Errors in trapped-ion quantum gates due to spontaneous photon scattering

Ozeri, Roee; Itano, Wayne M.; Blakestad, R. B.; Britton, J.; Chiaverini, John; Jost, John D.; Langer, C.; Leibfried, D.; Reichle, R.; Seidelin, S.; Wesenberg, J. H.; Wineland, David J.

doi:10.1103/physreva.75.042329

Cited by 166 publications

(234 citation statements)

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“…The relatively light mass yields deeper traps and higher motional frequencies for given applied potentials, and facilitates fast ion transport [9,10]. Light mass also yields stronger laser-induced effective spin-spin coupling (inversely proportional to the mass), which can yield less spontaneous emission error for a given laser intensity [11]. However, a disadvantage of 9 Be + ion qubits compared to some heavier ions such as 40 Ca + and 43 Ca + [12,13] has been the difficulty of producing and controlling the ultraviolet (313 nm) light required to drive 9 Be + stimulated-Raman transitions.…”

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High-Fidelity Universal Gate Set forBe9+Ion Qubits

et al. 2016

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We report high-fidelity laser-beam-induced quantum logic gates on magnetic-field-insensitive qubits comprised of hyperfine states in 9 Be + ions with a memory coherence time of more than 1 s. We demonstrate single-qubit gates with error per gate of 3.8(1) × 10 −5 . By creating a Bell state with a deterministic two-qubit gate, we deduce a gate error of 8(4) × 10 −4 . We characterize the errors in our implementation and discuss methods to further reduce imperfections towards values that are compatible with fault-tolerant processing at realistic overhead.Quantum computers can solve certain problems that are thought to be intractable on conventional computers. An important general goal is to realize universal quantum information processing (QIP), which could be used for algorithms having a quantum advantage over processing with conventional bits as well as to simulate other quantum systems of interest [1][2][3]. For large problems, it is generally agreed that individual logic gate errors must be reduced below a certain threshold, often taken to be around 10 −4 [4][5][6], to achieve fault tolerance without excessive overhead in the number of physical qubits required to implement a logical qubit. This level has been achieved in some experiments for all elementary operations including state preparation and readout, with the exception of two-qubit gates, emphasizing the importance of improving multi-qubit gate fidelities. [7,8]. As various ions differ in mass, electronic, and hyperfine structure, they each have technical advantages and disadvantages. For example, 9 Be + is the lightest ion currently considered for QIP, and as such, has several potential advantages. The relatively light mass yields deeper traps and higher motional frequencies for given applied potentials, and facilitates fast ion transport [9,10]. Light mass also yields stronger laser-induced effective spin-spin coupling (inversely proportional to the mass), which can yield less spontaneous emission error for a given laser intensity [11]. However, a disadvantage of 9 Be + ion qubits compared to some heavier ions such as 40 Ca + and 43 Ca + [12, 13] has been the difficulty of producing and controlling the ultraviolet (313 nm) light required to drive 9 Be + stimulated-Raman transitions. In the work reported here, we use an ion trap array designed for scalable QIP [14] and take advantage of recent technological developments with lasers and optical fibers that improve beam quality and pointing stability. We also implement active control of laser pulse intensities to re- duce errors. We demonstrate laser-induced single-qubit computational gate errors of 3.8(1) × 10 −5 and realize a deterministic two-qubit gate to ideally produce the Bell state |Φ + = 1 √ 2 (|↑↑ + |↓↓ ). By characterizing the effects of known error sources with numerical simulations and calibration measurements, we deduce an entangling gate infidelity or error of = 8(4) × 10 −4 , where = 1 -F, and F is the fidelity. Along with Ref.[13]; these appear to be the highest two-qubit gate fidelitie...

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High-Fidelity Universal Gate Set forBe9+Ion Qubits

et al. 2016

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“…During the sideband cooling process, ions experience recoil from both Raman and repumping pulses. The recoil heating due to Raman beams arises from transitions through the | 2 P 3/2 excited states [26]. The heating rate due to Raman scattering is estimated to be < 10 −4 quanta/µs for each motional mode [21], both theoretically and via calibration experiments on a single 25 Mg + for a given Raman beam intensity [27].…”

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“…The heating rate due to Raman scattering is estimated to be < 10 −4 quanta/µs for each motional mode [21], both theoretically and via calibration experiments on a single 25 Mg + for a given Raman beam intensity [27]. The Rayleigh scattering rate due to the Raman beams is estimated to be 50 % of the Raman scattering rate [26]. The resulting heating is independent of the frequency difference between Raman beams and all motional modes will heat each time the Raman beams are applied to the ions.…”

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Sympathetic Ground State Cooling and Time-Dilation Shifts in an Al27+ Optical Clock

et al. 2017

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We report on Raman sideband cooling of 25 Mg + to sympathetically cool the secular modes of motion in a 25 Mg + -27 Al + two-ion pair to near the three-dimensional (3D) ground state. The evolution of the Fock-state distribution during the cooling process is studied using a rate-equation simulation, and various heating sources that limit the efficiency of 3D sideband cooling in our system are discussed. We characterize the residual energy and heating rates of all of the secular modes of motion and estimate a secular motion time-dilation shift of −(1.9 ± 0.1) × 10 −18 for an 27 Al + clock at a typical clock probe duration of 150 ms. This is a 50-fold reduction in the secular motion time-dilation shift uncertainty in comparison with previous 27 Al + clocks. Trapped and laser-cooled ions are useful for many applications in quantum information processing and quantum metrology because of their isolation from the ambient environment and mutual Coulomb interaction [1][2][3][4][5][6]. The Coulomb interaction establishes normal modes of motion, called secular modes, which enable information exchange and entanglement between ions. For many operations in quantum information processing and metrology, these secular modes should ideally be prepared in their ground state. For example, in state-of-the-art trapped-ion optical clocks [7], uncertainty in the Doppler shift due to the residual excitation of these modes is a dominant contribution to the total clock uncertainty [8][9][10].All trapped-ion optical clocks to date have been operated with the ions' motion near the Doppler cooling limit [7][8][9][10]. For clocks based on quantum-logic spectroscopy of the 1 S 0 ↔ 3 P 0 transition in 27 Al + [11], the smallest uncertainty has been achieved by performing continuous sympathetic Doppler cooling on the logic ion ( 25 Mg + ) during the clock interrogation [8]. Due to the difficulty of performing accurate temperature measurements of trapped ions near the Doppler cooling limit, the uncertainty of the secular motion temperature was limited to 30 % [8].To reduce the secular motion time-dilation shift and its uncertainty, sub-Doppler cooling techniques can be employed [12][13][14][15][16][17]. These schemes have not previously been implemented in ion-based clock experiments due to high ambient motional heating rates, the need for extra cooling laser beams, and the difficulty of characterizing the resulting motional state distribution, which can be nonthermal [8,10,18]. For example, in sideband cooling, a non-thermal distribution can result from zero-crossings in the cooling transition Rabi rate as a function of the Fock state [19,20] and from cooling durations insufficient to reach equilibrium. Although sideband cooling can reach extremely low energies, a small non-thermal component of the distribution may contribute more than 90 % of the total energy [21], rendering the temperature measurement technique using motional sideband ratios unsuitable for determining the energy [12,13].Here we demonstrate sympathetic cooling of a 25 Mg + -27 ...

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“…During the sideband cooling process, ions experience recoil from both Raman and repumping pulses. The recoil heating due to Raman beams arises from transitions through the j 2 P 3=2 i excited states [31]. The heating rate due to Raman scattering is estimated to be <10 −4 quanta=μs for each motional mode [21], both theoretically and via calibration experiments on a single 25 Mg þ for a given Raman beam intensity [32].…”

mentioning

confidence: 99%

“…The heating rate due to Raman scattering is estimated to be <10 −4 quanta=μs for each motional mode [21], both theoretically and via calibration experiments on a single 25 Mg þ for a given Raman beam intensity [32]. The Rayleigh scattering rate due to the Raman beams is estimated to be 50% of the Raman scattering rate [31]. The resulting heating is independent of the frequency difference between Raman beams, and all motional modes will heat each time the Raman beams are applied to the ions.…”

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confidence: 99%

Trapped Ions Stopped Cold

Huntemann

2017

Physics

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We report on Raman sideband cooling of 25 Mg þ to sympathetically cool the secular modes of motion in a 25 Mg þ -27 Al þ two-ion pair to near the three-dimensional (3D) ground state. The evolution of the Fock-state distribution during the cooling process is studied using a rate-equation simulation, and various heating sources that limit the efficiency of 3D sideband cooling in our system are discussed. We characterize the residual energy and heating rates of all of the secular modes of motion and estimate a secular motion time-dilation shift of −ð1.9 AE 0.1Þ × 10 −18 for an 27 Al þ clock at a typical clock probe duration of 150 ms. This is a 50-fold reduction in the secular motion time-dilation shift uncertainty in comparison with previous 27 Al þ clocks. DOI: 10.1103/PhysRevLett.118.053002 Trapped and laser-cooled ions are useful for many applications in quantum information processing and quantum metrology because of their isolation from the ambient environment and the mutual Coulomb interaction [1][2][3][4][5][6]. The Coulomb interaction establishes normal modes of motion, called secular modes, which enable information exchange and entanglement between ions. For many operations in quantum information processing and metrology, these secular modes should, ideally, be prepared in their ground state. For example, in state-of-the-art trappedion optical clocks [7], uncertainty in the Doppler shift due to the residual excitation of these modes is a dominant contribution to the total clock uncertainty [8][9][10].All trapped-ion optical clocks to date have been operated with the ions' motion near the Doppler cooling limit [7][8][9][10]. For clocks based on quantum-logic spectroscopy of the 1 S 0 ↔ 3 P 0 transition in 27 Al þ [11], the smallest uncertainty has been achieved by performing continuous sympathetic Doppler cooling on the logic ion ( 25 Mg þ ) during the clock interrogation [8]. Because of the difficulty of performing accurate temperature measurements of trapped ions near the Doppler cooling limit, the uncertainty of the secular motion temperature was limited to 30% [8].To reduce the secular motion time-dilation shift and its uncertainty, sub-Doppler cooling techniques can be employed [12][13][14][15][16][17]. These schemes have not previously been implemented in ion-based clock experiments due to high ambient motional heating rates, the need for extra cooling laser beams, and the difficulty of characterizing the resulting motional state distribution, which can be nonthermal [8,10,18]. For example, in sideband cooling, a nonthermal distribution can result from zero crossings in the cooling transition Rabi rate as a function of the Fock state [19,20] and from cooling durations insufficient to reach equilibrium. Although sideband cooling can reach extremely low energies, a small nonthermal component of the distribution may contribute more than 90% of the total energy [21], rendering the temperature measurement technique using motional sideband ratios unsuitable for determining the energy [12,13].Here, we dem...

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Errors in trapped-ion quantum gates due to spontaneous photon scattering

Cited by 166 publications

References 57 publications

High-Fidelity Universal Gate Set forBe9+Ion Qubits

High-Fidelity Universal Gate Set forBe9+Ion Qubits

Sympathetic Ground State Cooling and Time-Dilation Shifts in an Al27+ Optical Clock

Trapped Ions Stopped Cold

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