Quantum gates are typically vulnerable to imperfections in the classical control fields applied to physical qubits to drive the gates. One approach to reduce this source of error is to break the gate into parts, known as textit{composite pulses} (CPs
), that typically leverage the constancy of the error over time to mitigate its impact on gate fidelity. Here we extend this technique to suppress textit{secular drifts} in Rabi frequency by regarding them as sums of textit{power-law drifts} whose first-order effects on over- or under-rotation of the state vector add linearly. We show that composite pulses that suppress the power-law drifts $t^p$ for all $p leq n$ are also high-pass filters of textit{filter order} $n+1$ cite{ball_walsh-synthesized_2015}. We present sequences that satisfy our proposed textit{power law amplitude} $text{PLA}(n)$ criteria, obtained with this technique, and compare their simulated performance under time-dependent amplitude errors to some traditional composite pulse sequences. We find that there is a range of noise frequencies for which the $text{PLA}(n)$ sequences provide more error suppression than the traditional sequences, but in the low frequency limit, non-linear effects become more important for gate fidelity than frequency roll-off. As a result, the previously known $F_1$ sequence, which is one of the two solutions to the $text{PLA}(1)$ criteria and furnishes suppression of both linear secular drift and the first order nonlinear effects, is a better noise filter than any of the other $text{PLA}(n)$ sequences in the low frequency limit.
Internal states of polar molecules can be controlled by microwave-frequency electric dipole transitions. If the applied microwave electric field has a spatial gradient, these transitions also affect the motion of these dipolar particles. This capabil
ity can be used to engineer phonon-mediated quantum gates between e.g. trapped polar molecular ion qubits without laser illumination and without the need for cooling near the motional ground state. The result is a high-speed quantum processing toolbox for dipoles in thermal motion that combines the precision microwave control of solid-state qubits with the long coherence times of trapped ion qubits.
High quality, fully-programmable quantum processors are available with small numbers (<1000) of qubits, and the scientific potential of these near term machines is not well understood. If the small number of physical qubits precludes practical quantu
m error correction, how can these error-susceptible processors be used to perform useful tasks? We present a strategy for developing quantum error detection for certain gate imperfections that utilizes additional internal states and does not require additional physical qubits. Examples for adding error detection are provided for a universal gate set in the trapped ion platform. Error detection can be used to certify individual gate operations against certain errors, and the irreversible nature of the detection allows a result of a complex computation to be checked at the end for error flags.
Hyperfine structure (HFS) of atomic energy levels arises due to interactions of atomic electrons with a hierarchy of nuclear multipole moments, including magnetic dipole, electric quadrupole and higher rank moments. Recently, a determination of the m
agnetic octupole moment of the $^{173}mathrm{Yb}$ nucleus was reported from HFS measurements in neutral ${}^{173}mathrm{Yb}$ [PRA 87, 012512 (2013)], and is four orders of magnitude larger than the nuclear theory prediction. Considering this substantial discrepancy between the spectroscopically extracted value and nuclear theory, here we propose to use an alternative system to resolve this tension, a singly charged ion of the same $^{173}mathrm{Yb}$ isotope. Utilizing the substantial suite of tools developed around $mathrm{Yb}^+$ for quantum information applications, we propose to extract nuclear octupole and hexadecapole moments from measuring hyperfine splittings in the extremely long lived first excited state ($4f^{13}(^2!F^{o})6s^2$, $J=7/2$) of $^{173}mathrm{Yb}^+$. We present results of atomic structure calculations in support of the proposed measurements.
The interaction between the electric dipole moment of a trapped molecular ion and the configuration of the confined Coulomb crystal couples the orientation of the molecule to its motion. We consider the practical feasibility of harnessing this intera
ction to initialize, process, and read out quantum information encoded in molecular ion qubits without optically illuminating the molecules. We present two schemes wherein a molecular ion can be entangled with a co-trapped atomic ion qubit, providing, among other things, a means for molecular state preparation and measurement. We also show that virtual phonon exchange can significantly boost range of the intermolecular dipole-dipole interaction, allowing strong coupling between widely-separated molecular ion qubits.
The Standard Model (SM) of particle physics fails to explain dark matter and why matter survived annihilation with antimatter following the Big Bang. Extensions to the SM, such as weak-scale Supersymmetry, may explain one or both of these phenomena b
y positing the existence of new particles and interactions that are asymmetric under time-reversal (T). These theories nearly always predict a small, yet potentially measurable ($10^{-27}$-$10^{-30}$ $e$ cm) electron electric dipole moment (EDM, $d_e$), which is an asymmetric charge distribution along the spin ($vec{S}$). The EDM is also asymmetric under T. Using the polar molecule thorium monoxide (ThO), we measure $d_e = (-2.1 pm 3.7_mathrm{stat} pm 2.5_mathrm{syst})times 10^{-29}$ $e$ cm. This corresponds to an upper limit of $|d_e| < 8.7times 10^{-29}$ $e$ cm with 90 percent confidence, an order of magnitude improvement in sensitivity compared to the previous best limits. Our result constrains T-violating physics at the TeV energy scale.
We measure and theoretically determine the effect of molecular rotational splitting on Zeeman relaxation rates in collisions of cold Triplet-Sigma molecules with helium atoms in a magnetic field. All four stable isotopomers of the imidogen (NH) molec
ule are magnetically trapped and studied in collisions with 3He and 4He. The 4He data support the predicted inverse square dependence of the collision induced Zeeman relaxation rate coefficient on the molecular rotational constant B. The measured 3He rate coefficients are much larger than 4He and depend less strongly on B, and the theoretical analysis indicates they are strongly affected by a shape resonance. The results demonstrate the influence of molecular structure on collisional energy transfer at low temperatures.
We observe magnetic trapping of atomic nitrogen (14^N) and cotrapping of ground state imidogen (14^NH, X-triplet-Sigma-). Both are loaded directly from a room temperature beam via buffer gas cooling. We trap approximately 1 * 10^11 14^N atoms at a pe
ak density of 5 * 10^11 cm^-3 at 550 mK. The 12 +5/-3 s 1/e lifetime of atomic nitrogen in the trap is limited by elastic collisions with the helium buffer gas. Cotrapping of 14^N and 14^NH is accomplished, with 10^8 NH trapped molecules at a peak density of 10^8 cm^-3. We observe no spin relaxation of nitrogen in collisions with helium.
The v = 1 -> 0 radiative lifetime of NH (X triplet-Sigma-, v=1,N=0) is determined to be tau_rad,exp. = 37.0 +/- 0.5 stat +2.0 / -0.8 sys miliseconds, corresponding to a transition dipole moment of |mu_10| = 0.0540 + 0.0009 / -0.0018 Debye. To achieve
the long observation times necessary for direct time-domain measurement, vibrationally excited NH (X triplet-Sigma-, v=1,N=0) radicals are magnetically trapped using helium buffer-gas loading. Simultaneous trapping and lifetime measurement of both the NH(v=1, N=0) and NH(v=0,N=0) populations allows for accurate extraction of tau_rad,exp. Background helium atoms are present during our measurement of tau_rad,exp., and the rate constant for helium atom induced collisional quenching of NH(v=1,N=0) was determined to be k_q < 3.9 * 10^-15 cm^3/s. This bound on k_q yields the quoted systematic uncertainty on tau_rad,exp. Using an ab initio dipole moment function and an RKR potential, we also determine a theoretical value of 36.99 ms for this lifetime, in agreement with our experimental value. Our results provide an independent determination of tau_rad,10, test molecular theory, and furthermore demonstrate the efficacy of buffer-gas loading and trapping in determining metastable radiative and collisional lifetimes.
Imidogen (NH) radicals are magnetically trapped and their Zeeman relaxation and energy transport collision cross sections with helium are measured. Continuous buffer-gas loading of the trap is direct from a room-temperature molecular beam. The Zeeman
relaxation (inelastic) cross section of magnetically trapped electronic, vibrational and rotational ground state imidogen in collisions with He-3 is measured to be 3.8 +/- 1.1 E-19 cm^2 at 710 mK. The NH-He energy transport cross section is also measured, indicating a ratio of diffusive to inelastic cross sections of gamma = 7 E4 in agreement with the recent theory of Krems et al. (PRA 68 051401(R) (2003))
