900 research outputs found
Phenomenological Study of Decoherence in Solid-State Spin Qubits due to Nuclear Spin Diffusion
We present a study of the prospects for coherence preservation in solid-state
spin qubits using dynamical decoupling protocols. Recent experiments have
provided the first demonstrations of multipulse dynamical decoupling sequences
in this qubit system, but quantitative analyses of potential coherence
improvements have been hampered by a lack of concrete knowledge of the relevant
noise processes. We present simulations of qubit coherence under the
application of arbitrary dynamical decoupling pulse sequences based on an
experimentally validated semiclassical model. This phenomenological approach
bundles the details of underlying noise processes into a single experimentally
relevant noise power spectral density. Our results show that the dominant
features of experimental measurements in a two-electron singlet-triplet spin
qubit can be replicated using a noise power spectrum associated
with nuclear-spin-flips in the host material. Beginning with this validation we
address the effects of nuclear programming, high-frequency nuclear-spin
dynamics, and other high-frequency classical noise sources, with conjectures
supported by physical arguments and microscopic calculations where relevant.
Our results provide expected performance bounds and identify diagnostic metrics
that can be measured experimentally in order to better elucidate the underlying
nuclear spin dynamics.Comment: Updated References. Related articles at:
http://www.physics.usyd.edu.au/~mbiercuk/Publications.htm
Symmetry-Enhanced Performance of Dynamical Decoupling
We consider a system with general decoherence and a quadratic dynamical
decoupling sequence (QDD) for the coherence control of a qubit coupled to a
bath of spins. We investigate the influence of the geometry and of the initial
conditions of the bath on the performance of the sequence. The overall
performance is quantified by a distance norm . It is expected that
scales with , the total duration of the sequence, as , where and are the number of pulses of the outer
and of the inner sequence, respectively. We show both numerically and
analytically that the state of the bath can boost the performance of QDD under
certain conditions: The scaling of QDD for a given number of pulses can be
enhanced by a factor of 2 if the bath is prepared in a highly symmetric state
and if the system Hamiltonian is SU(2) invariant.Comment: 9 pages, 4 figures, published versio
Concatenated Control Sequences based on Optimized Dynamic Decoupling
Two recent developments in quantum control, concatenation and optimization of
pulse intervals, are combined to yield a strategy to suppress unwanted
couplings in quantum systems to high order. Longitudinal relaxation and
transverse dephasing can be suppressed so that systems with a small splitting
between their energy levels can be kept isolated from their environment. The
required number of pulses grows exponentially with the desired order but is
only the square root of the number needed if only concatenation is used. An
approximate scheme even brings the number down to polynomial growth. The
approach is expected to be useful for quantum information and for
high-precision nuclear magnetic resonance.Comment: 4 pages, 1 figure, slightly modified incl. new abstract and title; to
appear in Phys. Rev. Let
Randomized Dynamical Decoupling Techniques for Coherent Quantum Control
The need for strategies able to accurately manipulate quantum dynamics is
ubiquitous in quantum control and quantum information processing. We
investigate two scenarios where randomized dynamical decoupling techniques
become more advantageous with respect to standard deterministic methods in
switching off unwanted dynamical evolution in a closed quantum system: when
dealing with decoupling cycles which involve a large number of control actions
and/or when seeking long-time quantum information storage. Highly effective
hybrid decoupling schemes, which combine deterministic and stochastic features
are discussed, as well as the benefits of sequentially implementing a
concatenated method, applied at short times, followed by a hybrid protocol,
employed at longer times. A quantum register consisting of a chain of spin-1/2
particles interacting via the Heisenberg interaction is used as a model for the
analysis throughout.Comment: 7 pages, 2 figures. Replaced with final version. Invited talk
delivered at the XXXVI Winter Colloquium on the Physics of Quantum
Electronics, Snowbird, Jan 2006. To be published in J. Mod. Optic
Enhanced Convergence and Robust Performance of Randomized Dynamical Decoupling
We demonstrate the advantages of randomization in coherent quantum dynamical
control. For systems which are either time-varying or require decoupling cycles
involving a large number of operations, we find that simple randomized
protocols offer superior convergence and stability as compared to deterministic
counterparts. In addition, we show how randomization always allows to
outperform purely deterministic schemes at long times, including combinatorial
and concatenated methods. General criteria for optimally interpolating between
deterministic and stochastic design are proposed and illustrated in explicit
decoupling scenarios relevant to quantum information storage.Comment: 4 pages, 3 figures, replaced with final versio
Magic composite pulses
I describe composite pulses during which the average dipolar interactions
within a spin ensemble are controlled while realizing a global rotation. The
construction method used is based on the average Hamiltonian theory and rely on
the geometrical properties of the spin-spin dipolar interaction only. I present
several such composite pulses robust against standard experimental defects in
NRM: static or radio-frequency field miscalibration, fields inhomogeneities.
Numerical simulations show that the magic sandwich pulse sequence, a pulse
sequence that reverse the average dipolar field while applied, is plagued by
defects originating from its short initial and final \pi/2 radio-frequency
pulses. Using the magic composite pulses instead of \pi/2 pulses improves the
magic sandwich effect. A numerical test using a classical description of NMR
allows to check the validity of the magic composite pulses and estimate their
efficiency.Comment: 22 pages, 6 figure
High-order noise filtering in nontrivial quantum logic gates
Treating the effects of a time-dependent classical dephasing environment
during quantum logic operations poses a theoretical challenge, as the
application of non-commuting control operations gives rise to both dephasing
and depolarization errors that must be accounted for in order to understand
total average error rates. We develop a treatment based on effective
Hamiltonian theory that allows us to efficiently model the effect of classical
noise on nontrivial single-bit quantum logic operations composed of arbitrary
control sequences. We present a general method to calculate the
ensemble-averaged entanglement fidelity to arbitrary order in terms of noise
filter functions, and provide explicit expressions to fourth order in the noise
strength. In the weak noise limit we derive explicit filter functions for a
broad class of piecewise-constant control sequences, and use them to study the
performance of dynamically corrected gates, yielding good agreement with
brute-force numerics.Comment: Revised and expanded to include filter function terms beyond first
order in the Magnus expansion. Related manuscripts available from
http://www.physics.usyd.edu.au/~mbiercu
Keeping a Quantum Bit Alive by Optimized -Pulse Sequences
A general strategy to maintain the coherence of a quantum bit is proposed.
The analytical result is derived rigorously including all memory and
back-action effects. It is based on an optimized -pulse sequence for
dynamic decoupling extending the Carr-Purcell-Meiboom-Gill (CPMG) cycle. The
optimized sequence is very efficient, in particular for strong couplings to the
environment.Comment: 4 pages, 2 figures; revised version with additional references for
better context, more stringent discussio
Exact Results on Dynamical Decoupling by -Pulses in Quantum Information Processes
The aim of dynamical decoupling consists in the suppression of decoherence by
appropriate coherent control of a quantum register. Effectively, the
interaction with the environment is reduced. In particular, a sequence of
pulses is considered. Here we present exact results on the suppression of the
coupling of a quantum bit to its environment by optimized sequences of
pulses. The effect of various cutoffs of the spectral density of the
environment is investigated. As a result we show that the harder the cutoff is
the better an optimized pulse sequence can deal with it. For cutoffs which are
neither completely hard nor very soft we advocate iterated optimized sequences.Comment: 12 pages and 3 figure
Towards optimized suppression of dephasing in systems subject to pulse timing constraints
We investigate the effectiveness of different dynamical decoupling protocols
for storage of a single qubit in the presence of a purely dephasing bosonic
bath, with emphasis on comparing quantum coherence preservation under uniform
vs. non-uniform delay times between pulses. In the limit of instantaneous
bit-flip pulses, this is accomplished by establishing a new representation of
the controlled qubit evolution, where the resulting decoherence behaviour is
directly expressed in terms of the free evolution. Simple analytical
expressions are given to approximate the long- and short- term coherence
behaviour for both ohmic and supra-ohmic environments. We focus on systems with
physical constraints on achievable time delays, with emphasis on pure dephasing
of excitonic qubits in quantum dots. Our analysis shows that little advantage
of high-level decoupling schemes based on concatenated or optimal design is to
be expected if operational constraints prevent pulses to be applied
sufficiently fast. In such constrained scenarios, we demonstrate how simple
modifications of repeated periodic echo protocols can offer significantly
improved coherence preservation in realistic parameter regimes.Comment: 13 figures,1 tabl
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