Time-potimal hamiltonian simulation and gate sythesis using homogeneous local unitaries

Quantum Information and Computation

Volumn 2, Issue 4, 2002, Pages 285-296

  Masanes, Ll ^a   Vidal, G ^b,c   Latorre, J I ^a  

^a UNIVERSITY OF BARCELONA   (Spain)

^b UNIVERSITY OF INNSBRUCK   (Austria)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

QUANTUM THEORY; QUBITS;

NONLOCAL; SOLID-STATE QUANTUM COMPUTERS; TIME-OPTIMAL; TWO-QUBIT;

HAMILTONIANS;

EID: 0041721813     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

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9. min) are the highest (lower) eigenvalue of H.
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17. Notice that this has important consequences for information processing, since irreducible representations of the permutation group are left invariant under symmetric evolutions, and the dimension of the largest representation grows only linearly with N. Therefore in this highly symmetric setting we cannot even exploit the exponential growth (in N) of dimension offered by quantum computers, and the system becomes useless for quantum computation unless some degree of inhomogeneity can be introduced.
18. M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information; Cambridge University Press, Cambridge, U.K., 2000.
19. This is equivalent to assume that each qubit is equally affected by the environment.
20. 2 - 1). Nevertheless the counting of degrees of freedom shows that this R belongs to a subset of SO(n - 1) and, in general, will not allow for a diagonalization of M unless this latter matrix is severely restricted. A complete study of hamiltonian simulation for qunits is made in [7].
21. Rajendra Bhatia Matrix Analysis, Chapter II. M. A. Nielsen and G. Vidal, Majorization and the interconversion of bipartite states; Quantum Information and Computation, Vol. 1, 1 (2001) 76.
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24. → when we rearrange them in decreasing order.
25. B. Kraus and J. I. Cirac, Optimal Creation of Entanglement Using a Two-Qubit Gate; quant-ph/0011050.
26. z} is HLU-equivalent to a gate with permuted components. The majorization relation ≺ is already defined to be invarinat under permutations, and this is why we do not consider permuted versions of vecλ′ in Eq. (22).
27. i : i, j = 1,2,3} .