Phase control of trapped ion quantum gates

Abstract

There are several known schemes for entangling trapped ion quantum bits for large-scale quantum computation. Most are based on an interaction between the ions and external optical fields, coupling internal qubit states of trapped ions to their Coulomb-coupled motion. In this paper, we examine the sensitivity of these motional gate schemes to phase fluctuations introduced through noisy external control fields, and suggest techniques for suppressing the resulting phase decoherence.

Errors in trapped-ion quantum gates due to spontaneous photon scattering

“…Again, to compare different ion species we examine ion-qubits that are encoded into hyperfine clock states. When the laser detuning is large compared to the hyperfine splitting, the differential light force between clock levels is negligible [4,57]. However, a phase gate can be applied between spin states in the rotated basis (superpositions of clock states that lie on the equatorial plane of the Bloch sphere) [53,54].…”

“…The beam polarizations are assumed to be linear, perpendicular to each other and to the magnetic field axis. The beams' relative frequencies can be arranged such that the final state is insensitive to the optical phase at the ions' position [57]. Generalizing this treatment to other Raman beam geometries is straightforward.…”

Intrinsic phonon effects on analog quantum simulators with ultracold trapped ions

“…Similarly, the coupling of the photon from the reference beam with the photon in the red-detuned beam with frequency ω L +ω 0 −µ leads to the effective red-detuned laser with the frequency difference ∆ω = ω 0 − µ given by the Hamiltonian H r H r =h Employing a superposition of multiple frequency components and adiabatically eliminating the dipole allowed excited states [22] allows one to show that the interaction of laser beams with ions consists of interactions between the reference beam ω L and the other frequencies. As a result, after the summations in Eqs.…”

“…A laser-ion interaction is imposed to create a spindependent force on the ions by using bichromatic laser beams to couple these clock states to a third state via stimulated Raman transitions [22]. Effectively, this process is equivalent to an off-resonant laser coupling to the two clock states by a small frequency detuning µ determined by the frequency difference of the bichromatic lasers.…”

“…In this case, the ground state of the magnetic field Hamiltonian has the spins aligned opposite to that of the field, while the highest-energy state has them aligned with the field. The magnetic field B(t) is made in the ydirection by directly driving a resonant radio-frequency field with frequency ω 0 between the two hyperfine states to implement the spin flips [23] or by indirect Raman coupling through a third state to effectively couple the two hyperfine states [22]. The full Hamiltonian is then H(t) = H ph + H LI (t) + H B (t).…”