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We describe a protocol for cross-platform verification of quantum simulators and quantum computers. We show how to measure directly the overlap Tr [ρ1ρ2] and the purities Tr ρ 2 1,2 , and thus a (mixed-state) fidelity, of two quantum states ρ1 and ρ2 prepared in separate experimental platforms. We require only local measurements in randomized product bases, which are communicated classically. As a proof-of-principle, we present the measurement of experiment-theory fidelities for entangled 10-qubit quantum states in a trapped ion quantum simulator.

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Brief treatment of purple membrane (PM) with dilute detergent can cause major disruption of the BR photocycle without disrupting the trimer structure of BR [Mukhopadhyay et al. (1996) Biochemistry 35, 9245-9252]. Normal photocyle behavior can be recovered by incubating the damaged membranes with a total extract of the five types of native lipids present in PM. It is shown here that full restoration can also be obtained with combinations of squalene (SQ) and phosphatidyl glycerophosphate (PGP) which act synergistically. The addition of SQ to suboptimal levels of PGP induces complete reconstitution, principally by restoring the characteristics of the fast M intermediate, Mf (as defined in Mukhopadhyay et al. (1996) Biochemistry 35, 9245-9252). The addition of small amounts of PGP to SQ, which alone is ineffective, also induces full reconstituion. At very high levels, full reconstitution can be obtained with PGP alone. These results, in combination with earlier studies which implicate an acidic amino acid residue [Bose et al. (1997) J. Phys. Chem. B 101, 10584-10587], suggest that a crucial interaction between a particular amino acid residue and a SQ-PGP lipid complex may be essential for normal BR photocycle activity.

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We present experiments on polarization gradient cooling of Ca+ multi-ion Coulomb crystals in a linear Paul trap. Polarization gradient cooling of the collective modes of motion whose eigenvectors have overlap with the symmetry axis of the trap is achieved by two counter-propagating laser beams with mutually orthogonal linear polarizations that are blue-detuned from the S 1/2 ↔ P 1/2 transition. We demonstrate cooling of linear chains of up to 51 ions and 2D-crystals in zig-zag configuration with 22 ions. The cooling results are compared with numerical simulations and the predictions of a simple model of cooling in a moving polarization gradient.

We have recently demonstrated the laser cooling of a single 40 Ca + ion to the motional ground state in a Penning trap using the resolved-sideband cooling technique on the electric quadrupole transition S 1/2 ↔ D 5/2 . Here we report on the extension of this technique to small ion Coulomb crystals made of two or three 40 Ca + ions. Efficient cooling of the axial motion is achieved outside the Lamb-Dicke regime on a two-ion string along the magnetic field axis as well as on two-and three-ion planar crystals. Complex sideband cooling sequences are required in order to cool both axial degrees of freedom simultaneously. We measure a mean excitation after cooling ofn COM = 0.30(4) for the centre of mass mode andn B = 0.07(3) for the breathing mode of the two-ion string with corresponding heating rates of 11(2) s −1 and 1(1) s −1 at a trap frequency of 162 kHz. The ground state occupation of the axial modes is above 75% for the two-ion planar crystal and the associated heating rates 0.8(5) s −1 at a trap frequency of 355 kHz.

Doppler and sideband cooling are long standing techniques that have been used together to prepare trapped atomic ions in their ground state of motion. In this paper we study how these techniques can be extended to cool both radial modes of motion of a single ion in a Penning trap. We numerically explore the prerequisite experimental parameters for efficient Doppler cooling in the presence of an additional oscillating electric field to resonantly couple the radial modes. The simulations are supported by experimental data for a single 40 Ca + ion Doppler cooled to ∼100 phonons in both modes at a magnetron frequency of 52 kHz and a modified cyclotron frequency of 677 kHz. For these frequencies, we then show that mean phonon numbers of 0.35(5) for the modified cyclotron and 1.7(2) for the magnetron motions are achieved after 68 ms of sideband cooling.