Efficient generation of random multipartite entangled states using time-optimal unitary operations

Abstract

We review the generation of random pure states using a protocol of repeated two qubit gates. We study the dependence of the convergence to states with Haar multipartite entanglement distribution. We investigate the optimal generation of such states in terms of the physical (real) time needed to apply the protocol, instead of the gate complexity point of view used in other works. This physical time can be obtained, for a given Hamiltonian, within the theoretical framework offered by the quantum brachistochrone formalism. Using an anisotropic Heisenberg Hamiltonian as an example, we find that different optimal quantum gates arise according to the optimality point of view used in each case. We also study how the convergence to random entangled states depends on different entanglement measures.

Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain

“…Our research also triggered a number of related works [31][32][33][34][35][36][37][38][39]. For example, the authors of [32][33][34] considered the problem of the generation of multipartite entanglement during the QB evolution of quantum states and unitaries, while those of [35][36][37][38][39] studied the QB in the context of non-Hermitian quantum mechanics (for a review of the latter works see, e.g., [40]).…”

Note on the Harmonic Approximation in the Treatment of Entanglement: N Cold Trapped Ions

“…For larger N , we numerically solve the set of (5) for the values of x c i . The integrals in (11) and in (14) can be performed in an algebraic way, but for the reasons mentioned above, the values of P g→∞ can be obtained in closed analytic form solely for N = 2, 3, that is, For illustrative purposes, we present in Table 1 some values of L g→∞ = 1−P g→∞ and of R g→∞ = (P g→∞ ) −1 obtained by us with the use of (12)- (13). In [9], the values of L g→∞ were found numerically to be about 0.52, 0.68, and 0.77 for N = 2, 3 and N = 4, respectively, where they were determined by the configuration interaction method.…”

“…We recall here that the 1-RDM is used to characterize the bipartite entanglement between the subsets of one particle and the remaining N − 1 particles [14]. The 1-RDM expressed in coordinates takes the form…”

Brachistochrone of entanglement for spin chains

“…Recently, some authors [57,58] started the study of the role of quantum entanglement during the QB evolution of multipartite distinguishable systems in a pure quantum state, finding that the entanglement is pivotal to the QB evolution if at least two subsystems actively evolve. Efficient generation of random multipartite entangled states has been also analyzed with the aid of time-optimal unitary operations [59]. More recently, the authors of [60] found that genuine tripartite entanglement is necessary during the QB evolution of a set of three qubits in the pure state, except for the case in which less than three qubits attend evolution.…”