Entanglement and quantum computation with ions in thermal motion

Abstract

With bichromatic fields it is possible to deterministically produce entangled states of trapped ions. In this paper we present a unified analysis of this process for both weak and strong fields, for slow and fast gates. Simple expressions for the fidelity of creating maximally entangled states of two or an arbitrary number of ions under non-ideal conditions are derived and discussed.

Sympathetic cooling in a large ion crystal

“…For trapped ion quantum computing, the computational fidelity is determined by the ion PF δx ξ i ≡ x ξ2 i (denoted by δx i and δz i for transverse and axial motion, respectively). When the quantum gate is operated by means of the transverse modes, the estimated infidelity is δF x i ∼ π 2 η 4 i /4 [3,29,30], where the Lamb-Dicke parameter η i ∼ |∆k| δx i with ∆k x the wavevector difference of the two Raman beams. Another possible source of error comes from the spatial non-uniformity of the laser intensity when a single beam addresses a specific ion; the ion's axial motion results in variation of the actual Rabi frequency.…”

“…Numerous advances have been achieved in this system, including realization of faithful quantum gates [1][2][3][4][5][6][7], preparation of many-body quantum states [8][9][10][11][12][13][14][15], and quantum teleportation [16,17]. There are also developments to scale up this system, based on either ion shuttling [18][19][20] or quantum networks [21][22][23][24][25][26]).…”

Fast geometric gate operation of superconducting charge qubits in circuit QED

“…Later investigation shows that the logical operation obtained is of the geometric nature [6] and therefore has high fidelity [7]. Meanwhile, it is shown that by periodically decoupling to the common phonon mode, the large detuning constrain can be removed [6] so that fast gate operation can be achieved [8]. Similar strategy can be adopted in cavity QED system with strong driven atoms [9], superconducting charge qubits in a microwave cavity by introducing ac magnetic flux [10] and superconducting flux qubits inductively coupled to a common resonator [11].…”

“…In this regime, there is no energy exchange between qubits and cavity. The effective coupling of energy conservation transitions can be determined by second-order perturbation theory [6]. Meanwhile, the coupling usually contains cavity-state-dependent energy shift, i.e., a † aσ z j terms.…”

“…Later investigation shows that the logical operation obtained is of the geometric nature [6] and therefore has high fidelity [7]. Meanwhile, it is shown that by periodically decoupling to the common phonon mode, the large detuning constrain can be removed [6] so that fast gate operation can be achieved [8].…”