Dissipative engineering of a tripartite Greenberger–Horne–Zeilinger state for neutral atoms

Abstract

The multipartite Greenberger–Horne–Zeilinger (GHZ) states are indispensable elements for various quantum information processing tasks. Here we put forward two deterministic proposals to dissipatively prepare tripartite GHZ states in a neutral atom system. The first scheme utilizes the polychromatic driving fields and the engineered spontaneous emission of Rydberg states to generate a tripartite GHZ state with a high efficiency, which is then optimized by introducing the Gaussian soft control pulse. In the second scenario, we exploit the natural spontaneous emission of the Rydberg states as a resource, thence a steady tripartite GHZ state with fidelity around 98% can be obtained by simultaneously integrating the switching driving of unconventional Rydberg pumping and the Rydberg antiblockade effect.

Quantum logic and entanglement by neutral Rydberg atoms: methods and fidelity

“…Reference [312] Dissipation with asymmetric interactions (section 5.3.1) 9 9 .88%; Bell state; upper right of page 3 of reference [272] Reference [272] 99.91%; two-qubit entanglement; text below figure 2 on page 4 of reference [313] Reference [313] 99.47%; three-qubit entanglement; text below figure 4 on page 4 of reference [314] Reference [314] 99.09%; three-qubit entanglement (via cavity); lower left of page 1642 of reference [315] Reference [315] Dissipation (section 5.3.2) 99.9%; Bell state; figure 2 on page 3 of reference [316] Reference [316] 99%; Bell state (via cavity); text above figure 7 on page 5 of reference [317] Reference [317] 99.7%; two-qubit entanglement; end of section 4 on page 2300 of reference [318] Reference [318] 99.98%; two-qubit entanglement; text above figure 3 on page 10124 of reference [319] Reference [319] 98.24%; three-qubit entanglement (via cavity); lower left of page 5 of reference [320] Reference [320] 99%; six-qubit entanglement; upper right of page 4 of reference [321] Reference [321] 99.24%; three-qubit entanglement; abstract of reference [322] Reference [322] 98%; three-qubit entanglement; abstract of reference [323] Reference [323] Compensating Rydberg interactions by using oscillating Ω (section 5.4) 9 9 .35%; CNOT gate; middle left on page 4 of reference [147] Reference [147] 99.6%; C Z gate; text below equation (10) on page 1203 of reference [148] Reference [148] 98%; Bell state; figure 9(c) on page 8 of reference [149] Reference [149] 99%; C Z gate; lower left of page 7 of reference [150] (fast) b Reference [150] 99.1%; SWAP gate; texts below figure 3 and 4(a) on pp 816 and 817 of reference [240] Reference [240] a Most references show more than one type of gates or entanglement, where an operation with larger fidelity is quoted. b Here, 'fast' only means that they do not depend on Rydberg excitation with a Rabi frequency derived with a perturbation theory via the antiblockade, while a practical experimental implementation has a speed limited by experimentally feasible parameters.…”

“…Then, |D becomes the only stable state in the process of dissipation. Later on, it was found that by choosing appropriate detunings, interactions between the states, and dissipation, entanglement with various forms can be created, shown in references [318,[321][322][323]. Dissipation can also be used to generate entanglement with dipole-dipole flip-flop processes as shown in reference [319].…”

Perfect NOT and conjugate transformations

“…As for preparation of quantum state, two examples are given in refs. [23,24]. It even plays a vital role in deciding if a theory of entanglement-entropy is renormalizable [25].…”

Implementation of Quantum Algorithms via Fast Three-Rydberg-Atom CCZ Gates

“…Then we utilize the formula to reformulate the Hamiltonian in a rotating frame with respect to as [ 67 , 68 ], where , , , and periodic boundary conditions of j is considered. While the condition of Rydberg blockade is satisfied, the simultaneous excitations of Rydberg atoms will be suppressed and the Equation ( A2 ) can be simplified as the effective Hamiltonian, i.e., the Equation ( 2 ) of the main text, …”