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arXiv:1803.02545 · Physical Review A

Comparing Zeeman qubits to hyperfine qubits in the context of the surface code: Yb+174 and Yb+171

Natalie C. Brown, Kenneth R. Brown

Published May 2, 2018• 36 citations
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Abstract

Many systems used for quantum computing possess additional states beyond those defining the qubit. Leakage out of the qubit subspace must be considered when designing quantum error correction codes. Here we consider trapped ion qubits manipulated by Raman transitions. Zeeman qubits do not suffer from leakage errors but are sensitive to magnetic fields to first order. Hyperfine qubits can be encoded in clock states that are insensitive to magnetic fields to first order, but spontaneous scattering during the Raman transition can lead to leakage. Here we compare a Zeeman qubit ($^{174}\mathrm{Yb}^{+}$) to a hyperfine qubit ($^{171}\mathrm{Yb}^{+}$) in the context of the surface code. We find that the number of physical qubits required to reach a specific logical qubit error can be reduced by using $^{174}\mathrm{Yb}^{+}$ if the magnetic field can be stabilized with fluctuations smaller than $10\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{G}$.

DOI
10.1103/physreva.97.052301

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Many systems used for quantum computing possess additional states beyond those defining the qubit. Leakage out of the qubit subspace must be considered when designing quantum error correction codes. Here we consider trapped ion qubits manipulated by Raman transitions. Zeeman qubits do not suffer from leakage errors but are sensitive to magnetic fields to first order. Hyperfine qubits can be encoded in clock states that are insensitive to magnetic fields to first order, but spontaneous scattering during the Raman transition can lead to leakage. Here we compare a Zeeman qubit (174Yb+^{174}\mathrm{Yb}^{+}174Yb+) to a hyperfine qubit (171Yb+^{171}\mathrm{Yb}^{+}171Yb+) in the context of the surface code. We find that the number of physical qubits required to reach a specific logical qubit error can be reduced by using 174Yb+^{174}\mathrm{Yb}^{+}174Yb+ if the magnetic field can be stabilized with fluctuations smaller than 10\ensuremathμG10\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{G}10\ensuremathμG.
Leakage errors take qubits out of the computational subspace and will accumulate if not addressed. A leaked qubit will reduce the effectiveness of quantum error correction protocols due to the cost of implementing leakage reduction circuits and the harm caused by interacting leaked states with qubit states. Ion trap qubits driven by Raman gates have a natural choice between qubits encoded in magnetically insensitive hyperfine states that can leak and qubits encoded in magnetically sensitive Zeeman states of the electron spin that cannot leak. In our previous work, we compared these two qubits in the context of the toric code with a depolarizing leakage error model and found that for magnetic-field noise with a standard deviation less than 32 $\ensuremath{\mu}\mathrm{G}$ that the 174Yb+^{174}\mathrm{Yb}^{+}174Yb+ Zeeman qubit outperforms the 171Yb+^{171}\mathrm{Yb}^{+}171Yb+ hyperfine qubit. Here we examine a physically motivated leakage error model based on ions interacting via the M\o{}lmer-S\o{}renson gate. We find that this greatly improves the performance of hyperfine qubits but the Zeeman qubits are more effective for magnetic-field noise with a standard deviation less than 10 $\ensuremath{\mu}\mathrm{G}$. At these low magnetic fields, we find that the best choice is a mixed qubit scheme where the hyperfine qubits are the syndrome qubits and the leakage is handled without the need of an additional leakage reduction circuit.
Quantum processors and atomic clocks based on trapped ions often utilize an ion's hyperfine transition as the qubit state or frequency reference, respectively. These states are a good choice because they are insensitive in first order to magnetic field fluctuations, leading to long coherence times and stable frequency splittings. In trapped ions, however, these states are still subject to the second order AC Zeeman effect due to the necessary presence of an oscillating magnetic field used to confine the ions in a Paul trap configuration. Here, we measure the frequency shift of the 2S1/2 hyperfine transition of a 171Yb+ ion caused by the radio frequency (RF) electromagnetic field used to create confinement in several microfabricated surface trap designs. By comparing different trap designs, we show that two key design modifications significantly reduce the AC Zeeman effect experienced by the ion: (1) an RF ground layer routed directly below the entire RF electrode, and (2) a symmetric RF electrode. Both of these changes lead to better cancellation of the AC magnetic field and, thus, overall reduced frequency shifts due to the AC Zeeman effect and reduced variation across the device. These improvements enable a more homogeneous environment for quantum computing and can reduce errors for precision applications such as atomic clocks.
We demonstrate the use of trapped ytterbium ions as quantum bits for quantum information processing. We implement fast, efficient state preparation and state detection of the first-order magnetic field-insensitive hyperfine levels of 171Yb+^{171}\mathrm{Yb}^{+}171Yb+, with a measured coherence time of 2.5s2.5\phantom{\rule{0.3em}{0ex}}\mathrm{s}2.5s. The high efficiency and high fidelity of these operations is accomplished through the stabilization and frequency modulation of relevant laser sources.
Population leakage outside the qubit subspace presents a particularly harmful source of error that cannot be handled by standard error correction methods. Using a trapped 171Yb+^{171}{\mathrm{Yb}}^{+}171Yb+ ion, we demonstrate an optical pumping scheme to suppress leakage errors in atomic hyperfine qubits. The selection rules and narrow linewidth of a quadrupole transition are used to selectively pump population out of leakage states and back into the qubit subspace. Each pumping cycle reduces the leakage population by a factor of $\ensuremath{\sim}3$, allowing for an exponential suppression in the number of cycles. We use interleaved randomized benchmarking on the qubit subspace to show that this pumping procedure has negligible side effects on the qubit subspace, bounding the induced qubit memory error by $\ensuremath{\le}2.0(8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{per}$ cycle, and qubit population decay to $\ensuremath{\le}1.4(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\text{ }\text{ }\mathrm{per}$ cycle. These results clear a major obstacle for implementations of quantum error correction and error mitigation protocols.
In some quantum computing architectures, entanglement of an arbitrary number of qubits can be generated in a single operation. This property has many potential applications, and may specifically be useful for quantum error correction (QEC). Stabilizer measurements can then be implemented using a single multiqubit gate instead of several two-qubit gates, thus reducing circuit depth. In this study, the toric code is used as a benchmark to compare the performance of two-qubit and five-qubit gates within parity-check circuits. We consider trapped ion qubits that are controlled via Raman transitions, where the primary source of error is assumed to be spontaneous photon scattering. We show that a five-qubit M\o{}lmer-S\o{}rensen gate offers an approximately 4040%40 improvement over two-qubit gates in terms of the fault tolerance threshold. This result indicates an advantage of using multiqubit gates in the context of QEC.
Trapped-ion qubits are among the most promising candidates for quantum computing, quantum information processing, and quantum simulation. In general, trapped ions are considered to have sufficiently long coherence times, which are mainly characterized under laser-free conditions. However, in reality, essential laser fields for quantum manipulation introduce residual light shift, which seriously degrades the coherence due to power fluctuations. Here, we present a comprehensive study of ac Stark shifts in the hyperfine energy levels of the Yb + 171 ion, revealing an asymmetric light shift between two circular polarizations in the clock qubit and pronounced vector light shifts in the Zeeman qubits. By precisely tuning these polarizations, a remarkable enhancement in coherence time is observed, reaching over a 100-fold for the clock qubit and more than 10-fold for the Zeeman qubits, when comparing conditions of maximum and minimum shifts. These findings advance the practical realization of scalable trapped-ion quantum processors, enabling deep quantum circuit execution and long-duration adiabatic operations.