Fault-Tolerant Operation of Bosonic Qubits with Discrete-Variable Ancillae

• URL: http://arxiv.org/abs/2310.20578v1
• Date: Tue, 31 Oct 2023 16:13:04 GMT
• Title: Fault-Tolerant Operation of Bosonic Qubits with Discrete-Variable Ancillae
• Authors: Qian Xu, Pei Zeng, Daohong Xu and Liang Jiang
• Abstract summary: We introduce essential building blocks of error-corrected gadgets by leveraging ancilla-assisted bosonic operations. We construct a universal set of error-corrected gadgets that tolerate a single photon loss and an arbitrary ancilla fault for four-legged cat qubits. Our estimates suggest that the overall noise threshold can be reached using existing hardware.
• Score: 4.478211895257931
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Fault-tolerant quantum computation with bosonic qubits often necessitates the use of noisy discrete-variable ancillae. In this work, we establish a comprehensive and practical fault-tolerance framework for such a hybrid system and synthesize it with fault-tolerant protocols by combining bosonic quantum error correction (QEC) and advanced quantum control techniques. We introduce essential building blocks of error-corrected gadgets by leveraging ancilla-assisted bosonic operations using a generalized variant of path-independent quantum control (GPI). Using these building blocks, we construct a universal set of error-corrected gadgets that tolerate a single photon loss and an arbitrary ancilla fault for four-legged cat qubits. Notably, our construction only requires dispersive coupling between bosonic modes and ancillae, as well as beam-splitter coupling between bosonic modes, both of which have been experimentally demonstrated with strong strengths and high accuracy. Moreover, each error-corrected bosonic qubit is only comprised of a single bosonic mode and a three-level ancilla, featuring the hardware efficiency of bosonic QEC in the full fault-tolerant setting. We numerically demonstrate the feasibility of our schemes using current experimental parameters in the circuit-QED platform. Finally, we present a hardware-efficient architecture for fault-tolerant quantum computing by concatenating the four-legged cat qubits with an outer qubit code utilizing only beam-splitter couplings. Our estimates suggest that the overall noise threshold can be reached using existing hardware. These developed fault-tolerant schemes extend beyond their applicability to four-legged cat qubits and can be adapted for other rotation-symmetrical codes, offering a promising avenue toward scalable and robust quantum computation with bosonic qubits.

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