Non-invasive mid-circuit measurement and reset on atomic qubits

Abstract

Mid-circuit measurement and reset of subsets of qubits is a crucial ingredient of quantum error correction and many quantum information applications. Measurement of atomic qubits is accomplished through resonant fluorescence, which typically disturbs neighboring atoms due to photon scattering. We propose and prototype a new scheme for measurement that provides both spatial and spectral isolation by using tightly-focused individual laser beams and narrow atomic transitions. The unique advantage of this scheme is that all operations are applied exclusively to the read-out qubit, with negligible disturbance to the other qubits of the same species and little overhead. In this letter, we pave the way for non-invasive and high fidelity mid-circuit measurement and demonstrate all key building blocks on a single trapped barium ion.

Figures (9)

• Figure 1: Proposed mid-circuit measurement and reset (MCMR) scheme in the atomic $^{138}$Ba$^+$ system. (a) Individual-addressing laser beams (at 532 nm for Ba$^+$, for example) conventionally drive stimulated Raman transitions and entangling gate operations MSInlek2017. (b) Beam layout for executing coherent quantum gates and dissipative mid-circuit operations. MCMR uses the same individual addressing 532 nm beams in (a) but now for Stark shifting selected auxiliary qubits during operations performed by the other global beams. (c-e) Sequence of qubit control for mid-circuit operations in $^{138}$Ba$^+$. Ground state qubit levels are Stark shifted by $\delta_{AC}$, with a smaller shift of the $D$ levels (not shown). Selective shelving, measurement, and reset operations are programmed by using the particular beams to shift levels and drive transitions as indicated.
• Figure 2: Measurement and reset experimental results (a) Histogram of 493 nm fluorescence counts from detection using MCMR light with a $1.5(2)$ MHz Stark shift. Detection fidelities of the dark and bright ion states are $98.6(4) \%$ and $97.0(5) \%$, respectively. Inset: As we increase the Stark shift, the ion state detection fidelity decreases due to 532 nm power instability. (b) Population in $\vert{0}\rangle$ during reset with a 2.6(3) MHz Stark shift (Fig.\ref{['fig:mcmrscheme']}e). The solid blue line is an exponential decay fit with $\tau_r=47~\mu$s. The reset fidelity saturates at the level of fidelity for 1762 nm electron shelving, $99.7(2) \%$ (orange dashed line). All error bars are derived using the standard deviation of a binomial distribution, where each point has 1000 shots.
• Figure 3: Time evolution of Ramsey fringe contrast on the 1762 nm transition, indicative of the data qubit coherence during MCMR. The blue circles serve as a baseline without MCMR light. The measurement is repeated with MCMR light on during the Ramsey delay time at two detunings of 2052 nm, 3.6 MHz (solid red squares) and 12 MHz (solid orange triangles). The empty red squares show the 3.6 MHz result without Blackman (BM) pulse shaping. The reported coherence times are from experimental fits to the data. With only 12 MHz Stark shift, decoherence is indistinguishable from the baseline. All error bars are derived using the standard deviation of a binomial distribution, where each point has 200 shots.
• Figure 4: Calculated errors for a $^{138}$Ba$^+$ ground state data qubit during MCMR operations as a function of 532 nm laser intensity ($\Omega_{2052}=2\pi\times2~$MHz, $T_\textrm{MCMR}=500~\mu$s). Dashed blue curve is photon absorption from neighboring auxiliary qubit emission at a distance of $d=4$$\mu$m; dotted blue curve is scattering from global MCMR beams; the solid blue curve is their sum, or the total error. Higher fidelity can be achieved by shortening the detection time with state-of-the-art detection techniques crain2019high, with the total error for $T_\textrm{MCMR}=36~\mu$s shown in the red curve.
• Figure 5: AC Stark shift of $^{138}$Ba$^+$. The external B field used here is 4.1 Gauss, which creates 4.59 MHz Zeeman splitting when there's no Stark shift. The zero energy is defined when both shifts are absent.