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Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions

Pedro Parrado-Rodríguez, Ciarán Ryan-Anderson, A. Bermúdez, Markus Müller

Published Jan 1, 2020• 52 citations
OpenAlex

Abstract

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.

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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.
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.
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]][[n, k>1, d]][[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.
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 execute a large number of quantum gates in parallel is a fundamental requirement for quantum error correction, allowing an error threshold to exist under the finite coherence time of physical qubits. Recently, two-dimensional ion crystals have been demonstrated as a plausible approach to scale up the qubit number in a trapped ion quantum computer. However, although the long-range Coulomb interaction between the ions enables their strong connectivity, it also complicates the design of parallel gates and leads to intrinsic crosstalk errors. Here we examine the effects of crosstalk errors on a rotated surface code. We show that, instead of the distance-3 code considered in previous works, a distance-5 code is necessary to correct the two-qubit crosstalk error. We numerically calculate the logical error rates and coherence times under various crosstalk errors, gate infidelities, and coherence times of the physical qubits, and we optimize the parallelism level according to the competition between different error sources. We show that a break-even point can be reached under realistic parameters. We further analyze the spatial dependence of the crosstalk, and discuss the scaling of the logical error rate versus the code distance for the long-term goal of a logical error rate below 10 − 10 .
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.
Building fault-tolerant quantum computers with large numbers of logical qubits requires both scalable hardware architectures and error-correcting codes that make efficient use of physical qubits. Photonic interconnects address both of these challenges by allowing the physical qubits to be distributed across multiple processors while providing the non-local connectivity necessary to implement resource-efficient codes such as high-rate quantum low-density parity-check (qLDPC) codes. A key requirement for realising this architecture is the ability to perform stabiliser measurements between remote processors, which has not previously been demonstrated experimentally. Here we report the first experimental demonstration of distributed quantum error detection and correction. We generate entanglement between network qubits in two separate trapped-ion processors and use it to perform remote syndrome measurements on data qubits. We first realise a distributed [[2, 1, 1]] repetition code, detecting phase-flip errors on a logical qubit encoded across the two modules in real time and suppressing logical errors. We then combine these mid-circuit syndrome measurements with real-time feedforward to actively correct arbitrary single-qubit Pauli errors on a distributed Bell state. These results provide an experimental foundation for quantum error correction (QEC) across modular quantum architectures.