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Complete methods set for scalable ion trap quantum information processing
J. P. Home, D. Hanneke, J. D. Jost, J. M. Amini, D. Leibfried, D. J. Wineland
TL;DR
The paper tests whether a trapped-ion quantum operation remains repeatable across repeated executions involving cooling, transport, gating, transfer, detection, and tomography. It combines these procedures and finds that the experimental operation is consistent with being the same on each repetition.
Problem
The work tests whether the gate operation is the same for each repetition.
Method
The experiment combines sympathetic cooling, two-mode geometric-phase gating, qubit-manifold transfers, sequential fluorescence readout, and tomography resampling.
Results
0.987(3) experimental fidelity is consistent with the gate operation being the same for each repetition.
Takeaways & Limitations
The experimental value is consistent with repeatable gate operation across repetitions.
Abstract
from arXiv · showhide
Large-scale quantum information processors must be able to transport and maintain quantum information, and repeatedly perform logical operations. Here we demonstrate a combination of all the fundamental elements required to perform scalable quantum computing using qubits stored in the internal states of trapped atomic ions. We quantify the repeatability of a multi-qubit operation, observing no loss of performance despite qubit transport over macroscopic distances. Key to these results is the use of different pairs of beryllium ion hyperfine states for robust qubit storage, readout and gates, and simultaneous trapping of magnesium re-cooling ions along with the qubit ions.
Materials and Methods
The supporting materials document implementation details for sympathetic cooling, geometric-phase gates, qubit-manifold transfer, state detection, and tomography error analysis.
- The supporting materials cover cooling, geometric-phase gates, qubit-manifold transfer, state detection, and quantum process tomography error analysis.
Sympathetic cooling.
Recombination leaves substantial motional energy, so each operation requires three cooling stages before the ions reach the ground state.
- 5.1 ms per ˆU is required for cooling, making it the limiting factor in operation time.Transport and separation takes 3.6 ms per ˆU.
- ∼0.94 ground-state preparation fidelity is achieved for each motional mode after Doppler and resolved-sideband cooling.Doppler cooling begins with mean vibrational occupation number n̄ ∼15.
- Higher motional excitation than in similar previous work is attributed primarily to voltage supplies updating below typical trap frequencies.The passage states that faster-update supplies could substantially reduce the cooling time.
Two-qubit logic gate.
The two-qubit gate uses state-dependent forces on two motional modes, with manifold transfers and spin-echo pulses arranged to implement and stabilize the phase operation.
- Two-qubit logic gate.: Two motional modes are excited simultaneously, speeding the gate for a given laser intensity and reducing spontaneous photon-scattering error.
- Two-qubit logic gate.: The force is applied for tG = 2π/δ, ensuring that spin states are disentangled from both motional modes.
- Two-qubit logic gate.: Qubits are transferred from the field-independent memory manifold into the gate manifold before the force pulses and transferred back afterward.The transfers use sequential R(π, φ) pulses on the corresponding transitions.
- Two-qubit logic gate.: Two spin-echo pulses are applied in the gate manifold so the final qubit phase depends on phase differences among the transfer and gate rotations.
- Two-qubit logic gate.: Non-zero phase differences from tunable Raman frequency sources are compensated by adjusting subsequent single-qubit gate phases.
Detection.
Each ion is read out individually through sequential population transfer and fluorescence detection, with preparation steps limiting contamination from the other ion.
- Detection.: State readout is performed sequentially because multiple detection apparatuses are unavailable.The ions are first separated into different zones for readout-level transfer.
- Detection.: Readout transfers memory populations into |2, 2⟩ and |1, −1⟩ before resonantly driving the |2, 2⟩↔|3, 3⟩ cycling transition.
- Detection.: ≈1 × 10−3 repumping probability over 200 µs contributes a smaller exponential component to the |1, −1⟩ photon-count distribution.Background scatter has a Poisson distribution with mean 0.4 counts.
- Detection.: Before detecting the second ion, the first is transferred to |1, −1⟩ so it contributes negligibly to the second fluorescence measurement.A protective transfer to |2, 1⟩ addresses possible residual population in the fluorescing state.
Tomography error analysis by resampling.
The analysis uses parametric bootstrap resampling and simulated repeated process maps to assess statistical uncertainty and reconstruction bias. The resulting fidelity comparison supports consistent gate operation across repetitions.
- Bootstrap model: The simulations incorporated photon-count probability distributions and normally distributed Rabi-frequency fluctuations consistent with observed intensity variations.These fluctuations affected preparation and analysis rotation angles θ.
- Reconstruction-bias assessment: 100 simulated data sets were generated from the experimentally obtained process map and the same map applied twice to assess reconstruction bias.Maximum-likelihood analysis was performed on each simulated data set.
- Conclusion: 0.987(3) was consistent with the simulated unbiased-reconstruction value, indicating that the gate operation was the same for each repetition.The comparison used the mean fidelity between reconstructed processes over the 36 input states.