307 research outputs found
Identification of Decoherence-Free Subspaces Without Quantum Process Tomography
Characterizing a quantum process is the critical first step towards applying
such a process in a quantum information protocol. Full process characterization
is known to be extremely resource-intensive, motivating the search for more
efficient ways to extract salient information about the process. An example is
the identification of "decoherence-free subspaces", in which computation or
communications may be carried out, immune to the principal sources of
decoherence in the system. Here we propose and demonstrate a protocol which
enables one to directly identify a DFS without carrying out a full
reconstruction. Our protocol offers an up-to-quadratic speedup over standard
process tomography. In this paper, we experimentally identify the DFS of a
two-qubit process with 32 measurements rather than the usual 256, characterize
the robustness and efficiency of the protocol, and discuss its extension to
higher-dimensional systems.Comment: 6 pages, 5 figure
An Arbitrary Two-qubit Computation In 23 Elementary Gates
Quantum circuits currently constitute a dominant model for quantum
computation. Our work addresses the problem of constructing quantum circuits to
implement an arbitrary given quantum computation, in the special case of two
qubits. We pursue circuits without ancilla qubits and as small a number of
elementary quantum gates as possible. Our lower bound for worst-case optimal
two-qubit circuits calls for at least 17 gates: 15 one-qubit rotations and 2
CNOTs. To this end, we constructively prove a worst-case upper bound of 23
elementary gates, of which at most 4 (CNOT) entail multi-qubit interactions.
Our analysis shows that synthesis algorithms suggested in previous work,
although more general, entail much larger quantum circuits than ours in the
special case of two qubits. One such algorithm has a worst case of 61 gates of
which 18 may be CNOTs. Our techniques rely on the KAK decomposition from Lie
theory as well as the polar and spectral (symmetric Shur) matrix decompositions
from numerical analysis and operator theory. They are related to the canonical
decomposition of a two-qubit gate with respect to the ``magic basis'' of
phase-shifted Bell states, published previously. We further extend this
decomposition in terms of elementary gates for quantum computation.Comment: 18 pages, 7 figures. Version 2 gives correct credits for the GQC
"quantum compiler". Version 3 adds justification for our choice of elementary
gates and adds a comparison with classical library-less logic synthesis. It
adds acknowledgements and a new reference, adds full details about the 8-gate
decomposition of topC-V and stealthily fixes several minor inaccuracies.
NOTE: Using a new technique, we recently improved the lower bound to 18 gates
and (tada!) found a circuit decomposition that requires 18 gates or less.
This work will appear as a separate manuscrip
Entanglement in continuous variable systems: Recent advances and current perspectives
We review the theory of continuous-variable entanglement with special
emphasis on foundational aspects, conceptual structures, and mathematical
methods. Much attention is devoted to the discussion of separability criteria
and entanglement properties of Gaussian states, for their great practical
relevance in applications to quantum optics and quantum information, as well as
for the very clean framework that they allow for the study of the structure of
nonlocal correlations. We give a self-contained introduction to phase-space and
symplectic methods in the study of Gaussian states of infinite-dimensional
bosonic systems. We review the most important results on the separability and
distillability of Gaussian states and discuss the main properties of bipartite
entanglement. These include the extremal entanglement, minimal and maximal, of
two-mode mixed Gaussian states, the ordering of two-mode Gaussian states
according to different measures of entanglement, the unitary (reversible)
localization, and the scaling of bipartite entanglement in multimode Gaussian
states. We then discuss recent advances in the understanding of entanglement
sharing in multimode Gaussian states, including the proof of the monogamy
inequality of distributed entanglement for all Gaussian states, and its
consequences for the characterization of multipartite entanglement. We finally
review recent advances and discuss possible perspectives on the qualification
and quantification of entanglement in non Gaussian states, a field of research
that is to a large extent yet to be explored.Comment: 61 pages, 7 figures, 3 tables; Published as Topical Review in J.
Phys. A, Special Issue on Quantum Information, Communication, Computation and
Cryptography (v3: few typos corrected
NMR Quantum Computation
In this article I will describe how NMR techniques may be used to build
simple quantum information processing devices, such as small quantum computers,
and show how these techniques are related to more conventional NMR experiments.Comment: Pedagogical mini review of NMR QC aimed at NMR folk. Commissioned by
Progress in NMR Spectroscopy (in press). 30 pages RevTex including 15 figures
(4 low quality postscript images
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