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Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation
A parametrization of the density operator, a coherence vector representation, which uses a basis of orthogonal, traceless, Hermitian matrices is discussed. Using this parametrization we find the…
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Differential geometry on SU(3) with applications to three state systems
The left and right invariant vector fields are calculated in an “Euler angle”-type parametrization for the group manifold of SU(3), referred to here as Euler coordinates. The corresponding left and…
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The geometry of SU(3)
The group SU(3) is parameterized in terms of generalized {open_quotes}Euler angles{close_quotes}. The differential operators of SU(3) corresponding to the Lie Algebra elements are obtained, the…
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A parametrization of bipartite systems based on SU(4) Euler angles
In this paper we give an explicit parametrization for all two-qubit density matrices. This is important for calculations involving entanglement and many other types of quantum information processing.…
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Polynomial-time simulation of pairing models on a quantum computer.
TLDR
The algorithm adiabatically finds the low-lying spectrum in the vicinity of the gap between the ground and the first excited states and provides a test of the applicability of the BCS Hamiltonian to mesoscopic superconducting systems, such as ultrasmall metallic grains.
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Efficient universal leakage elimination for physical and encoded qubits.
TLDR
A general method for removingDecoherence-induced leakage errors by using simple decoupling and recoupling pulse sequences that are experimentally accessible in a variety of promising quantum-computing proposals.
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Overview of quantum error prevention and leakage elimination
TLDR
It is shown how to generally remove mixing of an encoded subspace with external states (termed leakage errors) using decoupling controls using ‘leakage elimination operations’ or ‘LEOs’.
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Geometric Phases for Three State Systems
The adiabatic geometric phases for general three state systems are discussed. An explicit parameterization for space of states of these systems is given. The abelian and non-abelian connection…
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Comprehensive encoding and decoupling solution to problems of decoherence and design in solid-state quantum computing.
  • M. ByrdD. Lidar
  • Computer Science, Physics
    Physical review letters
  • 10 December 2001
TLDR
It is shown how the dominant decoherence processes can be identified empirically, in order to optimize the decoupling pulses, and removed the need for single-qubit operations, which pose a difficult design constraint.
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Numerical method for finding decoherence-free subspaces and its applications
TLDR
This work proposes an algorithm that can find the algebraic structure of decoherence-free subspaces (DFS's) for a given noisy quantum channel and proves that this algorithm will work for all cases with probability one, and it is more efficient than the algorithm proposed by Holbrook, Kribs, and Laflamme.
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