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Recent experimental advances have made it possible to implement logical multiqubit transversal gates on surface codes in a multitude of platforms. A transversal controlled- (t) gate on two surface codes introduces correlated errors across the code blocks and thus requires modified decoding compared to established methods of decoding surface-code quantum memory (SCQM) or lattice-surgery operations. In this work, we examine and benchmark the performance of three different decoding strategies for the t for scalable fault-tolerant quantum computation. In particular, we present a low-complexity decoder based on minimum-weight perfect matching (MWPM) that achieves the same threshold as the SCQM MWPM decoder. We extend our analysis with a study of tailored decoding of a transversal-teleportation circuit, along with a comparison between the performance of lattice-surgery and transversal operations under Pauli- and erasure-noise models. Our investigation builds toward systematic estimation of the cost of implementing large-scale quantum algorithms based on transversal gates in the surface code. Published by the American Physical Society2025 

Quantum states decohere through interaction with the environment. Quantum error correction can preserve coherence through active feedback wherein quantum information is encoded into a logical state with a high degree of symmetry. Perturbations are detected by measuring the symmetries of the state and corrected by applying gates based on these measurements. To measure the symmetries without perturbing the data, ancillary quantum states are required. Shor error correction uses a separate quantum state for the measurement of each symmetry. Steane error correction maps the perturbations onto a logical ancilla qubit, which is then measured to check several symmetries simultaneously. We experimentally compare Shor and Steane correction of bit flip errors using the Bacon-Shor code implemented in a chain of 23 trapped atomic ions. We find that the Steane method produces fewer errors after a single round of error correction and less disturbance to the data qubits without error correction. 

Lookup-table decoding is fast and distance preserving, making it attractive for near-term quantum computer architectures with small-distance quantum error-correcting codes. In this work, we develop several optimization tools that can potentially reduce the space and time overhead required for flag fault-tolerant quantum error correction (FTQEC) with lookup-table decoding on Calderbank-Shor-Steane (CSS) codes. Our techniques include the compact lookup-table construction, the meet-in-the-middle technique, the adaptive time decoding for flag FTQEC, the classical processing technique for flag information, and the separate $X$- and $Z$-counting technique. We evaluate the performance of our tools using numerical simulation of hexagonal color codes of distances 3, 5, 7, and 9 under circuit-level noise. Combining all tools can result in an increase of more than an order of magnitude in the pseudothreshold for the hexagonal color code of distance 9, from $(1.34\pm 0.01)\times {10}^{-4}$to $(1.43\pm 0.07)\times {10}^{-3}$. Published by the American Physical Society2024 

The Shor fault-tolerant error correction (FTEC) scheme uses transversal gates and ancilla qubits prepared in the cat state in syndrome extraction circuits to prevent propagation of errors caused by gate faults. For a stabilizer code of distance $d$that can correct up to $t=\lfloor (d-1)/2\rfloor$errors, the traditional Shor scheme handles ancilla preparation and measurement faults by performing syndrome measurements until the syndromes are repeated $t+1$times in a row; in the worst-case scenario, $(t+1{)}^2$rounds of measurements are required. In this work, we improve the Shor FTEC scheme using an adaptive syndrome measurement technique. The syndrome for error correction is determined based on information from the differences of syndromes obtained from consecutive rounds. Our protocols that satisfy the strong and the weak FTEC conditions require no more than $(t+3{)}^2/4-1$rounds and $(t+3{)}^2/4-2$rounds, respectively, and are applicable to any stabilizer code. Our simulations of FTEC protocols with the adaptive schemes on hexagonal color codes of small distances verify that our protocols preserve the code distance, can increase the pseudothreshold, and can decrease the average number of rounds compared to the traditional Shor scheme. We also find that for the code of distance $d$, our FTEC protocols with the adaptive schemes require no more than $d$rounds on average. 

Erasures, or errors with known locations, are a more favorable type of error for quantum error-correcting codes than Pauli errors. Converting physical noise into erasures can significantly improve the performance of quantum error correction. Here, we apply the idea of performing erasure conversion by encoding qubits into metastable atomic states, proposed by Wu, Kolkowitz, Puri, and Thompson [Nat. Comm. 13, 4657 (2022)], to trapped ions. We suggest an erasure-conversion scheme for metastable trapped-ion qubits and develop a detailed model of various types of errors. We then compare the logical performance of ground and metastable qubits on the surface code under various physical constraints and conclude that metastable qubits may outperform ground qubits when the achievable laser power is higher for metastable qubits. 

Conical intersections often control the reaction products of photochemical processes and occur when two electronic potential energy surfaces intersect. Theory predicts that the conical intersection will result in a geometric phase for a wavepacket on the ground potential energy surface, and although conical intersections have been observed experimentally, the geometric phase has not been directly observed in a molecular system. Here we use a trapped atomic ion system to perform a quantum simulation of a conical intersection. The ion’s internal state serves as the electronic state, and the motion of the atomic nuclei is encoded into the motion of the ions. The simulated electronic potential is constructed by applying state-dependent optical forces to the ion. We experimentally observe a clear manifestation of the geometric phase using adiabatic state preparation followed by motional state measurement. Our experiment shows the advantage of combining spin and motion degrees for quantum simulation of chemical reactions.