Error compensation of single-qubit gates in a surface-electrode ion trap using composite pulses

Abstract

The fidelity of laser-driven quantum logic operations on trapped ion qubits tend to be lower than microwavedriven logic operations due to the difficulty of stabilizing the driving fields at the ion location. Through stabilization of the driving optical fields and use of composite pulse sequences, we demonstrate high-fidelity single-qubit gates for the hyperfine qubit of a 171 Yb + ion trapped in a microfabricated surface-electrode ion trap. Gate error is characterized using a randomized benchmarking protocol and an average error per randomized Clifford group gate of 3.6(3) × 10 −4 is measured. We also report experimental realization of palindromic pulse sequences that scale efficiently in sequence length. The trapped atomic ion qubits feature desirable properties for use in a quantum computer such as long coherence times [1], high-fidelity qubit measurement [2], and universal logic gates [3]. The quality of quantum logic gate operations on trapped ion qubits has been limited by the stability of the control fields at the ion location used to implement the gate operations. For this reason, the logic gates utilizing microwave fields [4][5][6][7] have shown gate fidelities several orders of magnitude better than those using laser fields [8][9][10]. The laser beams used to drive either Raman gates for a hyperfine ion qubit or optical gates between metastable qubit states are subject to severe wave-front distortion in air due to turbulence, leading to amplitude and phase fluctuations of the optical field at the ion location that limited the gate fidelity in the 0.5% range [8,11].Microfabricated surface-electrode ion traps, where atomic ions are trapped above a two-dimensional surface of electrodes, can provide a scalable platform on which to build an ion-based quantum computer [12,13]. Experiments using surface traps have demonstrated coherence times of more than 1 s [14], state detection with fidelities greater than 99.9% [2], and low-error single-qubit gates [ 2.0(2) × 10 −5 ] using integrated microwave waveguides [4,7]. Use of high-power UV lasers close to the trap surface can lead to substantial charging due to unwanted exposure [15]. The recent development of single-mode fibers capable of delivering high-power UV laser beams [16] opens the possibility of significantly reducing the free-space UV beam path length and delivering a clean spatial mode to the ions, eliminating unwanted scattering off nearby trap structures.Here we demonstrate low-error single-qubit gates performed using stimulated Raman transitions on an ion qubit trapped in a microfabricated chip trap. Gate errors are measured using a randomized benchmarking protocol [8,17,18], where amplitude error in the control beam is compensated using various pulse sequence techniques [19,20]. Using B2 compensation [19], we demonstrate single-qubit gates with an average error per randomized Clifford group gate of 3.6(3) × 10 −4 . We also show that compact palindromic pulse compensation sequences (PDn) [20] compensate for amplitude errors as designed. Two hyperfin...

Co-designing a scalable quantum computer with trapped atomic ions

“…8,110 These small error-correcting procedures only require 17-25 total ions per logical qubit to generate fault-tolerant circuits that can have error thresholds near 10 − 3 . This error rate is compatible with the best current ion trap gates and measurements 20,25,26,[64][65][66] , and the whole procedure can easily fit within a single ELU. These small codes are only guaranteed to correct single errors, so the total number of reliable, but non-universal, operations on many logical qubits will scale as the error threshold divided by the square of the physical error per operation.…”

“…61 The design and fabrication of complex surface traps using silicon microfabrication processes has now matured, with examples of the Sandia high-optical access (HOA) trap 62 and the GTRI/Honeywell ball-grid array (BGA) trap 63 shown in Figure 3. Recent experiments have demonstrated high-performance qubit measurement 20 and single-qubit quantum gates [64][65][66] in such microfabricated surface traps that outperform conventional manually assembled macroscopic traps. The ability to design and simulate the electromagnetic trapping parameters prior to fabrication provides an attractive path to developing complex trap structures that are both repeatable and produced with high yield.…”

Detection of motional ground state population of a trapped ion using delayed pulses

“…The effect of undesired frequency components in square-shaped pulses has previously been reduced by employing amplitude-shaped pulses with a smooth rising and falling slope [13][14][15]. Furthermore, composite pulses, first developed in the context of nuclear magnetic resonance [16][17][18], are used in trapped ion systems to implement complex algorithms [19,20] or operations that are less sensitive to variations of the experimental parameters [21][22][23][24].…”

Simulating the performance of a distance-3 surface code in a linear ion trap

“…For this study, information will be stored in the hyperfine 'clock' states of 171 Yb + . While single-qubit operations in this system have displayed error rates below the surface code pseudothreshold [54,55] reported from Tomita and Svore [28], two-qubit gate fidelities are limited by a number of factors including spontaneous Raman scattering during gates and residual entanglement between the internal state and the motional modes of the ion. Compensation pulses have been developed with a predicted error rate due to scattering of 10 −4 [56] and control sequences have been implemented exhibiting single-and two-qubit gate fidelities of 99.9% using the hyperfine ground states of trapped 9 Be + [52] and 43 Ca + [51] ions, respectively.…”