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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. 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 requires only 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 comprised of only 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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This content will become publicly available on August 1, 2025
Fault-Tolerant Quantum Computation by Hybrid Qubits with Bosonic Cat Code and Single Photons
Hybridizing different degrees of freedom or physical platforms potentially offers various advantages in building scalable quantum architectures. Here, we introduce a fault-tolerant hybrid quantum computation by building on the advantages of both discrete-variable (DV) and continuous-variable (CV) systems. In particular, we define a CV-DV hybrid qubit with a bosonic cat code and a single photon, which is implementable in current photonic platforms. Due to the cat code encoded in the CV part, the predominant loss errors are readily correctable without multiqubit encoding, while the logical basis is inherently orthogonal due to the DV part. We design fault-tolerant architectures by concatenating hybrid qubits and an outer DV quantum error-correction code such as a topological code, exploring their potential merit in developing scalable quantum computation. We demonstrate by numerical simulations that our scheme is at least an order of magnitude more resource efficient compared to all previous proposals in photonic platforms, allowing us to achieve a record-high loss threshold among existing CV and hybrid approaches. We discuss the realization of our approach not only in all-photonic platforms but also in other hybrid platforms including superconducting and trapped-ion systems, which allows us to find various efficient routes toward fault-tolerant quantum computing.
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- PAR ID:
- 10530344
- Publisher / Repository:
- PRX Quantum
- Date Published:
- Journal Name:
- PRX Quantum
- Volume:
- 5
- Issue:
- 3
- ISSN:
- 2691-3399
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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