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Register a new userPreparation of GHZ states via Grovers quantum searching algorithm
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In this paper we propose an approach to prepare GHZ states of an arbitrary multi-particle system in terms of Grovers fast quantum searching algorithm. This approach can be regarded as an extension of the Grovers algorithm to find one or more items in an unsorted database.
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We present a scheme to prepare a quantum state in a ion trap with probability approaching to one by means of ion trap quantum computing and Grovers quantum search algorithm acting on trapped ions.
We study the entanglement content of the states employed in the Grover algorithm after the first oracle call when a few searched items are concerned. We then construct a link between these initial states and hypergraphs, which provides an illustration of their entanglement properties.
Grovers quantum algorithm improves any classical search algorithm. We show how random Gaussian noise at each step of the algorithm can be modelled easily because of the exact recursion formulas available for computing the quantum amplitude in Grovers algorithm. We study the algorithms intrinsic robustness when no quantum correction codes are used, and evaluate how much noise the algorithm can bear with, in terms of the size of the phone book and a desired probability of finding the correct result. The algorithm loses efficiency when noise is added, but does not slow down. We also study the maximal noise under which the iterated quantum algorithm is just as slow as the classical algorithm. In all cases, the width of the allowed noise scales with the size of the phone book as N^-2/3.
We investigate the performance of Grovers quantum search algorithm on a register which is subject to loss of the particles that carry the qubit information. Under the assumption that the basic steps of the algorithm are applied correctly on the correspondingly shrinking register, we show that the algorithm converges to mixed states with 50% overlap with the target state in the bit positions still present. As an alternative to error correction, we present a procedure that combines the outcome of different trials of the algorithm to determine the solution to the full search problem. The procedure may be relevant for experiments where the algorithm is adapted as the loss of particles is registered, and for experiments with Rydberg blockade interactions among neutral atoms, where monitoring of the atom losses is not even necessary.
It has recently been established that cluster-like states -- states that are in the same symmetry-protected topological phase as the cluster state -- provide a family of resource states that can be utilized for Measurement-Based Quantum Computation. In this work, we ask whether it is possible to prepare cluster-like states in finite time without breaking the symmetry protecting the resource state. Such a symmetry-preserving protocol would benefit from topological protection to errors in the preparation. We answer this question in the positive by providing a Hamiltonian in one higher dimension whose finite-time evolution is a unitary that acts trivially in the bulk, but pumps the desired cluster state to the boundary. Examples are given for both the 1D cluster state protected by a global symmetry, and various 2D cluster states protected by subsystem symmetries. We show that even if unwanted symmetric perturbations are present in the driving Hamiltonian, projective measurements in the bulk along with post-selection is sufficient to recover a cluster-like state. For a resource state of size $N$, failure to prepare the state is negligible if the size of the perturbations are much smaller than $N^{-1/2}$.
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