217 research outputs found
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
Experimental Implementation of a Concatenated Quantum Error-Correcting Code
Concatenated coding provides a general strategy to achieve the desired level
of noise protection in quantum information storage and transmission. We report
the implementation of a concatenated quantum error-correcting code able to
correct against phase errors with a strong correlated component. The experiment
was performed using liquid-state nuclear magnetic resonance techniques on a
four spin subsystem of labeled crotonic acid. Our results show that
concatenation between active and passive quantum error-correcting codes offers
a practical tool to handle realistic noise contributed by both independent and
correlated errors.Comment: 4 pages, 2 encapsulated eps figures. REVTeX4 styl
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
Robust Control of Quantum Information
Errors in the control of quantum systems may be classified as unitary,
decoherent and incoherent. Unitary errors are systematic, and result in a
density matrix that differs from the desired one by a unitary operation.
Decoherent errors correspond to general completely positive superoperators, and
can only be corrected using methods such as quantum error correction.
Incoherent errors can also be described, on average, by completely positive
superoperators, but can nevertheless be corrected by the application of a
locally unitary operation that ``refocuses'' them. They are due to reproducible
spatial or temporal variations in the system's Hamiltonian, so that information
on the variations is encoded in the system's spatiotemporal state and can be
used to correct them. In this paper liquid-state nuclear magnetic resonance
(NMR) is used to demonstrate that such refocusing effects can be built directly
into the control fields, where the incoherence arises from spatial
inhomogeneities in the quantizing static magnetic field as well as the
radio-frequency control fields themselves. Using perturbation theory, it is
further shown that the eigenvalue spectrum of the completely positive
superoperator exhibits a characteristic spread that contains information on the
Hamiltonians' underlying distribution.Comment: 14 pages, 6 figure
Design of Strongly Modulating Pulses to Implement Precise Effective Hamiltonians for Quantum Information Processing
We describe a method for improving coherent control through the use of
detailed knowledge of the system's Hamiltonian. Precise unitary transformations
were obtained by strongly modulating the system's dynamics to average out
unwanted evolution. With the aid of numerical search methods, pulsed
irradiation schemes are obtained that perform accurate, arbitrary, selective
gates on multi-qubit systems. Compared to low power selective pulses, which
cannot average out all unwanted evolution, these pulses are substantially
shorter in time, thereby reducing the effects of relaxation. Liquid-state NMR
techniques on homonuclear spin systems are used to demonstrate the accuracy of
these gates both in simulation and experiment. Simulations of the coherent
evolution of a 3-qubit system show that the control sequences faithfully
implement the unitary operations, typically yielding gate fidelities on the
order of 0.999 and, for some sequences, up to 0.9997. The experimentally
determined density matrices resulting from the application of different control
sequences on a 3-spin system have overlaps of up to 0.99 with the expected
states, confirming the quality of the experimental implementation.Comment: RevTeX3, 11 pages including 2 tables and 5 figures; Journal of
Chemical Physics, in pres
Benchmarking quantum control methods on a 12-qubit system
In this letter, we present an experimental benchmark of operational control
methods in quantum information processors extended up to 12 qubits. We
implement universal control of this large Hilbert space using two complementary
approaches and discuss their accuracy and scalability. Despite decoherence, we
were able to reach a 12-coherence state (or 12-qubits pseudo-pure cat state),
and decode it into an 11 qubit plus one qutrit labeled observable pseudo-pure
state using liquid state nuclear magnetic resonance quantum information
processors.Comment: 11 pages, 4 figures, to be published in PR
Spintronics and Quantum Dots for Quantum Computing and Quantum Communication
Control over electron-spin states, such as coherent manipulation, filtering
and measurement promises access to new technologies in conventional as well as
in quantum computation and quantum communication. We review our proposal of
using electron spins in quantum confined structures as qubits and discuss the
requirements for implementing a quantum computer. We describe several
realizations of one- and two-qubit gates and of the read-in and read-out tasks.
We discuss recently proposed schemes for using a single quantum dot as
spin-filter and spin-memory device. Considering electronic EPR pairs needed for
quantum communication we show that their spin entanglement can be detected in
mesoscopic transport measurements using metallic as well as superconducting
leads attached to the dots.Comment: Prepared for Fortschritte der Physik special issue, Experimental
Proposals for Quantum Computation. 15 pages, 5 figures; typos corrected,
references adde
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