62 research outputs found
Decoherence Rate of Semiconductor Charge Qubit Coupled to Acoustic Phonon Reservoir
We analyze decoherence of an electron in a double-dot due to the interaction
with acoustic phonons. For large tunneling rates between the quantum dots, the
main contribution to decoherence comes from the phonon emission relaxation
processes, while for small tunneling rates, the virtual-phonon, dephasing
processes dominate. Our results show that in common semiconductors, such as Si
and GaAs, the latter mechanism determines the upper limit for the double-dot
charge qubit performance measure.Comment: 4 pages, 2 figures, typos corrected, fig. 2 replaced by the improved
versio
Relaxation and Zeno effect in qubit measurements
We consider a qubit interacting with its environment and continuously
monitored by a detector represented by a point contact. Bloch-type equations
describing the entire system of the qubit, the environment and the detector are
derived. Using these equations we evaluate the detector current and its noise
spectrum in terms of the decoherence and relaxation rates of the qubit. Simple
expressions are obtained that show how these quantities can be accurately
measured. We demonstrate that due to interaction with the environment, the
measurement can never localize a qubit even for infinite decoherence rate.Comment: some clarifications added, to appear in Phys. Rev. Let
Decoherence and Quantum Walks: anomalous diffusion and ballistic tails
The common perception is that strong coupling to the environment will always
render the evolution of the system density matrix quasi-classical (in fact,
diffusive) in the long time limit. We present here a counter-example, in which
a particle makes quantum transitions between the sites of a d-dimensional
hypercubic lattice whilst strongly coupled to a bath of two-level systems which
'record' the transitions. The long-time evolution of an initial wave packet
is found to be most unusual: the mean square displacement of the particle
density matrix shows long-range ballitic behaviour, but simultaneously a kind
of weakly-localised behaviour near the origin. This result may have important
implications for the design of quantum computing algorithms, since it describes
a class of quantum walks.Comment: 4 pages, 1 figur
Quantum speedup of classical mixing processes
Most approximation algorithms for #P-complete problems (e.g., evaluating the
permanent of a matrix or the volume of a polytope) work by reduction to the
problem of approximate sampling from a distribution over a large set
. This problem is solved using the {\em Markov chain Monte Carlo} method: a
sparse, reversible Markov chain on with stationary distribution
is run to near equilibrium. The running time of this random walk algorithm, the
so-called {\em mixing time} of , is as shown
by Aldous, where is the spectral gap of and is the minimum
value of . A natural question is whether a speedup of this classical
method to , the diameter of the graph
underlying , is possible using {\em quantum walks}.
We provide evidence for this possibility using quantum walks that {\em
decohere} under repeated randomized measurements. We show: (a) decoherent
quantum walks always mix, just like their classical counterparts, (b) the
mixing time is a robust quantity, essentially invariant under any smooth form
of decoherence, and (c) the mixing time of the decoherent quantum walk on a
periodic lattice is , which is indeed
and is asymptotically no worse than the
diameter of (the obvious lower bound) up to at most a logarithmic
factor.Comment: 13 pages; v2 revised several part
On demand entanglement in double quantum dots via coherent carrier scattering
We show how two qubits encoded in the orbital states of two quantum dots can
be entangled or disentangled in a controlled way through their interaction with
a weak electron current. The transmission/reflection spectrum of each scattered
electron, acting as an entanglement mediator between the dots, shows a
signature of the dot-dot entangled state. Strikingly, while few scattered
carriers produce decoherence of the whole two-dots system, a larger number of
electrons injected from one lead with proper energy is able to recover its
quantum coherence. Our numerical simulations are based on a real-space solution
of the three-particle Schroedinger equation with open boundaries. The computed
transmission amplitudes are inserted in the analytical expression of the system
density matrix in order to evaluate the entanglement.Comment: 20 pages, 5 figure
Collective Decoherence of Nuclear Spin Clusters
The problem of dipole-dipole decoherence of nuclear spins is considered for
strongly entangled spin cluster. Our results show that its dynamics can be
described as the decoherence due to interaction with a composite bath
consisting of fully correlated and uncorrelated parts. The correlated term
causes the slower decay of coherence at larger times. The decoherence rate
scales up as a square root of the number of spins giving the linear scaling of
the resulting error. Our theory is consistent with recent experiment reported
in decoherence of correlated spin clusters.Comment: 4 pages, 4 figure
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