparate and unconnected ways. We report our initial experiences of designing a series of four mutually supportive tutorial activities that are based on the principles of scaffolding, social interaction, and experiential learning. The aim was to help students identify suitable research material that could be used as evidence in assignments and to promote their understanding of how evidence can be used effectively, through referencing, when writing reports and essays
Four activities to promote student engagement with referencing skills
Teaching academic writing skills in a way that engages students in deep learning is difficult and there is a risk of encouraging surface learning approaches. Moreover, linking the experience of the research process to understanding the provenance of research studies is difficult for students as they tend to experience research, referencing, citing, and related areas in disparate and unconnected ways. We report our initial experiences of designing a series of four mutually supportive tutorial activities that are based on the principles of scaffolding, social interaction, and experiential learning. The aim was to help students identify suitable research material that could be used as evidence in assignments and to promote their understanding of how evidence can be used effectively, through referencing, when writing reports and essays
Quantum Process Tomography of the Quantum Fourier Transform
The results of quantum process tomography on a three-qubit nuclear magnetic
resonance quantum information processor are presented, and shown to be
consistent with a detailed model of the system-plus-apparatus used for the
experiments. The quantum operation studied was the quantum Fourier transform,
which is important in several quantum algorithms and poses a rigorous test for
the precision of our recently-developed strongly modulating control fields. The
results were analyzed in an attempt to decompose the implementation errors into
coherent (overall systematic), incoherent (microscopically deterministic), and
decoherent (microscopically random) components. This analysis yielded a
superoperator consisting of a unitary part that was strongly correlated with
the theoretically expected unitary superoperator of the quantum Fourier
transform, an overall attenuation consistent with decoherence, and a residual
portion that was not completely positive - although complete positivity is
required for any quantum operation. By comparison with the results of computer
simulations, the lack of complete positivity was shown to be largely a
consequence of the incoherent errors during the quantum process tomography
procedure. These simulations further showed that coherent, incoherent, and
decoherent errors can often be identified by their distinctive effects on the
spectrum of the overall superoperator. The gate fidelity of the experimentally
determined superoperator was 0.64, while the correlation coefficient between
experimentally determined superoperator and the simulated superoperator was
0.79; most of the discrepancies with the simulations could be explained by the
cummulative effect of small errors in the single qubit gates.Comment: 26 pages, 17 figures, four tables; in press, Journal of Chemical
Physic
On the Hybrid Extension of CTL and CTL+
The paper studies the expressivity, relative succinctness and complexity of
satisfiability for hybrid extensions of the branching-time logics CTL and CTL+
by variables. Previous complexity results show that only fragments with one
variable do have elementary complexity. It is shown that H1CTL+ and H1CTL, the
hybrid extensions with one variable of CTL+ and CTL, respectively, are
expressively equivalent but H1CTL+ is exponentially more succinct than H1CTL.
On the other hand, HCTL+, the hybrid extension of CTL with arbitrarily many
variables does not capture CTL*, as it even cannot express the simple CTL*
property EGFp. The satisfiability problem for H1CTL+ is complete for triply
exponential time, this remains true for quite weak fragments and quite strong
extensions of the logic
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