Strategies for practical advantage of fault-tolerant circuit design in noisy trapped-ion quantum computers

Abstract

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. We characterize the recent demonstration of a fault-tolerant universal gate set in a trapped-ion quantum computer [Postler et al. Nature 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. 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, 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. We show that non-deterministic state preparation schemes 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.

36 pages, 26 figures

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• Solving an Industrially Relevant Quantum Chemistry Problem on Quantum Hardware
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• Dynamical subset sampling of quantum error correcting protocols
• Efficient fault-tolerant code switching via one-way transversal CNOT gates
• Quantum Circuit Discovery for Fault-Tolerant Logical State Preparation with Reinforcement Learning
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• Space-time correlations in monitored kinetically constrained discrete-time quantum dynamics
• Gaining confidence on the correct realization of arbitrary quantum computations
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• Experimental measurement and a physical interpretation of quantum shadow enumerators
• Noise-resilient and resource-efficient hybrid algorithm for robust quantum gap estimation
• Crosstalk Insensitive Trapped-Ion Entanglement through Coupling Matrix Engineering