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Register a new userA high-fidelity method for a single-step $N$-bit Toffoli gate in trapped ions
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Conditional multi-qubit gates are a key component for elaborate quantum algorithms. In a recent work, Rasmussen et al. (Phys. Rev. A 101, 022308) proposed an efficient single-step method for a prototypical multi-qubit gate, a Toffoli gate, based on a combination of Ising interactions between control qubits and an appropriate driving field on a target qubit. Trapped ions are a natural platform to implement this method, since Ising interactions mediated by phonons have been demonstrated in increasingly large ion crystals. However, the simultaneous application of these interactions and the driving field required for the gate results in undesired entanglement between the qubits and the motion of the ions, reducing the gate fidelity. In this work, we propose a solution based on adiabatic switching of these phonon mediated Ising interactions. We study the effects of imperfect ground state cooling, and use spin-echo techniques to undo unwanted phase accumulation in the achievable fidelities. For gates coupling to all axial modes of a linear crystal, we calculate high fidelities ($>$ 99%) $N$-qubit rotations with $N=$ 3-7 ions cooled to their ground state of motion and a gate time below 1~ms. The high fidelities obtained also for large crystals could make the gate competitive with gate-decomposed, multi-step variants of the $N$-qubit Toffoli gate, at the expense of requiring ground state cooling of the ion crystal.
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We implement all single-qubit operations with fidelities significantly above the minimum threshold required for fault-tolerant quantum computing, using a trapped-ion qubit stored in hyperfine atomic clock states of $^{43}$Ca$^+$. We measure a combined qubit state preparation and single-shot readout fidelity of 99.93%, a memory coherence time of $T^*_2=50$ seconds, and an average single-qubit gate fidelity of 99.9999%. These results are achieved in a room-temperature microfabricated surface trap, without the use of magnetic field shielding or dynamic decoupling techniques to overcome technical noise.
We present a new and simplified two-qubit randomized benchmarking procedure that operates only in the symmetric subspace of a pair of qubits and is well suited for benchmarking trapped-ion systems. By performing benchmarking only in the symmetric subspace, we drastically reduce the experimental complexity, number of gates required, and run time. The protocol is demonstrated on trapped ions using collective single-qubit rotations and the Molmer-Sorenson (MS) interaction to estimate an entangling gate error of $2(1) times 10^{-3}$. We analyze the expected errors in the MS gate and find that population remains mostly in the symmetric subspace. The errors that mix symmetric and anti-symmetric subspaces appear as leakage and we characterize them by combining our protocol with recently proposed leakage benchmarking. Generalizations and limitations of the protocol are also discussed.
We implement a two-qubit entangling M{o}lmer-S{o}rensen interaction by transporting two co-trapped $^{40}mathrm{Ca}^{+}$ ions through a stationary, bichromatic optical beam within a surface-electrode Paul trap. We describe a procedure for achieving a constant Doppler shift during the transport which uses fine temporal adjustment of the moving confinement potential. The fixed interaction duration of the ions transported through the laser beam as well as the dynamically changing ac Stark shift require alterations to the calibration procedures used for a stationary gate. We use the interaction to produce Bell states with fidelities commensurate to those of stationary gates performed in the same system. This result establishes the feasibility of actively incorporating ion transport into quantum information entangling operations.
We present a method that combines continuous and pulsed microwave radiation patterns to achieve robust interactions among hyperfine trapped ions placed in a magnetic field gradient. More specifically, our scheme displays continuous microwave drivings with modulated phases, phase flips, and $pi$ pulses. This leads to high-fidelity entangling gates which are resilient against magnetic field fluctuations, changes on the microwave amplitudes, and crosstalk effects. Our protocol runs with arbitrary values of microwave power, which includes the technologically relevant case of low microwave intensities. We demonstrate the performance of our method with detailed numerical simulations that take into account the main sources of decoherence.
We report the realization of an elementary quantum processor based on a linear crystal of trapped ions. Each ion serves as a quantum bit (qubit) to store the quantum information in long lived electronic states. We present the realization of single-qubit and of universal two-qubit logic gates. The qwo-qubit operation relies on the coupling of the ions through their collective quantized motion. A detailed description of the setup and the methods is included.
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