Building a fault-tolerant quantum computer requires more than improving physical hardware in isolation. Hardware-level design choices must be guided by the architecture of the full quantum computer and by the bottlenecks that ultimately limit its performance. The 133Ba+ ion is well suited for this kind of architecture-driven optimization. Its simple nuclear spin structure, with I = 1/2, enables fast, high-fidelity state preparation and measurement (SPAM). We leverage this advantage to demonstrate record SPAM fidelity, along with a state-preparation time more than three orders of magnitude faster than previous record-level SPAM demonstrations. This makes 133Ba+ especially promising as a reusable ancilla qubit for quantum error correction.The long-lived D5/2 state, with τ = 30 s, also makes 133Ba+ uniquely positioned to take advantage of the optical-metastable-ground (OMG) qubit protocol, which enables same-species sympathetic cooling. Within this protocol, we demonstrate a magic polarization condition that allows global gates with 532 nm light to be applied in one qubit subspace while leaving other subspaces largely unaffected. We also demonstrate stimulated Raman gates in both the ground and metastable qubit subspaces with errors below the fault-tolerance threshold, supported by a direct measurement of the spontaneous Raman scattering rate. The main practical drawback of 133Ba+ is its radioactivity. Here, we mitigate this challenge by demonstrating ion loading from a 133Ba target below the Nuclear Regulatory Commission exempt quantity of 10 µCi. This is enabled by a new autoionization loading scheme that substantially reduces loading times for barium ions.
Tips and Tricks for Building a Quantum Computer with 133Ba+
Building a fault-tolerant quantum computer requires more than improving physical hardware in isolation. Hardware-level design choices must be guided by the architecture of the full quantum computer and by the bottlenecks that ultimately limit its performance. The 133Ba+ ion is well suited for this kind of architecture-driven optimization. Its simple nuclear spin structure, with I = 1/2, enables fast, high-fidelity state preparation and measurement (SPAM). We leverage this advantage to demonstrate record SPAM fidelity, along with a state-preparation time more than three orders of magnitude faster than previous record-level SPAM demonstrations. This makes 133Ba+ especially promising as a reusable ancilla qubit for quantum error correction.The long-lived D5/2 state, with τ = 30 s, also makes 133Ba+ uniquely positioned to take advantage of the optical-metastable-ground (OMG) qubit protocol, which enables same-species sympathetic cooling. Within this protocol, we demonstrate a magic polarization condition that allows global gates with 532 nm light to be applied in one qubit subspace while leaving other subspaces largely unaffected. We also demonstrate stimulated Raman gates in both the ground and metastable qubit subspaces with errors below the fault-tolerance threshold, supported by a direct measurement of the spontaneous Raman scattering rate. The main practical drawback of 133Ba+ is its radioactivity. Here, we mitigate this challenge by demonstrating ion loading from a 133Ba target below the Nuclear Regulatory Commission exempt quantity of 10 µCi. This is enabled by a new autoionization loading scheme that substantially reduces loading times for barium ions.
Trapped-ion systems are leading candidates for quantum computing, offering long coherence times and high-fidelity gate operations. Scaling them, however, requires advanced capabilities such as mid-circuit measurement, qubit reset, and cooling, which together enable quantum error correction. One approach is the use of mixed qubit types, for example employing different ion species for cooling and computation. Recently, the omg blueprint [1] has gained attention as a method for coherently converting between qubit types within a single ion species, removing the overhead of mixed-species architectures while retaining their flexibility. In this thesis, we realise mixed qubit types in 137Ba+ using optical and metastable qubits. We demonstrate coherent control of both, as well as their coherent interconversion, achieving error rates at the 10−4 level suitable for NISQ applications. To enable selective control in multi-ion chains, we integrate a novel photonic chip for individual addressing of Raman beams [2]. We achieve cross-talk levels at or below 10−3 across all zones, and as low as 10−5 in some cases, establishing the scalability of our approach. Building on this, we present a new protocol for heralded state preparation and measurement (SPAM) [3]. This approach combines high-fidelity measurement with coherent conversion between qubit types to mitigate errors associated with qubit loss, decay, and imperfect SPAM. We demonstrate record-low SPAM error rates across optical, metastable, and ground-state qubits, with a minimum of 5(4)×10−6. This protocol can be integrated with erasure conversion techniques to enable in-sequence qubit loss correction, providing a pathway to scalable error correction even with finite qubit lifetimes. Finally, we introduce two-qubit operations through an implementation of the optical-transition dipole force (OTDF) gate [4]. This is the first implementation of the OTDF gate in 137Ba+, or in any ion with hyperfine structure, and it is directly compatible with our existing 532 nm laser system. Crucially, this gate operates in the σZ basis, avoiding the need for phase coherence between the driving field and the qubit, making it an excellent candidate for use in mixed-qubit-type systems. These results demonstrate the application of mixed-qubit-type architectures within a single ion species and establish a foundation for scaling trapped-ion quantum computers.
Atomic ions can be isolated from their environment through laser-cooling and trapping, making them useful for quantum information processing, measurement, and sensing. A variety of atomic ion species have been used as qubits. Hyperfine qubits with nuclear spin I = 1/2 have demonstrated the long qubit coherence times with simple, robust laser manipulation. Other qubits (I ≠ 1/2) have easily-prepared, long-lived metastable electronic excited states, and simple discrimination between these states allows high fidelity readout. However, none of the naturally- occurring, atomic ions with nuclear spin I = 1/2 have these excited states that are simultaneously long-lived and easy to prepare. We demonstrate loading, cooling, and qubit manipulation of an artificial, I = 1/2 species of barium with visible wavelength lasers: 133Ba+. We achieved a single shot qubit state preparation and readout fidelity of F = 0.9997, the lowest error rate ever achieved by any qubit on any platform.
High-fidelity operation of a radioactive trapped-ion qubit, 133Ba+
133Ba+ has been identified as an attractive ion for quantum information processing due to the unique combination of its spin-1/2 nucleus, visible wavelength electronic transitions, and long D-state lifetimes ($\\tau\\sim 1min).Usingamicrogramsourceofradioactivematerial,wetrapandlaser−coolthesynthetictextitA=133radioisotopeofbariumII(\\tau_{1/2} \\approx 10.5yr)inaradio−frequencyiontrap.Todemonstratehighfidelityqubitoperations,anumberofunknownstateenergieswereneeded.Wemeasuretheisotopeshiftandhyperfinestructureofthe6^2P_{1/2}\\leftrightarrow 5^2D_{3/2}$ electronic transition needed for laser cooling, state preparation, and state detection of the clock-state hyperfine and optical qubits. For high-fidelity operations with electron shelving, we report measurements of the 62P3/2 and 52D5/2 hyperfine splittings, as well as the~62P3/2leftrightarrow62S1/2 and ~62P3/2leftrightarrow52D5/2 transition frequencies. Using these transitions, we demonstrate high-fidelity \\ba \\ hyperfine qubit manipulation with electron shelving detection to benchmark qubit state preparation and measurement (SPAM). Using single-shot, threshold discrimination, we measure an average SPAM fidelity of mathcalF=0.99971(3), a factor of approx 2 improvement over the best reported performance of any qubit.Finally, we report the 62P1/2leftrightarrow52D3/2 electronic transition isotope shift for the rare \\textit{A} = 130 and 132 barium nuclides, completing the spectroscopic characterization necessary for laser cooling all long-lived barium II isotopes.
We present a novel protocol for high-fidelity qubit state preparation and measurement (SPAM) that combines standard SPAM methods with a series of in-sequence measurements to detect and remove errors. The protocol can be applied in any quantum system with a long-lived (metastable) level and a means to detect population outside of this level without coupling to it. We demonstrate the use of the protocol for three different qubit encodings in a single trapped 137Ba+ ion. For all three, we achieve the lowest reported SPAM infidelities of 7(4)×10−6 (optical qubit), 5(4)×10−6 (metastable-level qubit), and 8(4)×10−6 (ground-level qubit).
Quantum error correction of a grid-state qubit with state preparation and measurement errors below 10−3
Grid state qubits offer a hardware-efficient approach to large-scale fault-tolerant quantum computing. They access the information redundancy required for quantum error correction by exploiting the large Hilbert space naturally available in harmonic oscillators. Superconducting architectures are particularly suitable to implement grid state qubits due to their fast and high-fidelity operations. Grid states in superconducting circuits enable quantum error correction (QEC) with performance beyond break-even. However, the state preparation and measurements (SPAM) errors of grid states has been a significant limitation to computational performances. In this work, we leverage high-performance QEC to enable repeat-until-success state preparation of both cardinal and magic states of the single-mode grid-state qubit. We combine this with an improved measurement protocol that corrects for both finite-energy envelope and auxiliary qubit readout errors, and increases robustness to photon loss. Our experiments, using both techniques, achieve a combined state-preparation and measurement error below 10−3. This represents two orders-of-magnitude improvement over the state of the art, bringing this platform on par with standard SPAM error levels measured in transmon qubits.
Fault-tolerant quantum error correction provides a strategy to protect information processed by a quantum computer against noise which would otherwise corrupt the data. A fault-tolerant universal quantum computer must implement a universal gate set on the logical level in order to perform arbitrary calculations to in principle unlimited precision. In this paper we characterize the recent demonstration of a fault-tolerant universal gate set in a trapped-ion quantum computer [Postler et al., Nature (London) 605, 7911 (2022)] and identify aspects to improve the design of experimental setups to reach an advantage of logical over physical qubit operation. We show that various criteria to assess the break-even point for fault-tolerant quantum operations are within reach for the ion trap quantum computing architecture under consideration. Furthermore, we analyze the influence of crosstalk in entangling gates for logical state preparation circuits. These circuits can be designed to respect fault tolerance for specific microscopic noise models. We find that an experimentally informed depolarizing noise model captures the essential noise dynamics of the fault-tolerant experiment that we consider, and crosstalk is negligible in the currently accessible regime of physical error rates. For deterministic Pauli state preparation, we provide a fault-tolerant unitary logical qubit initialization circuit, which can be realized without in-sequence measurement and feed-forward of classical information. Additionally, we show that nondeterministic state preparation schemes, i.e., repeat until success, for logical Pauli and magic states perform with higher logical fidelity over their deterministic counterparts for the current and anticipated future regime of physical error rates. Our results offer guidance on improvements of physical qubit operations and validate the experimentally informed noise model as a tool to predict logical failure rates in quantum computing architectures based on trapped ions.