17 research outputs found
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
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
Controlling open quantum systems
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 2002.Includes bibliographical references (p. 79-86).This thesis describes the development and experimental verification (via liquid state nuclear magnetic resonance techniques) of new methods for controlling open quantum systems. First, methods that improve coherent control through the use of both strong control fields and detailed knowledge of the system's Hamiltonian are demonstrated. With the aid of numerical search methods, pulsed irradiation schemes are obtained that perform accurate, arbitrary, selective gates on multi-qubit systems. For a 3-qubit system, implementations show that the control sequences faithfully implement unitary operations with simulated gate fidelities on the order of 0.999 and experimentally determined projections of 0.99. Next, methods for controlling a quantum information in the presence of collective phase noise is demonstrated through the use of a decoherence free subspace (DFS). In addition to demonstrating the robustness of the DFS memory for both engineered and natural noise processes, a universal set of logical manipulations over the encoded qubit is realized. Dynamical control methods at the encoded level are used to implement noise-tolerant control over the DFS qubit in the presence of engineered phase noise significantly stronger than observed from natural noise sources.(cont.) Finally, we explore the use of noiseless subsystems, which offers the most general and efficient method for protecting quantum information in the presence of noise that has symmetry properties. We demonstrate the preservation of a bit of quantum information against all collective noise operators by encoding it into a 3 qubit noiseless subsystem. A complete set of input states were used to determine the superoperator for the implemented one-qubit process and confirm that the fidelity of entanglement is improved for a large, non-commuting set of engineered errors. To date, this is the largest set of error operators that have been successfully corrected for by any quantum code.by Evan M. Fortunato.Ph.D