Greenberger-Horne-Zeilinger state protocols for fully connected qubit networks

Abstract

We generalize the recently proposed Greenberger-Horne-Zeilinger tripartite protocol ͓A. Galiautdinov and J. M. Martinis, Phys. Rev. A 78, 010305͑R͒ ͑2008͔͒ to fully connected networks of weakly coupled qubits interacting by way of anisotropic Heisenberg exchange g͑XX + YY͒ + gZZ. Our model differs from the more familiar Ising-Heisenberg chain in that here every qubit interacts with every other qubit in the circuit. The assumption of identical couplings on all qubit pairs allows an elegant proof of the protocol for arbitrary N. In order to further make contact with experiment, we study fidelity degradation due to coupling imperfections by numerically simulating the N = 3 and 4 cases. Our simulations indicate that the best fidelity at unequal couplings is achieved when ͑a͒ the system is initially prepared in the uniform superposition state ͑similarly to how it is done in the ideal case͒ and ͑b͒ the entangling time and the final rotations on each of the qubits are appropriately adjusted.

Quantum information processing using quasiclassical electromagnetic interactions between qubits and electrical resonators

“…Third, because our coupling scheme gives an effective interaction ∝ (η iσ z i ) 2 [42,43], its strength does not decrease as the number of interacting qubits increases, in principle enabling multiqubit interactions or joint measurements to be implemented directly [80]. By contrast, in cQED, multiqubit interactions must either be engineered by cascading or combining pairwise interactions [24,25,[81][82][83][84] or using weaker, higher-order multiqubit couplings involving more than one virtual exchange of photons with the resonator. Multiqubit interactions may be of interest, for example, in clusterstate generation [85], quantum simulation of Fermionic systems [86], or syndrome extraction in quantum error-correction schemes such as surface codes [87] and low-density parity check codes [88].…”

Multiqubit Greenberger-Horne-Zeilinger state generated by synthetic magnetic field in circuit QED

“…Under the drive of huge potential application, many different protocols have been proposed to generate GHZ states in circuit QED setups [28][29][30][31][32][33][34][35]. Some of them are based on measurement, i.e., if a special measurement has a special result, the system is known to be in a GHZ state after the measurement [31,33,35].…”

Greenberger-Horne-Zeilinger generation protocol forNsuperconducting transmon qubits capacitively coupled to a quantum bus

“…Although the mathematical description of multipartite entanglement for more than three qubits is still debated [14][15][16] , GHZ states remain paradigmatic entangled states which are, in particular, useful for fault-tolerant quantum computing or quantum secret sharing 17 . So far, many different protocols have been proposed to generate such states in circuit QED setups [18][19][20][21][22][23] . Some of them are of probabilistic nature, i.e., if a measurement on the N -qubit system has a specific result, the system is known to be in a GHZ state after the measurement [19][20][21] .…”