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Register a new userHigh-fidelity Rydberg-blockade entangling gate using shaped, analytic pulses
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We show that the use of shaped pulses improves the fidelity of a Rydberg blockade two-qubit entangling gate by several orders of magnitude compared to previous protocols based on square pulses or optimal control pulses. Using analytical Derivative Removal by Adiabatic Gate (DRAG) pulses that reduce excitation of primary leakage states and an analytical method of finding the optimal Rydberg blockade we generate Bell states with a fidelity of $F>0.9999$ in a 300 K environment for a gate time of only $50;{rm ns}$, which is an order of magnitude faster than previous protocols. These results establish the potential of neutral atom qubits with Rydberg blockade gates for scalable quantum computation.
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We present a detailed error analysis of a Rydberg blockade mediated controlled-NOT quantum gate between two neutral atoms as demonstrated recently in Phys. Rev. Lett. 104, 010503 (2010) and Phys. Rev. A 82, 030306 (2010). Numerical solutions of a master equation for the gate dynamics, including all known sources of technical error, are shown to be in good agreement with experiments. The primary sources of gate error are identified and suggestions given for future improvements. We also present numerical simulations of quantum process tomography to find the intrinsic fidelity, neglecting technical errors, of a Rydberg blockade controlled phase gate. The gate fidelity is characterized using trace overlap and trace distance measures. We show that the trace distance is linearly sensitive to errors arising from the finite Rydberg blockade shift and introduce a modified pulse sequence which corrects the linear errors. Our analysis shows that the intrinsic gate error extracted from simulated quantum process tomography can be under 0.002 for specific states of $^{87}$Rb or Cs atoms. The relation between the process fidelity and the gate error probability used in calculations of fault tolerance thresholds is discussed.
Generating quantum entanglement in large systems on time scales much shorter than the coherence time is key to powerful quantum simulation and computation. Trapped ions are among the most accurately controlled and best isolated quantum systems with low-error entanglement gates operated via the vibrational motion of a few-ion crystal within tens of microseconds. To exceed the level of complexity tractable by classical computers the main challenge is to realise fast entanglement operations in large ion crystals. The strong dipole-dipole interactions in polar molecule and Rydberg atom systems allow much faster entangling gates, yet stable state-independent confinement comparable with trapped ions needs to be demonstrated in these systems. Here, we combine the benefits of these approaches: we report a $700,mathrm{ns}$ two-ion entangling gate which utilises the strong dipolar interaction between trapped Rydberg ions and produce a Bell state with $78%$ fidelity. The sources of gate error are identified and a total error below $0.2%$ is predicted for experimentally-achievable parameters. Furthermore, we predict that residual coupling to motional modes contributes $sim 10^{-4}$ gate error in a large ion crystal of 100 ions. This provides a new avenue to significantly speed up and scale up trapped ion quantum computers and simulators.
We implement a two-qubit logic gate between a $^{43}mathrm{Ca}^+,$ hyperfine qubit and a $^{88}mathrm{Sr}^+,$ Zeeman qubit. For this pair of ion species, the S--P optical transitions are close enough that a single laser of wavelength $402,mathrm{nm}$ can be used to drive the gate, but sufficiently well separated to give good spectral isolation and low photon scattering errors. We characterize the gate by full randomized benchmarking, gate set tomography and Bell state analysis. The latter method gives a fidelity of $99.8(1)%$, comparable to that of the best same-species gates and consistent with known sources of error.
Limits to Rydberg gate fidelity that arise from the entanglement of internal states of neutral atoms with the motional degrees of freedom due to the momentum kick from photon absorption and re-emission is quantified. This occurs when the atom is in a superposition of internal states but only one of these states is manipulated by visible or UV photons. The Schrodinger equation that describes this situation is presented and two cases are explored. In the first case, the entanglement arises because the spatial wave function shifts due to the separation in time between excitation and stimulated emission. For neutral atoms in a harmonic trap, the decoherence can be expressed within a sudden approximation when the duration of the laser pulses are shorter than the harmonic oscillator period. In this limit, the decoherence is given by simple analytic formulas that account for the momentum of the photon, the temperature of the atoms, the harmonic oscillator frequency, and atomic mass. In the second case, there is a reduction in gate fidelity because the photons causing absorption and stimulated emission are in focused beam modes. This leads to a dependence of the optically induced changes in the internal states on the center of mass atomic position. In the limit where the time between pulses is short, the decoherence can be expressed as a simple analytic formula involving the laser waist, temperature of the atoms, the trap frequency and the atomic mass. These limits on gate fidelity are studied for the standard $pi-2pi-pi$ Rydberg gate and a new protocol based on a single adiabatic pulse with Gaussian envelope.
We use coherent excitation of 3-16 atom ensembles to demonstrate collective Rabi flopping mediated by Rydberg blockade. Using calibrated atom number measurements, we quantitatively confirm the expected $sqrt{N}$ Rabi frequency enhancement to within 4%. The resulting atom number distributions are consistent with essentially perfect blockade. We then use collective Rabi $pi$ pulses to produce ${cal N}=1,2$ atom number Fock states with fidelities of 62% and 48% respectively. The ${cal N}=2$ Fock state shows the collective Rabi frequency enhancement without corruption from atom number fluctuations.
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