2014
DOI: 10.1016/j.physleta.2014.01.008
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Realization of quantum gates by Lyapunov control

Abstract: We propose a Lyapunov control design to achieve specific (or a family of) unitary time-evolution operators, i.e., quantum gates in the Schr\"{o}dinger picture by tracking control. Two examples are presented. In the first, we illustrate how to realize the Hadamard gate in a single-qubit system, while in the second, the controlled-NOT (CNOT) gate is implemented in two-qubit systems with the Ising and Heisenberg interactions. Furthermore, we demonstrate that the control can drive the time-evolution operator into … Show more

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Cited by 32 publications
(17 citation statements)
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“…First, we should note that the signs for each term in the diagonal-off entries do not depend on the entries' scripts in positions other than the parts in which the interaction is being applied, k , k in the expressions of the previous section (30), (32), (34), and (36). This is because Tr(σ * i s…”
Section: Structure Of Diagonal-off Entries Belonging To a Specific Blockmentioning
confidence: 99%
See 1 more Smart Citation
“…First, we should note that the signs for each term in the diagonal-off entries do not depend on the entries' scripts in positions other than the parts in which the interaction is being applied, k , k in the expressions of the previous section (30), (32), (34), and (36). This is because Tr(σ * i s…”
Section: Structure Of Diagonal-off Entries Belonging To a Specific Blockmentioning
confidence: 99%
“…For the controlled gates Λ n (U) proposed in [32], authors in [33] turn to a long factorization in terms of rotations and controlled gates Λ 1 (U) (which can also be obtained departing from the CNot gate and rotations). In any case, if a computational basis is used, the reproduction of the CNot gate can still bring certain difficulties in many quantum systems [34]. In the context of SU(2) reduction, CNot gate and inclusively Λ 1 (U) are directly obtained if the Bell basis is used as grammar:…”
Section: Su(2) Decomposition In the Context Of N−qubit Controlled Gatesmentioning
confidence: 99%
“…In recent years, numerous efforts have been devoted to investigate or improve the convergence of Lyapunov control for different quantum control models [5][6][7][8][9][10][11][12]. Meanwhile, Lyapunov control method is successfully employed for diverse quantum information processing tasks [12][13][14][15][16][17][18][19][20][21][22][23]. For example, it is recently used to realize topological modes [19], quantum synchronization [21] and speed up adiabatic passage [22].…”
Section: Introductionmentioning
confidence: 99%
“…Dong and his collogues have designed a development of the variable structure control approach with sliding modes to improve the robustness of quantum systems in which a sliding mode control method is presented for two-level quantum systems to treat bounded uncertainties in the system Hamiltonian [13]. In addition to these works, a Lyapunov control method is presented to attain a universal quantum control [14]. For the first time a sampling-based learning control (SLC) of inhomogeneous quantum ensembles is presented for overcoming the compensation for parameter dispersion [6].…”
Section: Introductionmentioning
confidence: 99%