Session W08: Quantum Gates

Dipolar Exchange Quantum Logic Gates Using Polar Molecules

A current challenge in quantum computing is efficiently scaling ensembles of qubits without sacrificing fidelity and experimental simplicity. We propose a two-qubit gate based on the dipolar exchange interaction between ultracold polar molecules trapped in an array of optical tweezers. This proposal uses two long-lived nuclear spin states as storage qubits, while a third rotationally excited state with rotation-hyperfine coupling enables switchable exchange interactions between molecules to generate an iSWAP gate. We simulate the dynamics of this system using the full Hamiltonian of NaCs and demonstrate a potential two-qubit gate fidelity of $>99.99\%$ in a coherent system that can be scaled by purely optical means.   

Trapped-ion spin-motion coupling with microwaves and a near-motional oscillating magnetic field gradient

\noindent We present a new method of spin-motion coupling for trapped ions using microwaves and a magnetic field gradient oscillating close to the ions' motional frequency. We demonstrate and characterize this coupling experimentally in a surface-electrode trap that incorporates current-carrying electrodes to generate the microwave field and the oscillating magnetic field gradient. Using this method, we perform resolved-sideband cooling of a single motional mode to its ground state [1]. We also perform entangling gates between two ions and present initial results on gate fidelity.\\ \noindent [1] R. Srinivas \textit{et al.} arXiv:1812.02098 (2018)   

Demonstration of a Mesoscopic Quantum Gate

Rydberg atoms are an exciting platform for large scale quantum computing with demonstrations of high fidelity entanglement and coherent control. The strong, long-range dipole-dipole interaction between Rydberg atoms creates a ‘dipole blockade’ which prevents the excitation of more than one atom within a radius $R<10~\mu$m to the Rydberg state. Using this effect we have previously demonstrated ground-state entanglement between a pair of atoms with a fidelity of 81\%. However, scaling from single atoms to atomic ensembles for optical interfacing introduces challenges due to the collective $\sqrt{N}$-enhancement from blockade giving number sensitivity to the excitation pulses. \\ We present recent results demonstrating an alternative mesoscopic gate scheme based on electromagnetically induced transparency (EIT), originally proposed by M\"{u}ller \emph{et al.}. This protocol provides a scalable approach to performing entanglement of large ensembles using a single control atom whilst circumventing challenges of the collective Rabi frequency. The resulting CNOT$^N$ gate protocol is therefore robust against number fluctuations and provides a route to creating useful entangled states for high-precision measurements beyond the standard quantum limit.   

Two-qubit gates with superconducting fluxonium circuits.

The superconducting fluxonium circuit is an artificial atom with a strongly anharmonic spectrum and with selection rules that are not typical for mainstream superconducting qubits. In the "sweet spot", its lowest energy transition has a small frequency and can have a very long coherence time [1], while its next transition has an order of magnitude higher frequency and a large transition matrix element. Therefore, similar to conventional atomic systems, the fluxonium offers a unique advantage of the possibility to use different transitions for memory storage and gate control. In this talk, we discuss various ways to make entangling gates between fluxoniums in the two-qubit system. In one example, a controlled-Z gate is activated by driving a transition leading out of the computational subspace while two qubits are kept at fixed frequencies at their sweet spots [2]. One more possible gate is mediated through a common resonator mode. [1] Long B. Nguyen, Yen-Hsiang Ling, Aaron Somoroff, Raymond Mencia, Nicholas Grabon, Vladimir E. Manucharyan, arXiv:1810.11006 (2018). [2] Konstantin N. Nesterov, Ivan V. Pechenezhskiy, Chen Wang, Vladimir E. Manucharyan, and Maxim G. Vavilov, Phys. Rev. A {\bf 98}, 030301 (2018).   

Versatile laser-free trapped-ion entangling gates

We present a general theory for laser-free entangling gates with trapped-ion hyperfine qubits, using either static or oscillating magnetic-field gradients combined with a pair of uniform microwave fields symmetrically detuned about the qubit frequency. By transforming into a `bichromatic' interaction picture, we show that either ${\hat{\sigma}_{\phi}\otimes\hat{\sigma}_{\phi}}$ or ${\hat{\sigma}_{z}\otimes\hat{\sigma}_{z}}$ geometric phase gates can be performed. The gate basis is determined by selecting the microwave detuning. The driving parameters can be tuned to provide intrinsic dynamical decoupling from qubit frequency fluctuations. The ${\hat{\sigma}_{z}\otimes\hat{\sigma}_{z}}$ gates can be implemented in a novel manner which eases experimental constraints. We present numerical simulations of gate fidelities assuming realistic parameters.   

Continuous Variable Quantum Gates in a System of Trapped Ions

Motional states of trapped ions are attractive for quantum information processing because they offer, in principle, a larger Hilbert space compared to the ion’s spin degree of freedom in the same physical system. Here we report on recent progress to explore the feasibility of continuous variable approach to quantum computations with just a single trapped $^{171}\mathrm{Yb}^+$ ion. By applying spin dependent force at the frequency corresponding to a difference between the frequencies of two modes of motion we implement a gate corresponding to a swap of populations of the modes conditioned on the internal state of the ion. We utilize this gate in an efficient scheme to produce maximally entangled (NOON) states of up to 4 phonons. We devise and implement an algorithm to perform a single-shot measurement of the Wigner function of the motional state and also a measurement of the overlap between quantum states belonging to two different motional modes. Finally we discuss the applicability of this gate to universal quantum computing with continuous variables.   

Robust Entangling Quantum Logic Gates Using Adiabatic Rydberg Dressing

The Rydberg blockade mechanism has been used to entangle two qubits encoded in the hyperfine ground manifold of neutral atoms. Thermal motion of atoms limits the gate fidelity in protocols involving resonant excitation to Rydberg states, as the internal atomic states and external motional states become entangled, leading to different random phases accumulated by the computational basis states. An adiabatic Rydberg-dressing protocol provides intrinsic robustness against thermal Doppler inhomogeneities by suppressing the mixing of bright and dark states, and a common-mode cancellation of single-atom and two-atom Doppler shifts. Moreover, one can overcome additional residual errors by combining adiabatic dressing with the tools of microwave (or Raman) based quantum control. We study a variety of protocols and pinpoint the major sources of error and how to cancel them. Entangling gate fidelities of 0.99 are well within reach and higher fidelities are possible if Rydberg lifetimes can be increased. \\ [1] L. Isenhower, et al, PhysRevLett.104.010503 \\ [2] T. Wilk, et al, PhysRevLett.104.010502 \\ [3] Y. Y. Jau et al, NatPhys.3487 \\ [4] H. Levine et al, PhysRevLett.121.123603 \\ [5] T. Keating et al, PhysRevA.91.012337 \\ [6] J. Lee et al, PhysRevA.95.041801   

High fidelity lossless neutral atom qubit state detection in a state-dependent optical lattice

Accurate qubit state detection is essential to a quantum computer. We demonstrate a lossless state measurement of \textasciitilde 160 neutral atom qubits in a 3D optical lattice with a fidelity of 0.9994, \textasciitilde 20 times lower error than in any previous lossless measurement in a neutral atom array. The atoms' wavefunction is coherently split by state-dependent motion, transferred into an optical lattice with an order of magnitude shorter lattice spacing and then imaged. In mapping the internal states to spatial positions, this technique is reminiscent of the Stern-Gerlach experiment. Since the measurement causes essentially no loss, we can reuse the atoms. We also demonstrate that we can replace atoms that are lost to background gas collisions during the experiment.   

Leaking mitigation using a mixed ion scheme

Hyperfine qubits are often favored in ion trapped quantum computers for their low memory errors. However, these ions also contain other energy states than those defining the qubit. These extra states lead to leakage errors. Zeeman qubits suffer from high memory errors, but do not have leakage energy states. Leakage errors are especially detrimental and cannot be handled by standard Pauli error correction codes. Often, extra circuitry is implemented to handle leakage errors at the cost of additional gate overhead. In this work, we proposed a mixed species layout to mitigate leakage effects. In our system, we mixed hyperfine ($^{171}$Yb$^+$) and Zeeman qubits ($^{174}$Yb$^+$) to reduce leakage errors at the cost of increasing memory errors. We find that at certain magnetic field stabilities, the mixed species system outperforms a pure hyperfine system.