Constraints on measurement-based quantum computation in effective cluster states

Klagges, Daniel; Schmidt, K. P.

doi:10.48550/arxiv.1111.5945

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“…39 (and generalizations thereof). With series expansions, it can be obtained using Takahashi's degenerate perturbation theory 21 as discussed recently 5 . The explicit expression of d reads…”

Section: Fidelitymentioning

confidence: 99%

“…As a consequence, simpler models containing solely two-spin interactions have been proposed in the literature having the cluster Hamiltonian as an effective low-energy model. But it has been shown recently that it is very challenging to protect approximative cluster states against additional perturbations 5 . Another approach to study such systems efficiently, could be to prepare the cluster Hamiltonian with a quantum simulator [6][7][8] .…”

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Fate of the cluster state on the square lattice in a magnetic field

et al. 2012

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The cluster state represents a highly entangled state which is one central object for measurementbased quantum computing. Here we study the robustness of the cluster state on the two-dimensional square lattice at zero temperature in the presence of external magnetic fields by means of different types of high-order series expansions and variational techniques using infinite Projected Entangled Pair States (iPEPS). The phase diagram displays a first-order phase transition line ending in two critical end points. Furthermore, it contains a characteristic self-dual line in parameter space allowing many precise statements. The self-duality is shown to exist on any lattice topology. I. MOTIVATIONThe exploitation of quantum mechanics to build a quantum computer is a very active area in current research, because it is expected to be capable of solving classically hard problems in a polynomial amount of time 1 yielding a deeper understanding of the quantum world. To this end it has been shown that a universal quantum computer can be built by only a small set of elementary operations, namely arbitrary single-qubit rotations plus certain two-qubit gates like CZ or cNOT 2,3 . Especially the two-qubit operations turn out to be complicated to implement in experiment.Measurement-based quantum computing is a fascinating alternative approach for a quantum computer 4 . The essential idea is to prepare a highly-entangled initial quantum state on which only single-qubit measurement are sufficient to run a quantum algorithm. Meaurements with respect to an arbitrary basis are easy to perform in experiment. This feature comes with the price, that the initial state is hard to prepare in nature. One class of such highly-entangled states useful for measurementbased quantum computation are cluster states.One natural way of realizing a cluster state would be to cool down appropriate Hamiltonians having the cluster state as a ground state. Indeed, so-called cluster Hamiltonians exist but contain typically multi-site interactions which are very rare in nature. As a consequence, simpler models containing solely two-spin interactions have been proposed in the literature having the cluster Hamiltonian as an effective low-energy model. But it has been shown recently that it is very challenging to protect approximative cluster states against additional perturbations 5 . Another approach to study such systems efficiently, could be to prepare the cluster Hamiltonian with a quantum simulator 6-8 . However simulating multi-spin interactions with respect to the desired topology will probably be a challenge.In any case it is important to check whether the cluster state is stable and protected against additional perturbations. This has been the subject of several works in recent years which mostly concentrate on additional magnetic fields as a perturbation 9,10 . The latter studies either investigated the change of entanglement of the perturbed cluster state or explored the complete breakdown of the cluster state due to a phase transition which serves a...

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Section: Fidelitymentioning

confidence: 99%

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confidence: 99%