Physical qubits in experimental quantum information processors are inevitably exposed to different sources of noise and imperfections, which lead to errors that typically accumulate hindering our ability to perform long computations reliably. Progress towards scalable and robust quantum computation relies on exploiting quantum error correction (QEC) to actively battle these undesired effects. In this work, we present a comprehensive study of crosstalk errors in a quantum-computing architecture based on a single string of ions confined by a radio-frequency trap, and manipulated by individually-addressed laser beams. This type of errors affects spectator qubits that, ideally, should remain unaltered during the application of single- and two-qubit quantum gates addressed at a different set of active qubits. We microscopically model crosstalk errors from first principles and present a detailed study showing the importance of using a coherent vs incoherent error modelling and, moreover, discuss strategies to actively suppress this crosstalk at the gate level. Finally, we study the impact of residual crosstalk errors on the performance of fault-tolerant QEC numerically, identifying the experimental target values that need to be achieved in near-term trapped-ion experiments to reach the break-even point for beneficial QEC with low-distance topological codes.
Physical qubits in experimental quantum information processors are inevitably exposed to different sources of noise and imperfections, which lead to errors that typically accumulate hindering our ability to perform long computations reliably.Progress towards scalable and robust quantum computation relies on exploiting quantum error correction (QEC) to actively battle these undesired effects.In this work, we present a comprehensive study of crosstalk errors in a quantumcomputing architecture based on a single string of ions confined by a radio-frequency trap, and manipulated by individuallyaddressed laser beams.This type of errors affects spectator qubits that, ideally, should remain unaltered during the application of single-and two-qubit quantum gates addressed at a different set of active qubits.We microscopically model crosstalk errors from first principles and present a detailed study showing the importance of using a coherent vs incoherent error modelling and, moreover, discuss strategies to actively suppress this crosstalk at the gate level.Finally, we study the impact of residual crosstalk errors on the performance of fault-tolerant QEC numerically, identifying the experimental target values that need to be achieved in near-term trapped-ion experiments to reach the break-even point for beneficial QEC with low-distance topological codes.
The design and performance analysis of quantum error correction (QEC) codes are often based on incoherent and independent noise models since it is easy to simulate. However, these models fail to capture realistic hardware noise sources, such as correlated errors (crosstalk), which can significantly impact QEC code performance, especially when they occur between data and ancillary qubits. In this paper, we systematically study various types of crosstalk noise and quantify their effects on surface codes through memory and stability experiments. Based on our findings, we introduce crosstalk-robust implementations of QEC via flag qubit designs and redundant stabilizer checks. We perform both numerical and analytical studies to demonstrate the efficacy of these strategies. In addition, we analyze logical crosstalk in an
[[n,k>1,d]]code block and establish analytical conditions under which physical crosstalk does not lead to logical crosstalk. Together, our analytical and numerical results shed light on designing QEC codes that are robust against hardware realistic crosstalk noise, paving the way for reliable experimental realization of fault-tolerant quantum computing.
Crosstalk between target and neighboring spectator qubits due to spillover of control signals represents a major error source limiting the fidelity of two-qubit entangling gates in quantum computers. We show that in our laser-driven trapped-ion system coherent crosstalk error can be modeled as residual Xσ[over ^]_{ϕ} interaction and can be actively canceled by single-qubit echoing pulses. We propose and demonstrate a crosstalk suppression scheme that eliminates all first-order crosstalk utilizing only local control of target qubits, as opposed to an existing scheme which requires control over all neighboring qubits. We report a two-qubit Bell state fidelity of 99.52(6)% with the echoing pulses applied after collective gates and 99.37(5)% with the echoing pulses applied to each gate in a five-ion chain. This scheme is widely applicable to other platforms with analogous interaction Hamiltonians.
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.
The ability to perform entangling operations in parallel with a low error is essential for a large-scale fault-tolerant quantum computer. However, for trapped-ion systems, it is a challenging task due to the crosstalk resulting from the collective motional modes. Here, we develop a highly paralleled quantum circuit demonstrating a logical qubit based on the Steane code and study the impact of the crosstalk error on the performance of the fault-tolerant protocol. We show that the crosstalk indeed greatly destroys the fault-tolerant property of the quantum error correction. To achieve the break-even point with encoded qubits, we identify the suppression requirement of the crosstalk error to be less than ${10}^{\ensuremath{-}6}$ for the Steane code. Furthermore, to mitigate the crosstalk below the fault-tolerant threshold, we propose a highly efficient optimization scheme by utilizing the programmable optical tweezer array. Overall, we make an elegant combination of the pulse-control optimization of parallel gate operations with the fault-tolerant protocol on the error-protected universal quantum computer.
Quantum error correction (QEC) is beginning to enable logical operations that outperform their unencoded physical counterparts, but useful fault-tolerant computation will require more than low-error quantum memory. An effective architecture must orchestrate efficient logical encoding, low-overhead logical operations, and access to the non-Clifford resources required for universal computation. Here, we introduce and experimentally validate such an architecture based on the
[[20,2,6]] C4-Helix code, designed for the early fault-tolerant regime. Using Quantinuum Helios, a 98-qubit trapped-ion quantum processor, we experimentally demonstrate the principal components of this architecture: we perform repeated quantum error correction with an error of
4.6−2.6+6.2×10−5 per logical qubit per QEC cycle. We benchmark the complete Clifford group on the two logical qubits of a single codeblock under active error correction, obtaining an error of
2.8−1.6+1.0×10−4 per two-qubit logical Clifford. We further demonstrate a fault-tolerant chain-map interface between
C4-Helix and a distance-5 surface code, preparing a heterogeneous three-logical-qubit GHZ state with a fidelity lower bound of
99.925−0.245+0.068%. In each case, the encoded implementation outperforms its corresponding unencoded physical baseline without relying on postselection. Circuit-level simulations indicate that improvements in physical fidelity bring the same architecture into the
10−6-
10−8 logical-error regime targeted for early fault-tolerant computation. Together, these results establish
C4-Helix as a hardware-validated fault-tolerant architecture rather than a bare quantum memory.