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arXiv:0810.0977 · Physical Review A

Constrained optimization of sequentially generated entangled multiqubit states

Hamed Saberi, Andreas Weichselbaum, Lucas Lamata, David Pérez-Garcı́a, Jan von Delft, E. Solano

Published Aug 26, 2009• 17 citations
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Abstract

We demonstrate how the matrix-product state formalism provides a flexible structure to solve the constrained optimization problem associated with the sequential generation of entangled multiqubit states under experimental restrictions. We consider a realistic scenario in which an ancillary system with a limited number of levels performs restricted sequential interactions with qubits in a row. The proposed method relies on a suitable local optimization procedure, yielding an efficient recipe for the realistic and approximate sequential generation of any entangled multiqubit state. We give paradigmatic examples that may be of interest for theoretical and experimental developments.

DOI
10.1103/physreva.80.022334

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We consider a sequential implementation of the optimal quantum cloning machine of Gisin and Massar and propose optimization protocols for experimental realization of such a quantum cloner subject to the real-life restrictions. We demonstrate how exploiting the matrix-product state (MPS) formalism and the ensuing variational optimization techniques reveals the intriguing algebraic structure of the Gisin-Massar output of the cloning procedure and brings about significant improvements to the optimality of the sequential cloning prescription of Delgado et al. [Phys. Rev. Lett. 98, 150502 (2007)]. Our numerical results show that the orthodox paradigm of optimal quantum cloning can in practice be realized in a much more economical manner by utilizing a considerably lesser amount of informational and numerical resources than hitherto estimated. Instead of the previously predicted linear scaling of the required ancilla dimension DDD with the number of qubits nnn, our recipe allows a realization of such a sequential cloning setup with an experimentally manageable ancilla of dimension at most D=3D=3D=3 up to n=15n=15n=15 qubits. We also address satisfactorily the possibility of providing an optimal range of sequential ancilla-qubit interactions for optimal cloning of arbitrary states under realistic experimental circumstances when only a restricted class of such bipartite interactions can be engineered in practice.
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Matrix product states can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system [Sch\"on et al., Phys. Rev. Lett. 95, 110503 (2005)]. We introduce a family of states that extends this definition to two dimensions. Like in matrix product states, expectation values of few body observables can be efficiently evaluated and, for the case of translationally invariant systems, the correlation functions decay exponentially with the distance. We show that such states are a subclass of projected entangled pair states and investigate their suitability for approximating the ground states of local Hamiltonians.
Abstract We present a protocol for generating multiqubit quantum states with translationally invariant pairwise entanglement, addressing the challenge posed by restricted qubit connectivity in current digital quantum computing platforms Our method relies on sequences of local single-qubit rotations and controlled operations, and we analyze two distinct configurations: a star topology, which produces cyclic permutation invariant entanglement patterns, and a linear topology, which enables translationally invariant entanglement across the chain. Using a variant of the time-dependent density matrix renormalization group (tDMRG) algorithm, we show that in the linear configuration the resulting bulk entanglement is independent of the number of qubits, demonstrating the scalability of the approach. Moreover, by alternating local unitaries along the chain, we uncover a periodic regime in which nearest-neighbor entanglement exhibits a dimerized structure. These results provide a practical and experimentally feasible pathway for realizing highly symmetric entangled states in near-term quantum devices.
Not all unitary operations upon a set of qubits can be implemented by sequential interactions between each qubit and an ancillary system. We analyze the specific case of sequential quantum cloning, 1-->M, and prove that the minimal dimension D of the ancilla grows linearly with the number of clones M. In particular, we obtain D=2M for symmetric universal quantum cloning and D=M+1 for symmetric phase-covariant cloning. Furthermore, we provide a recipe for the required ancilla-qubit interactions in each step of the sequential procedure for both cases.