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Fast quantum logic gates with trapped-ion qubits
V. M. Schäfer, C. J. Ballance, K. Thirumalai, L. J. Stephenson, T. G. Ballance, A. M. Steane, D. M. Lucas
TL;DR
Fast gates require precise pulse-parameter control because large phase-space displacements break the underlying assumption. The paper uses controlled Raman-beam pulses and reports low gate errors, while radial-mode excitation constrains gates near 800 ns.
Problem
Large phase-space displacements necessary for fast gates break the underlying assumption, motivating precise control of pulse parameters.
Method
The approach uses precisely controlled Raman-beam pulse parameters, with light supplied by a frequency-doubled Ti:sapphire laser.
Results
0.22(3)% error was reported for the tg = 1.6 µs gate, while the lowest measured error after calibration was 0.15(3)%.
Takeaways & Limitations
Fast gates are insensitive to errors associated with motional decoherence or heating.
Takeaways & Limitations
Errors due to radial mode excitation are largest for gates around tg = 800 ns because the Raman beat note is close to radial-mode resonances.
Abstract
from arXiv · showhide
Quantum bits based on individual trapped atomic ions constitute a promising technology for building a quantum computer, with all the elementary operations having been achieved with the necessary precision for some error-correction schemes. However, the essential two-qubit logic gate used for generating quantum entanglement has hitherto always been performed in an adiabatic regime, where the gate is slow compared with the characteristic motional frequencies of ions in the trap, giving logic speeds of order 10kHz. There have been numerous proposals for performing gates faster than this natural "speed limit" of the trap. We implement the method of Steane et al., which uses tailored laser pulses: these are shaped on 10 ns timescales to drive the ions' motion along trajectories designed such that the gate operation is insensitive to optical phase fluctuations. This permits fast (MHz-rate) quantum logic which is robust to this important source of experimental error. We demonstrate entanglement generation for gate times as short as 480ns; this is less than a single oscillation period of an ion in the trap, and 8 orders of magnitude shorter than the memory coherence time measured in similar calcium-43 hyperfine qubits. The method's power is most evident at intermediate timescales, where it yields a gate error more than ten times lower than conventional techniques; for example, we achieve a 1.6 us gate with fidelity 99.8%. Still faster gates are possible at the price of higher laser intensity. The method requires only a single amplitude-shaped pulse and one pair of beams derived from a continuous-wave laser, and offers the prospect of combining the unrivalled coherence properties, operation fidelities and optical connectivity of trapped-ion qubits with the sub-microsecond logic speeds usually associated with solid state devices.
Numerical modelling
The study models fast trapped-ion gates beyond the Lamb-Dicke regime and uses numerical optimization to identify experimentally practical pulse sequences.
- Numerical modelling: Large phase-space displacements make field curvature relevant, so the Lamb-Dicke approximation breaks down and modifies the force and motional trajectory.The resulting dynamics include wavefunction squeezing.
- Numerical modelling: The full Hamiltonian is numerically integrated with a split-operator method while averaging over initial optical phases to model coherent gate error.
- Numerical modelling: Candidate pulse sequences are optimized from random seeds, screened for error below 10^-4 in the Lamb-Dicke approximation, and refined with the full solver.
- Numerical modelling: Low coherent error and low integrated pulse area select sequences that reduce photon scattering and avoid fragile large motional excitations.
- Numerical modelling: The seven-segment symmetric pulse shape provides enough parameters for dense good solutions while remaining easy to implement and verify.Its edge rise-time can vary from zero to the segment length without changing fidelity when the Rabi frequency is rescaled.
Raman beams
The Raman-beam system combines a frequency-doubled Ti:sapphire source with AOM-based amplitude shaping and phase-chirp mitigation for the gate pulses.
- Raman beams: The Raman beams originate from a frequency-doubled Ti:sapphire laser delivering 1.8 W at 397 nm.
- Raman beams: Shaped pulses are generated by a pair of AOMs, using an AWG for the stepped RF signal and a DDS source for the second AOM.The AOMs have a 24 ns rise time.
- Raman beams: Optical phase chirps become significant during RF-amplitude switching, but driving the AOM at 200 MHz minimizes their contribution to gate error.
Pulse calibration
Pulse calibration controls the shaped-gate parameters and verifies that theoretical settings can produce stable, high-fidelity optical pulses.
- Pulse calibration: Fast, high-fidelity gates require precise control of pulse parameters, including peak power, Raman beat-note frequency, and the final Ramsey π/2-pulse phase offset.The phase offset compensates for single-qubit phase acquired during the gate.
- Pulse calibration: Pulse-segment amplitudes were adjusted against photodiode measurements to match theoretically predicted optimum levels.The relative amplitudes were set with ±0.2% accuracy.
- Pulse calibration: Optical pulse timing precision was measured as 0.2 ns standard deviation of fitted pulse lengths.The AWG waveform used a 5.0 ns risetime to spread pulse edges across several time points.
- Pulse calibration: Theoretically predicted beat-note frequencies and beam powers were empirically optimized, with optimized values agreeing well with theory.
- Pulse calibration: After optical phase-chirp minimization, linear single-parameter optimization replaced the initially used Nelder-Mead procedure.
Experimental procedure
The experiment uses cooled 43Ca+ ions in a linear Paul trap and measures entanglement-gate errors through a Ramsey-interferometer protocol with partial tomography.
- Experimental procedure: The gates were performed in a blade-type linear Paul trap using 43Ca+ qubit states at a magnetic field of 14.6 mT.
- Experimental procedure: The axial frequency and ion spacing were configured to suppress radial-mode coupling while matching the travelling standing-wave periodicity.The spacing was 121/2λz, with λz = 283 nm.
- Experimental procedure: Ions were Doppler cooled to n̄ ≈ 1.8 and sideband cooled further to n̄ <∼ 0.05 before the gate experiment.
- Experimental procedure: An entangled state was created from |↓↓⟩ by placing the geometric phase gate in one arm of a spin-echo Ramsey interferometer.
- Experimental procedure: Gate errors were determined by partial tomography measuring the fidelity of the created state.
Error analysis
The error analysis identifies radial-mode excitation as the largest error near 800 ns, while motional heating and decoherence contribute negligibly to fast-gate errors. It also reports calibrated gate errors and experimental error checks.
- 0.15(3)% was the lowest measured error after calibrating experimental parameters.
- 0.28(3)% was the measured error after calibration, with uncertainties reported as statistical only.
- Concatenated sequences of up to 7 gates showed no evidence for coherent errors, and the main error sources were summarized for the lowest-error and fastest gates.
- ϵg < 5 × 10−2 at tg = 800 ns was achieved for radial-mode excitation errors with the final Raman-beam alignment.
- Motional decoherence and heating contribute negligibly to gate error despite an axial center-of-mass heating rate of approximately 100 s−1.
AUTHOR INFORMATION
The authors declare no competing financial interests and provide correspondence and request information.
- The authors declare no competing financial interests and provide correspondence and requests information.
DATA AVAILABILITY
The data supporting the paper’s plots and other findings are available from the corresponding author upon reasonable request.
- Data supporting the plots and other findings are available from the corresponding author upon reasonable request.