Abstract
We present a protocol to prepare decoherence-free cluster states using ultracold atoms loaded in a two dimensional superlattice. The superlattice geometry leads to an array of $2\ifmmode\times\else\texttimes\fi{}2$ plaquettes, each of them holding four spin-$1∕2$ particles that can be used for encoding a single logical qubit in the twofold singlet subspace, insensitive to uniform magnetic field fluctuations in any direction. Dynamical manipulation of the supperlattice yields distinct inter- and intraplaquette interactions and permits us to realize one qubit and two qubit gates with high fidelity, leading to the generation of universal cluster states for measurement based quantum computation. Our proposal based on inter- and intraplaquette interactions also opens the path to study polymerized Hamiltonians which support ground states describing arbitrary quantum circuits.
Highlights
Quantum technology, in particular quantum information processing and quantum metrology, requires the precise preparation of quantum states that outperform a given task better than any classical strategy
In the model we propose here, the generation of a universal cluster state demands: (i) the ability to perform one qubit gates to prepare all logical qubits in the initial state |+ = 1/ (2)[|0 + |1 ], and (ii) the realization of controlled-phase gates, U = diag(1, 1, 1, −1), between nearest logical qubits, i.e. between plaquettes, to create a maximally entangled 2D cluster state
II we present the general ideas for generating cluster states within a decoherence free subspace (DFS) using optical superlattices
Summary
In particular quantum information processing and quantum metrology, requires the precise preparation of quantum states that outperform a given task better than any classical strategy. Using as qubits two internal states of atoms in a 2D optical lattice, it is possible to create a highly entangled quantum state by means of controlled collisions[4], which is a prerequisite for the generation of universal cluster state. We extend the earlier proposals [9, 10] by removing the requirement of equal coupling strengths for all six pairs within the plaquette (more feasible for 2D optical superlattices), while we still obtain the effective Hamiltonian within the logical subspace sufficient for universal gates. We include tunable Ising-type interactions between neighboring spins (attainable with neutral atoms in optical lattices [13]) and use the optimal control techniques to find efficient and robust pulse sequences for the logical coupling gate.
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